Socio-Economic Planning Sciences 65 (2019) 20–35 Contents lists available at ScienceDirect Socio-Economic Planning Sciences journal homepage: www.elsevier.com/locate/seps Evaluation of efficiency in Colombian hospitals: An analysis for the post- T reform period Víctor Giméneza, William Prietob, Diego Priora, Emili Tortosa-Ausinac,∗ a Department of Business, Universitat Autònoma de Barcelona, Bellaterra, Barcelona, Spain b Faculty of Economic and Administrative Sciences, Universidad Católica de Colombia, Bogotá, Colombia c Department of Economics, Universitat Jaume I, Castelló, Spain A R T I C L E I N F O A B S T R A C T Keywords: In this study we analyze the performance of 602 level 1 Colombian hospitals for the period 2009–2013. The Hospitals analysis is carried out from both static and temporal perspectives in order to evaluate the evolution of total factor Efficiency productivity (change in hospital performance) and its components throughout the period. The study also ex- Quality plores a question relevant not only to the Colombian health system, but to many others around the world, of Bad outputs whether primary care centers excessively refer patients to high-level hospitals, thereby negatively affecting the Global Malmquist-Luenberger indexJEL quality, efficiency, and effectiveness of all healthcare service provision. The results demonstrated that adjusted Classifications: C61 production (service provision) and levels of quality and referrals to higher-level hospitals could be improved, on H51 average, by 44%. This increase in health service provision levels and their quality can be achieved by reducing I18 personnel expenditure (by an average of 22%), expenditure on medicines (by 20%), and purchasing expenses (by 11%). The temporal analysis shows that total factor productivity (hospital performance change) worsened by 1% during the period, mainly due to the technological backlash experienced despite a slightly positive evolution in efficiency. 1. Introduction compliance with quality standards endorsed by the scientific commu- nity within the healthcare sector. This situation therefore requires In the early 1990s, under the principles of efficiency, universality, suitable evidence on the current status of efficiency and quality of solidarity, comprehensiveness, unity, and participation, Law 100 public hospitals. (1993) ushered in the most significant reform to the healthcare system From an operational point of view, the regulations establish that all in Colombia's modern history. The fundamental objective of the new affiliates, without discrimination, will receive an integrated healthcare system was to ensure universal coverage in the healthcare system, protection plan known as the Obligatory Healthcare Plan (OHP), which particularly for the poor and vulnerable sectors of the population. In covers preventive care, medical-surgical care and essential medications. this way, the new regulation sought to gradually extend the system's The Solidarity and Guarantee Fund (FOSYGA), affiliated to the Ministry coverage, establish free basic care and improve the organization of of Health, is responsible for collecting contributions. The insurance healthcare services in a decentralized manner, while also preventing carriers (EPS), as the administrative and funding bodies, collect the inefficient use of healthcare resources. contributions, remitting to FOSYGA the difference between the pre- The government has critical responsibilities to evaluate the results mium they receive for each affiliate and the corresponding contribu- of the healthcare system in relation to the principles of efficiency and tions from affiliates with formal and independent work contracts. The professional quality and suitability, and to create a policy for managing insurance premium the EPS receive from FOSYGA is a capitation pay- healthcare information. Under the law, efficiency is a priority objective, ment unit (UPC) adjusted for age and gender, which is established and the system must guarantee the effective provision of healthcare to annually by the National Council for Social Security in Healthcare. the entire population through the use of technology, resources and Affiliates are free to choose both their EPS and the healthcare promo- available services. In turn, as regards quality and professional suit- tion institution (IPS) subscribed to the EPS network services. In turn, ability, the statute states that the system's services must be user-focused the IPS may be either public entities (public hospitals), or mixed, pri- through medical and technical appropriation that guarantees vate, community or charitable entities that provide healthcare services ∗ Corresponding author. E-mail address: tortosa@uji.es (E. Tortosa-Ausina). https://doi.org/10.1016/j.seps.2018.02.002 Received 20 June 2017; Received in revised form 31 December 2017; Accepted 6 February 2018 Available online 15 February 2018 0038-0121/ © 2018 Elsevier Ltd. All rights reserved. V. Giménez et al. Socio-Economic Planning Sciences 65 (2019) 20–35 to affiliates. Care services are classified according to levels of com- assuming proportional changes in both good and bad outputs, while plexity: level 1 covers outpatient care and inpatient care, level 2 offers Jahanshahloo et al. [2] and Hadi Vencheh et al. [4] propose models specialized outpatient care, while levels 3 and 4 provide specialized with multiple outputs, including bad or undesirable outputs. However, inpatient care. to the best of our knowledge, this is the first study using a global The Department of Industry and Trade has made several re- Malmquist-Luenberger index to assess the temporal evolution of pro- commendations to improve the provision of insurance and healthcare ductivity, technological change and efficiency in the hospital sector. services in the system.1 One of these suggestions is to construct relative Two particular issues are of special interest for our purposes: first, efficiency indicators for provision of insurance and healthcare services the trade-off between efficiency and quality and, second, the effects of to promote a mechanism of competition by comparison. The present the reform in the healthcare system. The trade-off between efficiency study responds to this recommendation by carrying out a temporal ef- and quality in the provision of healthcare services is often considered ficiency analysis for level 1 public hospitals for the period 2009–2013. relevant since pressures on production can indirectly affect quality Therefore, the aim of the study is to assess efficiency and productivity provision. The literature reports evidence for and against this re- levels and temporal evolution of hospital performance in Colombia lationship. For instance, Prior [6] found that between 30% and 40% of during a recent period corresponding to the post-reform (i.e., applica- Catalonian hospitals upheld the postulates of Total Quality Manage- tion of Law 100) era. The reason for choosing level 1 public hospitals is ment (that is, maximum improvement in desirable outputs simulta- twofold. First, quantitative and qualitative information is more readily neously induces reduction in the undesirable attributes of bad quality). available for level 1 public hospitals than for other healthcare service Navarro-Espigares and Torres [7] carried out a temporal DEA analysis providers, and is more frequent in the sample of public hospitals using the Malmquist index to characterize the relationship between monitored by the Ministry of Health. Our database contains some in- quality and efficiency in hospitals in a region of Spain from 1997 to teresting variables particularly related to the quality of the healthcare 2004, finding a slight association between efficiency indicators and provision process, which should be considered as bad outputs, i.e., quality indicators. Yang and Zeng [8] three-stage DEA study, also im- variables (such as waiting time or re-admissions within 20 days) whose plemented by estimating a Malmquist index to measure changes in decreases imply improvements in performance. The second reason is productivity, efficiency and quality in hospitals in the city of Shenzhen that performance of level 1 public hospitals may directly affect the ef- (China) from 2006–2010, does not dismiss the possibility of a re- ficiency and effectiveness further up the healthcare system, since they lationship between efficiency and quality, particularly in small and are generally the initial contact for a healthcare system user and, as medium hospitals. such, they should be able to deal efficiently and effectively with many Several scholars have explored the effects of healthcare system re- of the patients and avoid unnecessary referral to higher levels. In this forms using non-parametric and parametric frontier models. Arocena line, we address the additional research question of whether too many and García Prado [9] and [10] report interesting comparisons of market patients are referred to higher levels from primary care levels, which and cooperative reforms incorporating hospital management incentives could increase costs and reduce quality in the more complex hospitals. in both cases. Arocena and García Prado [9], using a nonparametric This is a common concern among healthcare managers. Finally, the methodology to estimate a productivity index, determine how public analyzed period (2009–2013) was chosen due to the availability of hospitals in Costa Rica respond to reforms to the healthcare system consistent and comparable data.2 implemented between 1997 and 2001. The results indicate an increase The literature on healthcare sector efficiency is extensive, has a in productivity associated with increases in quality, promoted mainly variety of aims, and applies to different countries.3 Recent develop- by technical and scale efficiency rather than a regressive technological ments in the literature have extended productivity analysis to include change. In their study, Hu et al. [10] found the reform had a more minimization of bad outputs. In this line, Scheel [1], Jahanshahloo positive effect on efficiency for the inland Chinese provinces compared et al. [2], Ozcan et al. [3] and Hadi Vencheh et al. [4] propose alter- to those located on the coast. Both studies considered data with mul- natives within the data envelopment analysis framework [5] to include tiple products and also included bad outputs. Although the reform in bad outputs. Scheel [1] suggests new radial efficiency measures, Costa Rica is geared more toward a cooperative model, evidence sug- gests that the relationship between efficiency and quality of service responds appropriately to reforms that attempt to align their incentives 1 Department of Industry and Trade. Problem of competence in the health sector in with those of public hospital administration. This also appears to be Colombia, presentation given at the 2nd annual meeting of the work group for trade and confirmed by Alonso et al. [11], who compare hospitals with traditional competence, June 2012. 2 The issue as to the transfer of patients to levels of greater complexity by hospitals has administrations in Madrid. Their results suggest that what makes the to do with productivity increases in public hospitals. If we do not take into account difference is management, rather than the particular management quality indicators, hospitals transfer patients whose problems can be resolved in level 1 model the hospitals adopt. Likewise, the studies by Matranga and Sa- complexity. These transfers are made to higher levels of complexities with more ex- pienza [12] and Fidler et al. [13] also incorporate bad outputs. Their pensive technologies, which increase the cost for a given level of production which, results are congruent with the above evidence since the inefficiency of cæteris paribus, would erode efficiency. This is a result of keeping productivity levels to hold contract services with EPSs. In other words, by increasing the number of patients, public hospitals may be attributed to congestion, purely technical in- productivity levels increase, but without improving quality services, this increment will efficiency, and the need to align the incentives of hospital management reduce efficiency as long as it deviates health issues that can be solved in levels of service to the reform objectives. In particular, Fidler et al. [13] showed how the with lower costs. For this reason, hospitals are not interested in transferring a smaller combination of public resources and private management generated a number of patients because it affects productivity—for a given level of resources. In this way, fewer transfers imply losses in productivity with regard to other hospitals which are new corporate culture with greater flexibility to correct inefficiencies competitors for service provision. While users can resort to other hospitals, access to by reducing size and generating economies of scale. More recently, levels of greater complexity depend on the authorization of medical professionals in each Chen et al. [14] found that the changes introduced in the healthcare hospital. For this same reason, increases in production which are not accompanied by sector in China during the last thirty years have improved the cost ef- improvements in quality are considered a bad output. 3 ficiency of the whole system, especially after the public subsidies and Some representative examples of this can be found in Nunamaker [49], Lewin [50], Harris et al. [51], Valdmanis et al. [52], Weng et al. [53], Harrison et al. [54], Dexter and medical insurance reform. O'Neill [55], Hollingsworth [56,57], Pina and Torres [58], Solà and Prior [46], Dalmau- Turning to studies on the healthcare sector in Colombia, Sarmiento Atarrodona and Puig-Junoy [59], Helmig and Lapsley [60], Field and Emrouznejad [61], et al. [15] analyzed the efficiency of public hospitals in 2003, while Ersoy et al. [62], Sahin and Ozcan [63], Giokas [64], Ouellette and Vierstraete [65], McPake et al. [16] carried out a parametric estimation of time series Athanassopoulos and Gounaris [42], Gerdtham et al. [66], Biørn et al. [67], Kirigia et al. [68], Ferrier and Valdmanis [69], Prior [6], Grosskopf et al. [70,71], Harrison et al. [54], and a graphed trend analysis together with qualitative methods to Wang et al. [72], Cordero et al. [73], Martini et al. [74], O'Neill [75], Kalhor et al. [76], evaluate the impact of reform in five hospitals in Bogotá, monitored Ozcan [77] Chen et al. [14], Büchner et al. [78] or Jola-Sanchez et al. [79]. from 1996 to 1998. The study finds evidence of increased activities and 21 V. Giménez et al. Socio-Economic Planning Sciences 65 (2019) 20–35 productivity following the implementation of Law 100 (1993) without D (x , y, b) = max (β (y + βgy , b − βgb)) (2) relevant effects on quality of healthcare service provision. Similarly, Pinzón-Martínez [17] estimated nonparametric frontiers using a model The above DDF determines the maximum increase and reduction β which evaluates the performance of low-complexity public hospitals, attainable both in good and bad outputs, respectively, over the vector finding that 70% of the institutions analyzed operate with an average g = (gy , gb) that defines the desirable directions for improvement for efficiency coefficient of 72.2%. Tamayo and Maldonado [18] estimated both types of outputs. In this study we use the vector of M + H com- technical efficiency in public hospitals for the period 2002–2005 with ponents g = (y, b) as suggested by Chung et al. [20] and Oh [24]. information from the hospital information system (“Sistema de In- The GML index for the years t and t + 1 is defined as [24]: formación Hospitalaria”, SIHO). The main contribution of their study is the alternative classification of five homogeneous groups, which differs 1 + DG (x t , y t , bt ) GMLt , t + 1 (x t , y t , bt , x t + 1, y t + 1 , bt + 1) = from the usual classification by complexity of services. 1 + DG (x t + 1, y t + 1 , bt + 1) (3) The rest of this article is organized as follows. The next section where DG (x , y, b) = max (β (y + βgy , b − βgb) ∈ P (x )) is the DDF de- (Section 2) describes the methodology used in this paper. The sample and variables selected as inputs, products and quality for the healthcare fined over the global production possibilities set P G (x ) , i.e., a value of provision process are shown in Section 3. Results are discussed in GMLt , t + 1 greater than the unit represents an improvement in pro- Section 4, and finally, Section 5 presents the main conclusions, lim- ductivity between years t and t + 1, since the distance to the global itations and future research lines. frontier was greater in t than in t + 1. A value less than the unit for GMLt , t + 1 represents a deterioration in the corresponding period. Expression (3) can be decomposed in the following way: 2. Methodology 1 + DG (x t , y t , bt ) 2.1. Measuring efficiency and its evolution over time GMLt , t + 1 (x t , y t , bt , x t + 1, y t + 1 , bt + 1) = 1 + DG (x t + 1, y t + 1 , bt + 1) 1 + Dt (x t , y t , bt ) Temporal efficiency studies often use the Malmquist index [19]. = 1 + Dt + 1 (x t + 1, y t + 1 , bt + 1) This index explains the change in total productivity of factors as a G t t t product of change in efficiency, or “catching up”, and technological ⎡ 1 + D (x , y , b ) ⎤ 1 + Dt (x t , yt , bt ) change. Chung et al. [20] modified the Malmquist index in order to × ⎢ G t + 1 t + 1 t + 1 ⎥ ⎢ 1 + D (x , y , b ) ⎥ adapt it to cases of directional distance functions (DDF). These have t + 1 t + 1 t + 1 t + 1 ⎣ 1 + D (x , y , b ) ⎦ been widely used in efficiency measurement studies, which incorporate TE t + 1 BPGtt+, t1+ 1 ⎤ the environmental impact of the units analyzed by looking at bad = × ⎡ TE t ⎢ BPGtt , t + 1 ⎥ outputs of the production process [21–23]. The new index is known as ⎣ ⎦ the Mamlquist-Luenberger index. = EC t , t + 1 × BPC t , t + 1 (4) However, both indexes suffer from two problems [24,25]. First, their circularity is not assured. Circularity is when the change in pro- where EC t , t + 1 collects the technical efficiency change or catching up ductivity performance is explained through resulting changes in pro- between the year t and t + 1. If EC t , t + 1 > 1, there was an improvement ductivity in the different sub-periods it is comprised of. Secondly, there in technical efficiency during the period. In other words, the unit is is the possibility of infeasibility in the calculation of cross-distance closer to its contemporary frontier in the year t + 1 than in t. A lower functions between the periods necessary to calculate it. In spite of it value is interpreted conversely. The term BPC t , t + 1 is a measure of the being a necessary and sufficient condition of technical change, being technological change in the period, i.e., it describes how the con- Hicks-neutral to ensure circularity [26], or that a determined data temporary frontiers displaced during the period. Equation (4) shows structure ensures the absence of feasibility problems [27], its empirical that the expression for the calculation of BPC t , t + 1 is: compliance is often difficult. Pastor and Lovell [25] proposed a mod- G t t t 1 + D (x , y , b ) ification of the Malmquist index to correct these two deficiencies, which BPGtt+, t1+ 1 ⎡ 1 + Dt (x t , yt , bt ) ⎤ BPC t , t + 1 = = ⎢ ⎥ they called the global Malmquist index. Oh [24] then adapted the BPGtt,t+1 ⎢ 1 + D G (x t + 1, y t + 1, bt + 1) ⎥ global Malmquist-Luenberger index (henceforth GML) in a similar way. ⎣ 1 + D t + 1 (x t + 1, y t + 1, bt + 1) ⎦ (5) This study uses the GML proposed by Oh [24] for the temporal analysis of productivity, which in our specific context refers to hospital where: performance. There are two reasons for choosing the GML to analyze 1 performance of level 1 hospitals in Colombia. The first concerns with BPGtt+, t1+ 1 = 1 + DG (x t + 1, yt + 1, bt + 1) the existence of bad outputs to be minimized in the service provision 1 + Dt + 1 (x t + 1, yt + 1, bt + 1) (6) process, especially related to quality variables. The second refers to compliance with circularity and feasibility implicit in that of the GML. In the above expression BPGtt+, t1+ 1 corresponds to the inverse of the The choice of the GML therefore complies with both the empirical and quotient between distance to the frontier defined by P G (x ) and to the the theoretically desirable properties in any temporal study of hospital contemporary frontier defined by P G (x ) for the period t + 1. If performance. BPC t , t + 1 > 1 it is because the frontier in t + 1 is closer to the global The description of the GML in the case of health (hospital) service frontier than in t, implying that technological progress has taken place. provision in Colombia can be performed as follows. Let K hospitals with The case of BPC t , t + 1 < 1 represents the opposite situation.4 information available on their production systems for the years Various methods can be used to calculate DG (x t , y t , bt ) and t = 1...T . Since each hospital's service provision vector is composed of M D (x t , y t , bt ) . In this study we use data enveloping analysis models [5] t outputs y ∈ R+M and H bad outputs b ∈ R+H through consumption of N widely used in efficiency studies [30]. The calculation of Dt (x t , y t , bt ) is inputs x ∈ R+N , then the production possibilities set is defined by: made by solving the following linear program for each hospital ana- lyzed under the assumption g = (y, b) [31]: P (x ) = {(y, b) x can produce (y, b)} (1) The axioms that the above technology must meet are those com- 4 The technical change component, apart from exhibiting progress or regress, can also monly required by the theory of production [28]. The efficiency of any be adapted to quantify the potential existence of biased technical change. In order to of the pertaining units at P (x ) can be measured through the following maintain the length of this paper in a reasonable dimension, we do not enter in this directional distance function, DDF [22,24,29]: potential extension. 22 V. Giménez et al. Socio-Economic Planning Sciences 65 (2019) 20–35 Max β become: K t s. t . ∑k = 1 λk ykm ≥ ymot (1 + β ) m = 1... M gml BPC × EC = BPC t , t + 1 × EC t , t + 1 = gml BPC × EC t , t + 1 (13) K t ∑k = 1 λk bkh ≤ bhot (1 − β ) h = 1... H K We will refer to the decomposition in both expressions (11) and (13) t ∑k = 1 λk xkn ≤ x not n = 1... N as the bipartite decomposition of the relative contributions to the K ∑k = 1 λk = 1 changes in the distribution of hospital performance. β ≥ 0; λk ≥ 0 k = 1... K (7) As indicated above, we use kernel smoothing to estimate the den- sities, which involves selecting a kernel and a bandwidth (h).5 Of the where β is the maximum increase and reduction attainable simulta- choices available (e.g., Epanechnikov, triangular, Gaussian etc.), we t neously in the good and bad outputs, respectively; ykm represents output chose the popular (Gaussian kernel). The impact on the final outcome t m of unit k in year t, bkh the bad output h of unit or hospital k in year t, is, however, much lower than that of the bandwidth, which smooths the t and xkn the input n used by hospital k in year t; ymot , bhot , x not are the number bumps under each curve—higher values of h tend to smooth observed levels of outputs, bad outputs and inputs, respectively, for the more, low values of h tend to smooth less, providing more detail. Given hospital evaluated in year t. the relevance of this decision, we consider both a global (same amount Analogously, for the calculation of DG (x t , y t , bt ) , the following of smoothing at all data points, see Ref. [32] and local bandwidth linear program is used: (varying amount of smoothing dependent on the structure of the data at Max β a given point, see Ref. [33]. K t+1 T T Counterfactual distributions are not common in the field of hospital s. t . ∑k = 1 ∑t λk ykm ≥ ymot (1 + β ) m = 1... M performance measurement (or health and healthcare in general), al- K t+1 T T ∑k = 1 ∑t λk bkh ≤ bhot (1 − β ) h = 1... H though they are more widely used in other fields. We have followed K t+1 ∑k = 1 ∑t λkT xknT ≤ x not n = 1... N Kumar and Russell [34] approach in the context of macroeconomic K t+1 convergence, which combines the (deterministic) frontier production ∑k = 1 ∑t λkT = 1 function literature [35] with the distribution dynamics approach to T convergence analysis [36,37]. Kumar and Russell [34] contribution was β ≥ 0; λk ≥ 0 k = 1... K (8) soon followed by extensions of the model that factored in the con- The main difference from (7) is that the frontier is determined by tribution of human capital [38] and financial development [39] to considering all the observations for the period. productivity growth and convergence. One of the main advantages of the bipartite decomposition sug- 2.2. Bipartite decomposition of the relative contributions to hospital gested is that we focus on how the entire distributions of hospital per- performance formance evolve, instead of concentrating on few summary statistics such as the mean or standard deviation. Therefore, we can detect In accordance with the expressions detailed above, the global possible groups of hospitals which perform poorly or, at the opposite Malmquist-Luenberger index (GML ) index, which captures changes in extreme, clusters of benchmarks to be imitated. Any summary statistic, hospital performance, can be decomposed into technical change (EC ) such as the mean, would conceal this meaningful information. and best practice gap change (BPC ). Apart from analyzing the con- tributions of each of these components makes to the overall hospital performance change between t (2009) and t + 1 (2013), as measured by 3. Sample and variables GML , on average, we can also evaluate what the largest contributors are via an analysis of counterfactual distributions. To this end, we use Three subtypes of level 1 hospitals were identified based on the nonparametric density estimation, based on kernel smoothing. services they provide. The first group consists of hospitals with facilities Specifically, we rewrite expression (4) above as follows: for outpatient consultations and emergency care only. Hospitals in the second group, in addition to the services provided by the first group, gml EC × BPC = EC t , t + 1 × BPC t , t + 1 (9) also have inpatient beds. Finally, the third group contains hospitals according to which gml EC × BPC indicates that the change in hospital that, in addition to the above, have operating rooms for simple surgical performance is obtained by successively multiplying its two compo- procedures. These structural differences indicate that the production nents which, in turn, enables us to construct counterfactual distribu- process is not totally homogeneous and, consequently, a joint evalua- tions by sequentially introducing each component. tion does not seem advisable. In particular, the counterfactual hospital performance change at- Table 1 reports the distribution of the data available by level 1 tributable to changes in efficiency isolates the effect on the distribution of hospital subtype. The sample consists of 602 hospitals for which com- changes due to efficiency only, assuming BPC does not contribute to the plete information was obtained. The tendency during the period studied change in hospital performance (gml ), and it corresponds to the fol- was to reduce the number of hospitals with surgical capacity, and in- lowing expression crease the number of hospitals with inpatient capacity. The table shows that some hospitals changed category during the period, which could gml EC = EC t , t + 1 (10) make interpretation of results more difficult in these special cases. For Continuing with the sequential decomposition, we would proceed as this reason, and due to space restrictions, results will be presented only follows: at aggregate level. As indicated earlier, data were obtained from the information gml EC × BPC = EC t , t + 1 × BPC t , t + 1 = gml EC × BPC t , t + 1 (11) system on public hospital management, SIHO. It is one of the most We can invert the order of the sequential decomposition. In such a complete available databases since it provides information on physical, case, the counterfactual hospital performance change attributable to human and financial resources and, simultaneously, it builds different best practice gap change would be: output aggregates relevant for an analysis of efficiency. By law,6 it is mandatory that health care provision institutions report the necessary gml BPC = BPC t , t + 1 (12) In this case we would be isolating the effect on the distribution of 5 The interested reader can refer to Silverman [80], Scott [81], Li and Racine [82] and, best practice gap changes only, assuming EC does not contribute to the more recently, Henderson and Parmeter [83]. 6 change in hospital performance (gml ). Hence expression (11) would Article 52 of Law 812 of 2013, Colombia. 23 V. Giménez et al. Socio-Economic Planning Sciences 65 (2019) 20–35 Table 1 All these variables were deflated to be expressed in 2008 prices, Number of hospitals by type. thus preventing the price effect from distorting the efficiency measures. Year Surgical With hospitalization Without hospitalization Total 2009 76 450 76 602 3.2. Outputs 2010 66 460 76 602 2011 60 470 72 602 The most commonly used outputs in evaluating non-teaching hos- 2012 57 468 77 602 pitals are outpatients and inpatients. The main difficulty in computing 2013 49 476 77 602 the latter is not so much their number, but rather their complexity. For this reason, some type of homogenized measurement is generally as- and sufficient information that is established by the Comprehensive sociated with the complexity of each illness or condition. Several stu- Health Care Information System. As a consequence, all public hospitals dies have also included service quality provided by hospitals. For in- report complete health care service provision budgetary information to stance, Solà and Prior [46] use nosocomial infections as a measure of the Ministry of Health. In the period from 2009 to 2013, the records of technical quality. Nosocomial infections are contracted during hospital the database show the existence of 949 public hospitals, of which the stays and are closely linked to poor sterilization and disinfecting of national level hospital and mental health hospitals are not taken into surgical instruments and equipment, among other causes. Other vari- account. In this sense, the data on which this research is based con- ables have also been used to measure quality, such as hospital re-ad- templates all public hospitals during the period of analysis. Specifically, missions within a given period related to the same condition. In addi- the distribution of the universe of hospitals corresponds to 802 level 1 tion to variables associated with technical quality, Vuori [47] hospitals, 121 level 2 hospitals and 26 level 3 hospitals. In the esti- recommends using other variables more closely related to quality of mation of the DEA model, 602 level 1 complexity hospitals were used, service, one of which is patient satisfaction. Hospital quality would thus which represents 75% of the total universe of level 1 public hospitals comprise a technical component as well as service quality. Note that registered in the SIHO database. from a methodological point of view, quality variables used in the hospital (health) sector often improve when their value is minimized and as such they should be considered as undesirable or bad outputs. 3.1. Selection of inputs The inputs, outputs, and quality variables were obtained from the hospital information system (SIHO) of the Ministry of Health and Social A relevant question when evaluating efficiency in the hospital Protection of the Republic of Colombia, following Tamayo and (health) sector is which inputs and outputs to use to represent the Maldonado [18]. The period of study for which information is available production process. A large number of operational variables have been and comparable is 2009–2013. used in both categories [40], as they often depend on available data- Quantification of service provision levels is always complex in the bases. The most commonly used input variables can be grouped into case of hospitals. The difficulty lies in the wide variety of services three main categories. The first category refers to investment in capital. provided and their varied levels of complexity. To overcome this pro- Ozcan and Luke [41] proposed measuring capital investment with two blem, all the production will be summarized in a single variable. In this indicators: the number of operational beds (as a measure of hospital case, production can be added because information was available on size), and the complexity of services provided, measured as the number the “relative value unit” (UVR). This is the criteria used to determine of diagnostic and special services offered exclusively by the hospital. the complexity of the treated cases when the health care providers (IPS) The second input category concerns personnel. This variable has fre- bill their services to the insurance carriers (EPS). Combining all pro- quently been used in studies, either expressed in terms of physical units duction into a single variable makes it easier to include other variables of available personnel, which are generally transformed to full time such as those related to quality without affecting the discriminatory equivalent (FTE) persons in a complete working day, or in monetary capacity of the model. Therefore, the final chosen output variable was: terms. Studies normally differentiate personnel according to their functions: medical care (sometimes distinguishing between doctors and • Weighted production (O ). A sum of the weighted services provided by 1 nurses), administrative or other functions. Examples of specification of their UVR.7 personnel as an input can be found for instance in Athanassopoulos and Gounaris [42] and Ozcan and Luke [41]. The third common category of Table 2 presents the descriptive statistics for the inputs and outputs inputs in the literature is operational expenditures. This variable gen- selected. erally covers other expenditures that are not related to personnel, such The tendency for inputs I1 and I2 grew over the period studied, al- as amortizations, supplies, and especially the purchase of goods and though growth was higher for purchases of goods and services, while services necessary to provide the service [41]. The inputs selected for our study were the following: 7 Public hospitals produce a heterogeneous variety of health services. In order to obtain an aggregate measurement of public hospitals' service provision, several methodologies • Total spending on purchase of goods and services (I ). Expressed in 1 have been proposed recently—particularly for the case of Colombia. Cortés-Martínez [84], Gómez Duque [85] and Sarmiento Gómez et al. [86] described a weighted pro- thousand billions of Colombian pesos. • Total spending on medicines (I ). Expressed in thousand billions of duction measurement that is based on creating equivalent relations among health ser- 2 vices. For instance, if the equivalent measure is the cost of a surgery, all health services Colombian pesos. will be compared to this cost in order to get a relative weight among total production. • Total monthly spending on administrative personnel (I ). Expressed 3 According to Sarmiento Gómez et al. [86], the relative value unit was first calculated by the health and social security public institute, with the purpose of measuring different in thousand billions of Colombian pesos. • Total monthly spending on medical personnel (I ). Expressed in 4 technical complexity levels among public hospitals production. This relative unit was made by a group of experts whose expertise is relevant as to set a specific value for each thousand billions of Colombian pesos. service produce by hospitals. In doing this, the experts take into account how complex is the service provision in terms of knowledge, skills, and technological inputs. Therefore, The staff variables have been expressed in monetary terms because delivering a surgery have a higher weight that a medical consultation, given that the former requires a higher specialized set of skills and more complex technological inputs. the information in physical units was not available in the database. Today, the relative value unit estimates are given by the Ministry of Health and Social However, this should not be a problem, since the differences in salaries Protection to public hospitals in order to calculate an aggregate production level. Public between the different Colombian public hospitals are not high. In ad- hospitals used this relative unit value to provide an estimate of aggregate production dition, this option has been used previously in the literature [43–45]. which later on is available in the public hospital database. 24 V. Giménez et al. Socio-Economic Planning Sciences 65 (2019) 20–35 Table 2 Descriptive statistics for inputs and outputs. Year Statistic Inputs Outputs Spending on purchase of goods and Spending on medicinesa Spending on administration Spending on assistance Weighted production servicesa (I1) (I2 ) personnela (I3 ) personnela (I4 ) (O1 ) 2009 Mean 422,000.00 245,000.00 18,300.00 15,400.00 129,027.60 Std. Dev. 560,000.00 344,000.00 162,000.00 11,400.00 189,931.20 2010 Mean 442,000.00 262,000.00 12,000.00 15,300.00 128,607.30 Std. Dev. 641,000.00 345,000.00 10,200.00 11,800.00 192,601.20 2011 Mean 491,000.00 281,000.00 12,700.00 15,600.00 128,163.20 Std. Dev. 684,000.00 393,000.00 12,000.00 11,600.00 194,068.00 2012 Mean 524,000.00 297,000.00 13,300.00 17,000.00 134,804.10 Std. Dev. 744,000.00 426,000.00 10,800.00 14,500.00 216,702.80 2013 Mean 631,000.00 316,000.00 14,200.00 17,600.00 139,664.90 Std. Dev. 920,000.00 499,000.00 13,600.00 14,100.00 220,145.90 Total Mean 502,000.00 280,000.00 14,100.00 16,200.00 132,053.40 Std. Dev. 723,000.00 406,000.00 73,100.00 12,800.00 203,018.80 a In thousands billions of 2008 Colombian pesos. the rising tendency was more moderated in the area of medicines. for the rest of variables, hospitals which refer fewer patients to higher Personnel expenditure reflected an upward trend in spending on nur- levels without negatively affecting the rest of the variables would sing staff, and a falling trend in administrative personnel expenses, function more effectively, thus reducing congestion at more specialized despite showing higher average spending since 2010. The trend was higher levels. This would contribute to a more efficient and effective therefore toward an increase in real terms of all inputs during the management of resources in the whole healthcare system. On the other period. Production levels, however, stagnated until 2011, showing a hand, high values of the total variable waiting time in days (Q2 ) could moderate increase during the final two years of the period. be also interpreted as a high-quality level of the evaluated hospital, Consequently, costs increased in the 2009–2011 period even though contrary to what is supposed here. However, the reason for considering adjusted production did not. it as an indicator to be minored is that, at the same value of the rest of We selected several quality variables to reflect performance from a the quality variables, shorter waiting times would be preferred by pa- technical perspective such as patient satisfaction: tients. Additionally, although in some of the municipalities there are different health providers, in most of them the choice is low or non- • Satisfied patients (Q ). Number of patients who claimed to be satisfied 1 existent. Regarding the variable patients referred to higher levels (Q5 ) it in the survey carried out by the Ministry of Health and Social should be highlighted that access to the levels of higher complexity Protection. For technical purposes, this variable was considered as depends on the authorization of medical professionals in each hospital. an output hospitals should maximize, given the supplies used, to- Therefore, low levels in this variable should not be related to the fact gether with adjusted production.8 that patients seek care directly at higher level medical facilities, except • Total wait in days (Q2 ). Total number of days patients had to wait for in cases of manifest severity. In addition, interviews with expert ana- an appointment until. lysts in the Colombian health system revealed their concern for what • Total minutes waiting in the emergency room (Q3 ). Total number of they considered to be and excessive and unjustified, from a technical minutes waiting to be attended in the emergency room. point of view, level of referred patients to higher level hospitals, which • Re-admission within 20 days (Q4 ). Total number of patients re-ad- was causing both technical and cost inefficiencies. mitted to hospital in a period of less than 20 days after discharge for A technical quality variable often used in the hospital efficiency the same condition. literature is the number of nosocomial infections [46]. However, we did • Patients referred to higher levels (Q5 ). Total number of patients re- not include this variable in our study because level 1 hospitals do not ferred to higher levels. perform the complex surgical procedures often associated with this type of infection, especially through the use of poorly disinfected instru- The final four variables were considered as bad outputs, since the ments and equipment. Therefore, it is an appropriate variable for minimization of their value would lead to improved quality. Regarding healthcare units with high numbers of surgical procedures, but not for the referred patients variable (Q5 ), we assumed that, as with the value primary care centers where surgical activity is low or non-existent. Table 3 shows the descriptive statistics for the quality variables con- sidered in our case. 8 According to the Act 1011 of 2006, each public hospital must report the number of Both the number of satisfied patients and the total number of satisfied patients to the Ministry of Health and Social Protection, which is the institution minutes waiting to be attended in the emergency room remained fairly in charge of providing technical assistance for its measurement. The variable is obtained from a survey that is applied to patients that have received services in public hospitals, stable during the study period. We found the same result in the total therefore it is applied to patients once they have been discharged. Although there is not a number of days waiting for an appointment, with the exception of technical requirement to undertake a sample design when implementing a survey to 2010, in which it fell noticeably. measure patient satisfaction, there is an explicit requirement to obtain a measurement The number of re-admissions in less than 20 days for the same that compares perceptions of the services that have been received to the expectations that condition was also stable for the period, with upturns in 2010 and patients might have before receiving them in public hospitals (Act 1011, Art.32). This has been done in the specialized literature in Colombia [87–89] by identifying gaps between 2011. However, a clear incremental tendency in the number of patients what it is expected by patients, and what patients perceived they have received in each of referred to higher-level hospitals is observed from 2009 to 2013. the following aspects of public hospitals services: (1) infrastructural conditions; (2) ad- Ideally, level 1 hospitals would only refer essential cases to higher-level ministrative protocols and processes; and (3) health outcomes. Because of the lack of a hospitals, thus allowing them to operate as efficiently as possible, rather standard scientific norm, there is not certainty about having all public hospitals doing a sample design that includes a random selection of patients when they apply a satisfaction than using them to resolve cases that should be treated in primary care survey, before sending data to the Ministry of Health and Social Protection. However, centers. It would therefore be interesting to contain or reduce this they are compelled by law to use scientific criteria in order to develop a quality im- variable whenever it does not negatively impact on the other quality provement plan, that is later on audited by the Ministry of Health and Social Protection. 25 V. Giménez et al. Socio-Economic Planning Sciences 65 (2019) 20–35 Table 3 Descriptive statistics for the quality variables. Year Statistic Satisfied patientsa Total waitb (Q2 ) Total waiting in emergencies' Re-admission within 20 daysa Patients referred to higher levels (number of (Q1 ) roomc (Q3 ) (Q4 ) patients)a (Q5 ) 2009 Mean 2043.527 37,017.5 192,183.8 10.55814 2413.093 Std. Dev. 5003.232 79,710.4 636,781.7 79.18977 7446.975 2010 Mean 1936.935 31,364.660 213,367.200 5.636213 2355.669 Std. Dev. 3808.124 70,745.860 685,429.200 18.62527 5398.188 2011 Mean 1882.042 29,637.12 190,967 7.566445 2636.186 Std. Dev. 3677.645 65,983.130 594,297.900 43.82092 5994.869 2012 Mean 2027.188 27,636.700 193,785.500 5.594684 2814.231 Std. Dev. 4187.541 61,436.480 544874.100 16.89938 6356.719 2013 Mean 2257.995 25,421.08 189,033.1 6.036545 3359.571 Std. Dev. 4339.927 52,834.26 439,126.7 22.24471 7056.597 Total Mean 2029.537 30,215.41 195,867.3 7.078405 2715.750 Std. Dev. 4228.322 66,822.700 585,888.200 43.18319 6497.871 a Number of patients. b Days. c Minutes. variables. However, an upward trend in patient referrals to higher le- Table 4 vels is observed for the period. This fact, together with an increase in Mean efficiency levels. the weighted production during that period and the other variables Subtype 2009 2010 2011 2012 2013 Mean remaining fairly stable, may reflect a low filtering and resolution of cases in primary care, which may be leading to an unnecessary number Without hospitalization 0.405 0.390 0.428 0.341 0.326 0.377 of cases referred to higher level hospitals. With hospitalization 0.531 0.447 0.496 0.403 0.498 0.475 Surgical 0.319 0.191 0.327 0.230 0.215 0.260 Mean 0.489 0.411 0.471 0.379 0.453 0.441 4. Results and discussion Efficiency levels were estimated for each year by calculating the Table 5 directional distance function (static analysis). The changes in hospital Mean efficiency scores by departments. performance during the period were also quantified (temporal analysis), Department # obs. 2009 2010 2011 2012 2013 Mean eff. and are explained, in turn, as a result of the product of efficiency change (or catch up) and technological change. The concept of effi- Antioquia 110 0.765 0.635 0.688 0.575 0.659 0.664 ciency change refers to whether hospitals are closer to or further away Arauca 2 0.282 0.092 0.127 0.198 0.241 0.188 from observed best practices—which are determined by units (hospitals) Atlántico 11 0.163 0.115 0.064 0.154 0.293 0.158 Bogotá, D.C. 9 0.566 0.540 0.625 0.411 0.391 0.507 lying on the frontier. The technological change, in contrast, refers to Bolívar 11 0.199 0.183 0.340 0.488 0.574 0.357 how these have moved over the time period, i.e., to shifts of the fron- Boyacá 55 0.329 0.346 0.478 0.377 0.357 0.377 tier. Caldas 22 0.521 0.431 0.550 0.429 0.486 0.483 Caquetá 5 0.237 0.187 0.124 0.268 0.276 0.218 Casanare 3 0.436 0.358 0.444 0.497 0.468 0.441 4.1. Results for hospital efficiency Cauca 15 0.249 0.138 0.140 0.064 0.095 0.137 Cesar 16 0.320 0.189 0.402 0.304 0.479 0.339 4.1.1. General trends Chocó 1 0.696 0.508 0.527 0.461 0.581 0.555 As explained above, three categories of hospitals were considered to Córdoba 9 0.194 0.184 0.180 0.176 0.227 0.192 Cundinamarca 34 0.301 0.249 0.327 0.285 0.391 0.311 evaluate efficiency. The procedure used was as follows: (i) to evaluate Guaviare 1 0.385 0.000 0.149 0.205 0.000 0.148 type 1 hospitals we also included those from types 2 and 3 as possible Huila 30 0.515 0.486 0.430 0.451 0.477 0.472 benchmarks; (ii) to evaluate type 2 hospitals, type 3 hospitals were also La Guajira 11 0.220 0.177 0.221 0.270 0.422 0.262 included; (iii) finally, hospitals in the type 3 category were evaluated Magdalena 20 0.257 0.209 0.261 0.158 0.401 0.257 separately. The rationale behind this procedure is that type 3 hospitals Meta 11 0.611 0.276 0.424 0.263 0.344 0.384 Nariño 48 0.562 0.578 0.540 0.377 0.496 0.510 are those with more complex activities, which could imply higher costs Norte de Santander 10 0.472 0.268 0.341 0.175 0.235 0.298 and, ultimately, worse efficiency results. Therefore, it makes little sense Putumayo 2 0.265 0.150 0.304 0.237 0.358 0.263 to compare them with hospitals whose activities are less complex—i.e., Quindío 8 0.505 0.465 0.444 0.422 0.470 0.461 hospitals with more elementary production processes. This procedure Risaralda 12 0.440 0.336 0.360 0.214 0.205 0.311 Santander 62 0.641 0.521 0.548 0.397 0.453 0.512 was proposed by Banker [48]; but the idea has also been also con- Sucre 19 0.353 0.182 0.296 0.175 0.223 0.246 sidered from other perspectives.9 Tolima 31 0.433 0.447 0.499 0.357 0.512 0.450 Estimated efficiency levels are presented in Tables 4 and 5, calcu- Valle del Cauca 34 0.447 0.338 0.513 0.444 0.482 0.445 lated by solving linear programming problem (7). Efficiency scores may Mean 21.5 0.489 0.411 0.471 0.379 0.453 0.441 take the value of zero as a minimum as long as it does not have an upper bound; the lower its value, the higher the efficiency level. A value of zero represents efficiency, and high values represent inefficiency. Their coefficient 0.319 in the table for year 2009 for surgery hospitals should interpretation is the maximum proportion in which each hospital can be that this group of hospitals was able to increase its adjusted pro- improve observed production and quality levels without increasing its duction level (O1) and number of satisfied patients (Q1) by an average of consumption of inputs. For example, the interpretation of the 31.90%, while simultaneously reducing the variables associated with quality (Q2 to Q5 ) by the same proportion. All these improvements should be possible without the need to use more inputs than those 9 From a methodological perspective see, for instance, Battese et al. [90], Balaguer-Coll observed. et al. [91], from an empirical point of view see, for instance, Tortosa-Ausina [92]. 26 V. Giménez et al. Socio-Economic Planning Sciences 65 (2019) 20–35 The average efficiency during the period was 0.441 (see Tables 4 greater number of public hospitals with a less developed network of and 5), which can be considered relatively high according to the in- health provision have lower efficiency scores compared with other terpretation described in the previous paragraph. From a management departments with fewer public hospitals with better networks of health point of view, high levels of inefficiency imply there is leeway to in- provision. This would increase costs in health provision in each de- crease the quantity and quality of services without consuming more partment for a given level of outputs. Then, if a public hospital is in a inputs. Whether the weighted production depends on how many pa- better developed network then it could be able to reduce the effect of tients visit a center and with which conditions, an aspect relatively market failures associated with moral hazard and adverse selection, beyond hospital's control (although prevention campaigns can play an improving efficiencies, in comparison with a public hospital located in important role), the potential for improvement in the dimensions of less developed networks for a given level of outputs. This is particularly quality (Q1 to Q5 ) seems clear, even assuming that the observed pro- relevant for the departments of, for instance, Cauca, Guaviare, Atlán- duction and inputs levels are maintained. tico, and Arauca which have better efficiency scores in comparison to A secondary aim of this research is to quantify avoidable referrals to Antioquia, Santander and Bogotá. higher level hospitals (measured by variable Q5). This is a complex Second, there might be government failure when trying to correct question, the response to which would probably require fieldwork in market failures generated by asymmetric spatial concentration of public collaboration with medical professionals. However, the methodology hospitals. After the regulatory change,12 departments have a greater used allows us to make an initial approximation. As indicated in the deal of autonomy in allocating public resources to improve coverage previous paragraphs, the results point to a potential average reduction using demand subsidies. Nowadays local governments oversee and al- of 44.1%. This high percentage indicates that the system is probably locate subsidies to improve health coverage for low income individuals. bearing higher costs than it actually should, as well as affecting effec- This new mechanism of allocating public resources may have increased tiveness and quality further up the healthcare system. the interest of private parties to capture public interest of improving Results by hospital type show that inefficiency is greater in centers health provision. This affects efficiency scores regardless of both the with inpatient beds and without operating rooms (0.475, see Table 4). number of hospitals, and how well they are connected in a network of Therefore, the largest group in the sample is also the least efficient, a health providers. Then, new policies aimed at fostering coverage might circumstance that holds throughout the entire period. The most effi- have increased the incentive of capturing local government institutions cient hospitals, with an efficiency coefficient of 0.260, are those that of private parties,13 boosting the spending of public hospitals due to have operating rooms, which is also the case for all the years analyzed. corruption in public resources management for a given level of outputs. These results seems to evidence for the presence of scope economies, as This seems to be case of the provinces of Casanare, Huila and Chocó hospitals offering a more complete catalog of services appear to take which have according to 2013/14 transparency index a medium and advantage of the use of fixed inputs in a more consistent way. This high risk of corruption14 and have also lower levels of efficiency. situation is dependent on the environmental conditions as big hospitals located in urban areas, or closer to them, can take advantage of the potential scope economies. 4.1.2. On the sources of inefficiencies: slacks As shown in Table 5, the departments with the most efficient hos- The methods used allowed us to measure the potentially achievable pitals were Cauca (0.137) and Guaviare (0.148), followed by the reductions for each input category. In other words, the reductions that Atlántico (0.158) and Arauca (0.188), while the least efficient were could be achievable in each input additionally to the potential im- Antioquia (0.664), Chocó (0.555) and Santander (0.512). Bogotá D.C. provement for the good and bad outputs shown in Tables 4 and 5. This also had a high level of inefficiency (0.507). information is obtained from the slacks in linear programming problem The differences among departments might be related to the ex- (7). Results are shown in Table 6. istence of market and government failures. First of all, there is a higher The items with the highest reduction potential (above 20% on concentration of public hospitals in urban areas in the departments average) are those associated with personnel and medicine. Reductions whose economic performance is better—including lower unemploy- in the personnel category are 21.19% and 23.06% for administrative ment rates. This asymmetric spatial allocation of public hospitals and medical care personnel, respectively, which must be interpreted around the country could affect the spending level per hospital in each with certain caution. The healthcare sector must have a permanent department which, in turn, increases inefficiencies. The market failure operating capacity to attend and deal with unpredictable events such as affects the provision of health services on less accountable levels related accidents, epidemics, and so on; this requirement can lead to excess to adverse selection and moral hazard10 in affiliation due to incomplete resources on average, especially in personnel. information on health status, especially when there is not a well es- However, the data indicate a growing tendency to inefficiency in tablished network of health providers.11 Therefore, departments with a personnel costs for the period, for which it would be advisable to reduce these areas or, at the very least, limit their growth, since there are 10 Asymmetric information concerning present and future patients' health status is a (footnote continued) major source of inefficiency for public hospitals, because it increases operational costs. proper, effective, and continued health services. This type of organization has also been One way in which this happens is moral hazard. According to Cutler and Zeckhauser [93], advocated by Act. 1438, which defines a NHP as a set of organizations that manages to set moral hazard causes both over-consumption and over-provision of health services, be- up agreements to provide an efficient, equitable, complete, and continuous health service. cause there is an incentive to spend more (when offering a generous insurance), and The concept is built upon a network framework developed by both the Pan American because there is an incentive to manipulate consumption to induce a demand of services Health Organization (PAHO) and The World Health Organization (WHO) in 2010, ac- that is not required. Therefore, for a given level of health status, a public hospital would cording to which a NHP is a set of linked organizations willingly open to be audited in spend more resources than the necessary to achieve it. Moral hazard refers to a funda- terms of resources management and health outcomes, whose main purpose is to share mental trade-off between risk sharing, and incentives to deviate from cost-efficient be- resources to provide equitable, and comprehensive health care services to a defined po- havior. With more generous insurance programs to reduce the risk of having a negative pulation [95]. 12 outcome on health status, there are higher chances of over consumption and over service Law 100 in 1993. 13 provision. These deviations are a source of inefficiency for public hospitals. We refer here to a non-productive illegal rent seeking activity that increases both 11 Because there exists an uneven distribution of health providers in rural areas, which private benefits and social costs. According to Lambsdorff [96], it is corruption when it in turn reduces coverage and quality in health services provision, the Ministry of Health trespasses laws or rules that have been set up to protect social benefits. It is usually and Social Protection has supported an organization known as Network of Health conceived in a principal-agent model when the actions of the agent are meant to increase Providers (NHP). According to the Ministry of Health and Social Protection [94], a NHP is its own benefit, without considering the principal's benefit. 14 an articulated set of either or both private and public health care providers located in a The measurement is known as an index that accounts for the transparency of public geographical area that is defined by the integrated model of health care provision in institutions. The measurement of 2013 is available at http://indicedetransparencia.org. Colombia. As an organization, it shares resources to provide access to health care through co/ITD/Gobernaciones. 27 V. Giménez et al. Socio-Economic Planning Sciences 65 (2019) 20–35 Table 6 Table 7 Additional reductions achievable in inputs after improving the good and bad outputs, Additional reductions achievable in inputs after improving the good and bad outputs by average 2009–2013 (%). departments, average 2009–2013. Year Descriptive Spending Spending Spending on Spending Department Spending Spending Spending on Spending Mean statistics on on administration on on on administration on purchase medicines personnel (I3 ) assistance purchase medicines personnel (I3 ) assistance goods and (I2 ) personnel goods and (I2 ) personnel services (I4 ) services (I4 ) (I1) (I1) 2009 Mean 14.39 13.86 19.16 22.81 Antioquia 13.86 26.24 24.46 42.69 29.99 Std. Dev. 21.99 22.86 24.10 25.27 Arauca 19.29 15.79 26.00 7.71 15.30 2010 Mean 7.78 14.24 21.49 22.68 Atlántico 8.10 9.74 16.76 3.67 8.39 Std. Dev. 17.54 21.59 25.36 26.13 Bogotá, D.C. 20.08 45.51 44.29 39.62 37.82 2011 Mean 16.18 27.95 21.92 22.68 Bolívar 13.17 19.58 23.63 31.06 23.70 Std. Dev. 24.31 29.31 25.21 24.94 Boyacá 4.14 15.15 21.27 22.54 17.13 2012 Mean 5.77 20.32 20.27 21.74 Caldas 2.69 36.09 32.82 9.52 18.13 Std. Dev. 14.95 25.95 23.28 24.86 Caquetá 22.96 2.30 24.08 30.91 22.23 2013 Mean 9.86 26.59 23.13 25.38 Casanare 23.56 16.94 22.64 19.33 20.36 Std. Dev. 19.22 27.43 23.38 26.63 Cauca 13.02 11.95 3.01 3.36 6.94 Total Mean 10.80 20.59 21.19 23.06 Cesar 13.07 10.59 19.84 21.09 17.14 Std. Dev. 20.24 26.25 24.30 25.59 Chocó 25.66 4.36 52.57 61.13 40.97 Córdoba 9.53 4.65 27.84 25.61 18.65 Cundinamarca 8.07 27.79 3.31 13.50 13.24 actually considerable margins for reduction. An alternative option may Guaviare 30.00 7.99 29.13 32.61 26.47 Huila 11.02 32.40 13.79 9.43 15.21 be to use some of the excess personnel spending to offer new services, La Guajira 23.38 6.02 15.38 18.12 16.21 open new primary care centers to improve coverage, or to raise current Magdalena 9.83 10.96 14.55 26.35 17.61 quality levels. Meta 14.50 8.53 20.79 13.48 14.16 As an illustration, there are thirteen hospitals in which spending on Nariño 17.19 39.92 14.56 13.04 19.55 Norte de 9.79 6.17 11.52 26.17 15.96 administrative personnel is higher than on nursing staff, whereas the Santander opposite would seem more logical. In these cases, the potential to re- Putumayo 36.04 0.00 17.31 17.09 17.51 duce spending on administrative personnel will be much higher than in Quindío 0.00 27.26 14.98 14.39 14.20 other hospitals with similar levels of production and quality, but with Risaralda 0.89 24.35 21.34 4.26 11.02 fewer administrative personnel. Santander 5.64 16.22 29.42 27.07 21.08 Sucre 9.72 11.16 12.05 15.75 12.89 Regarding spending on medicines, we estimated a potential average Tolima 18.71 9.80 11.99 15.10 14.14 reduction of 20.59%. Note that the potential reduction in this area in- Valle del 3.83 27.19 27.10 17.75 18.72 creases considerably after 2011, almost doubling by 2013. This in- Cauca dicates a growth of inefficiency in managing medicine purchases. It Mean 10.80 20.59 21.19 23.06 19.74 would therefore be advisable to analyze the causes of this increase and introduce remedial measures into the system. Procurement of goods Table 8 and services is the area showing the most moderate potential reduction Total annual improvement achievable in quality (%) after improving the good and bad (10.80%); no clear rising or falling tendency was identified and it is outputs by year, average. apparently the most controlled area. Table 7 shows that the departments with the lowest potential for Year Satisfied Total wait Total waiting Re- Patients reducing their expenditure were Cauca (6.94%), the Atlantic (8.39%) patients in admission referred emergencies' within 20 to higher and Risaralda (11.02%), suggesting that they managed their spending room days levels more efficiently. At the other extreme, the departments with the highest excess costs were Antioquia (29.99%), Chocó (40.97%) and the capital, (Q1 ) (Q2 ) (Q3 ) (Q4 ) (Q5 ) Bogotá D.C. (37.82%). 2009 Mean 185.338 53.469 57.926 36.678 53.337 The number of patients treated is often a variable relatively out of Std. Dev 361.826 34.979 35.192 44.161 33.614 the control of an hospital, although it could be sometimes reduced by 2010 Mean 108.335 49.709 43.414 23.514 43.409 prevention and vaccination campaigns. Hence, it is interesting to Std. Dev 371.118 33.933 32.344 33.719 30.938 quantify the maximum improvements that could be achieved in each of 2011 Mean 116.280 52.350 49.847 27.007 49.368 Std. Dev 246.259 31.411 31.679 36.157 29.999 the quality variables, as shown in Tables 8 and 9. These values are 2012 Mean 120.790 41.766 38.699 25.707 41.612 obtained from the optimal values of the program 7. Specifically, for the Std. Dev 455.697 28.228 28.414 34.272 28.601 variable satisfied patients (Q1) it is obtained from the expression 2013 Mean 195.672 51.710 48.120 28.515 49.240 ymot (1 + β *) + sm* , where sm* is the slack variable of the constrain asso- Std. Dev 442.896 32.295 32.587 39.288 31.433 ciated with the good output. For the rest of the quality variables, the Total Mean 145.283 49.801 47.601 28.284 47.393 Std. Dev 384.470 32.504 32.739 37.960 31.237 maximum potential improvements are obtained from the expression bhot (1 − β *) − sh* , where sh* is the optimum value of the slack variable of the constrain associated with each bad output. The results show that provided by the hospitals. The number of patients re-admitted within during the 2009–13 period the quality variable with the greatest po- 20 days (Q4 ) could improve by approximately 28%. Since this variable tential for improvement was patient satisfaction (Q1), standing at is probably the most directly related to the technical quality of care it is 143.283% per year. The variables total wait (Q2 ), total waiting in not a negligible improvement despite being the quality variable with emergencies' room (Q3), and patients referred to higher levels (Q5) the least potential for improvement. The detailed analysis by years does stand with a potential improvement between 47 and 50%. In this case, not reveal any remarkable trend (see Table 8. The results by department it should be highlighted that these quality variables are often associated (see Table 9), show that the departments with a better performance in with a more objective criteria than Q1 confirming again the existence of average levels of quality have been Guaviare, Cauca and Arauca all of considerable deficiencies in the quality levels of the health services them with potential improvements lower than 25%. On the other hand, 28 V. Giménez et al. Socio-Economic Planning Sciences 65 (2019) 20–35 Table 9 Total improvement achievable in quality (%) after improving the good and bad outputs by department, average 2009–2013. Department Satisfied patients Total wait Total waiting in emergencies' room Re-admission within 20 days Patients referred to higher levels Mean (Q1 ) (Q2 ) (Q3 ) (Q4 ) (Q5 ) Antioquia 183.799 70.939 68.556 46.585 67.090 87.394 Arauca 18.781 23.260 21.052 23.106 29.606 23.161 Atlántico 151.087 24.461 22.659 8.272 20.294 45.355 Bogotá, D.C. 119.056 72.375 57.139 41.147 75.032 72.950 Bolívar 265.767 42.215 38.706 22.139 39.582 81.682 Boyacá 75.529 42.749 25.830 9.152 41.331 38.918 Caldas 206.491 57.450 48.026 49.897 51.120 82.597 Caquetá 99.926 33.845 26.837 16.344 21.636 39.718 Casanare 55.007 46.928 46.877 46.558 44.052 47.884 Cauca 18.205 15.346 17.135 20.741 18.880 18.061 Cesar 155.950 35.610 47.707 27.400 37.378 60.809 Chocó 96.941 55.462 55.462 45.302 57.924 62.218 Córdoba 251.539 45.697 39.938 28.559 34.132 79.973 Cundinamarca 47.053 29.490 23.241 20.052 19.212 27.810 Guaviare 14.763 22.647 14.763 14.763 14.763 16.340 Huila 78.667 49.687 48.658 24.073 52.587 50.734 La Guajira 28.437 29.605 38.161 16.455 26.982 27.928 Magdalena 165.633 29.567 32.955 20.250 27.637 55.208 Meta 265.419 41.151 42.369 21.759 40.002 82.140 Nariño 202.635 54.638 52.008 7.264 53.130 73.935 Norte de Santander 41.214 31.765 43.009 7.862 33.481 31.466 Putumayo 83.256 31.611 26.947 0.000 26.276 33.618 Quindío 112.427 56.581 55.187 44.782 59.245 65.644 Risaralda 117.062 46.951 32.869 45.321 35.186 55.478 Santander 139.788 55.498 55.266 23.893 54.351 65.759 Sucre 117.440 27.242 37.536 13.104 30.921 45.249 Tolima 128.248 49.277 57.566 45.971 47.341 65.681 Valle del Cauca 115.955 51.683 50.847 39.285 50.187 61.591 Mean 145.283 49.801 47.601 28.284 47.393 63.672 four departments (Bolívar, Meta, Caldas and Antioquia) have the worst the global Malmquist-Luenberger index (GML ), along with the decom- results with average potential increases of quality over 80%. position between efficiency change (EC ) and technological change (also referred to as best-practice change, BPC ).15 A value higher than unity means that hospital performance (total 4.2. Temporal analysis factor productivity) improved in the period considered, whereas a lower value indicates deterioration in its performance. Focusing on the Table 10 reports the results for the evolution of total factor pro- components of performance change, the catching up component (effi- ductivity (i.e., change in hospital performance), defined in Section 2 as ciency change, EC ) shows how a hospital's proximity to the efficient good practices frontier changed for the period. A value greater than one Table 10 Total factor productivity, efficiency and technological changes. Mean values. means that during the period the hospitals were closer to the best ob- served practices. Technological change (best practice change, BPC ) Hospital Type 2009–2010 2010–2011 2011–2012 2012–2013 Mean measures frontier shifts, which serves as a reference for measuring the efficiency of hospitals off the efficient frontier. Once again, a value Surgical Efficiency Change 1.079 0.928 1.057 0.970 1.008 greater than one indicates an improvement or, in other words, that best Technological 0.903 1.070 0.960 1.007 0.985 practices were able to achieve more output with the same or less input. Change A value lower than one implies the opposite. Total Factor 0.967 0.992 1.013 0.971 0.986 The lower right cell in Table 10 shows that the hospitals' perfor- Productivity mance change (productivity change) in the period was 0.99. This means With Hospitalization Efficiency Change 1.074 0.979 1.087 0.958 1.024 that the productivity for the period worsened, on average, by 1%. The Technological 0.906 1.019 0.932 1.074 0.983 most deterioration, by 2.4%, was seen in hospitals with no inpatient Change capacity. An analysis of the determining components of productivity Total Factor 0.971 0.987 1.003 1.012 0.993 reveals that catch up was slightly positive in the period. The index has a Productivity Without Hospitalization value of 1.022, but the best practices (technological change) worsened, Efficiency Change 1.044 0.977 1.069 1.009 1.025 showing a coefficient of 0.982. As a result, the changes in efficiency Technological 0.898 0.986 0.984 1.021 0.972 were due in part to a worsening of efficient units, which led to a drop in Change the total factor productivity for the period. Nevertheless, a detailed Total Factor 0.922 0.951 1.031 1.002 0.976 analysis shows that for the periods 2011–2012 and 2012–2013, pro- Productivity Efficiency Change 1.071 0.972 1.081 0.966 1.022 ductivity tentatively started on the road to recovery after an initially (Mean) poor performance. Taking into account that the static analysis revealed Technological 0.905 1.021 0.942 1.059 0.982 notable levels of inefficiency, and the temporal analysis showed small Change (Mean) Total Factor 0.964 0.983 1.008 1.005 0.990 15 Productivity As pointed out in the theoretical section of this paper, remember that the technical (Mean) change described here can signal both progress or regress, but it quantifies all kinds of biased or neutral estimations of technical change. 29 V. Giménez et al. Socio-Economic Planning Sciences 65 (2019) 20–35 Table 11 also appreciated that the results have not changed hardly in quantity or Change in hospital performance and its decomposition, Colombian departments, average interpretation. The only exception is for the 2012–2013 period, in (2009–2013). which contradictory results are obtained with the new estimation with Efficiency Technological Change in hospital respect to the initial one. Therefore, we consider that the results ob- change change performance tained originally can be considered as robust given the small changes observed after the removing simultaneously both variables. Antioquia 1.027 0.988 1.002 Arauca 1.013 1.016 1.017 Atlántico 0.992 0.994 0.966 4.3. Bipartite decomposition of the contributions to performance change Bogotá, D.C. 1.043 1.003 1.037 Bolívar 0.950 1.009 0.954 Boyacá 1.018 0.959 0.955 The results corresponding to the bipartite decomposition explained Caldas 1.017 0.973 0.977 in Section 4.3 are reported in Fig. 1. They refer to the changes in hos- Caquetá 1.004 0.992 1.000 pital performance for the entire period, i.e., between 2009 and 2013.16 Casanare 0.999 0.992 0.988 Fig. 1 is split into four sub-figures, those in the upper and lower panels Cauca 1.041 1.004 1.035 Cesar 0.988 0.977 0.954 corresponding to the two directions of the sequential order of the Chocó 1.021 0.978 0.992 analysis. Specifically, the upper panel (sub-Fig. 1 a, corresponding to Córdoba 1.010 0.993 0.985 the contribution of efficiency change, and 1.b, corresponding to the Cundinamarca 0.999 0.988 0.978 contribution of best practice gap change) refers to the decomposition in Guaviare 1.103 0.935 1.041 Huila 1.019 0.965 0.971 Equation (11), and the lower panel (sub-Fig. 1 c, corresponding to the La Guajira 0.974 0.985 0.953 contribution of best practice gap change, and 1.d, corresponding to the Magdalena 0.992 1.007 0.982 contribution of efficiency change) represents the decomposition in Meta 1.078 0.976 1.034 Equation (13). Nariño 1.030 0.979 0.989 As indicated in Section 2.2, the analysis was carried out using kernel Norte de Santander 1.058 0.973 1.014 Putumayo 0.992 1.016 1.000 smoothing (Gaussian kernel), and considering several bandwidth Quindío 1.006 0.965 0.972 choices, both to acknowledge this rich literature and also to increase Risaralda 1.054 0.960 1.002 the robustness of the results. Therefore, whereas results in Fig. 1 were Santander 1.055 0.970 1.007 obtained using a global (direct plug-in) bandwidth [32], in Fig. 2 we Sucre 1.052 0.994 1.035 Tolima 1.011 1.004 0.999 also report findings considering a bandwidth that smooths locally—i.e., Valle del Cauca 1.010 0.979 0.976 depending on the data in each region of the distribution [33]. Mean 1.022 0.982 0.990 The density in Fig. 1 a points to greater disparity in the contribu- tions of efficiency to hospital performance change between 2009 and 2013 (i.e., to the global non-radial Malmquist index). This is the changes in productivity, we can deduce that there is no clear im- counterfactual hospital performance change attributable to changes in provement trend in productivity and in the components that contribute efficiency only ( gml EC ), i.e. we isolate the effect of changes in effi- to an improvement in performance for level 1 hospitals; rather, in- ciency. The remarkable heterogeneity is revealed by the long tails of the efficiency levels are consolidated. density (particularly the upper tail), as well as the existence of several The departments with higher increases in total factor productivity bumps (corresponding to more hospitals). However, given that prob- were Guaviare, with 4.1%, Sucre and Cauca with 3.5%, and the capital abilistic mass tends to concentrate more tightly around unity, the final Bogotá, D.C. (3.7%) (see Table 11). Note also that these three depart- average effect is slightly positive, as revealed by the vertical solid line ments and the capital are the only ones where total factor productivity in Fig. 1 a (which is the average of gml EC between 2009 and 2014). and its two components improved. This means not only that efficiency The upper panel in Fig. 1 displays the contribution of best practice improved, but also that the frontier area with which they were com- change (Fig. 1b). However, in this case its effect is not isolated, since we pared improved as well. Guaviare and Cauca also appeared in the list of combine it with the effect of efficiency change ( gml EC × BPC ). The con- more efficient departments in the static analysis. The temporal analysis tribution of best practice change (technological change) is, on average, confirmed that they also have the most active productivity improve- detrimental, since the average hospital performance change—r- ment. The case of Bogotá D.C., the country's capital, is particularly epresented by the dashed vertical line in Fig. 1 b—shifts leftwards, notable for its economic importance and population concentration. leading to an overall negative performance change. The negative con- Although the static analysis showed room for improvement in efficiency tribution of best practice change is due to a high number of hospitals in results, the evolution during the period of productivity was positive, the (0.5, 1.0) interval, revealed by the high probabilistic mass. In con- although much remains to be done to improve efficiency. The depart- trast, several hospitals also excel in terms of best practice change, since ments with the worst evolution were La Guajira, Bolívar, Cesar, and there is also probabilistic mass in the (1.0, 2.0) interval, but it is much Boyacá—all with a drop in the total factor productivity of more than lower than that corresponding to efficiency change. Fig. 2a and 2 b 4%. report the results corresponding to the local bandwidths, pointing in the As mentioned in section 3.2, Q2 and Q5 are variables that can be same direction and, therefore, corroborating the results, although the interpreted in a contrary way to the one proposed in this article, as well trends are much smoother. as being a non-standard choice of variables in the literature. For this The lower panels of both Fig. 1 (global bandwidth) and 2 (local reason, a re-estimation of the model was carried out to check the ro- bandwidth) report results analogous to the upper panel, but first iso- bustness of the results before changes in the specification of these lating the best practice change effect. In the case of the global band- variables. Specifically, the calculations have been carried out again, width (Fig. 1c and 2 c), the densities are tighter compared to the effect eliminating them. The two variables have been eliminated at the same of isolating the efficiency change, indicating fewer disparities among time instead of eliminating them one at a time because the impact on hospitals in terms of best practice gap change. However, the existence the results will always be greater the more variables are modified as it is of probabilistic mass in the vicinity of 2 (Fig. 1c) indicates that some a non-parametric technique such as the DEA based on linear pro- (very few) hospitals excel in this particular regard. All in all, the results gramming. The results obtained after this estimation (see Table 12) shows very small global differences in the results, both in the Total 16 Factor Productivity as well as and in its explanatory components. It is Results for each of the sub-periods analyzed are not reported here due to space restrictions, but are available upon request. 30 V. Giménez et al. Socio-Economic Planning Sciences 65 (2019) 20–35 Table 12 Total factor productivity, efficiency and technological changes without Q2 and Q5 (robustness analysis). Mean values. Hospital Type 2009–2010 2010–2011 2011–2012 2012–2013 Mean Surgical Efficiency Change 1.107 0.912 1.096 0.977 1.023 Technological Change 0.894 1.085 0.941 0.983 0.976 Total Factor Productivity 0.976 0.986 1.026 0.960 0.987 With Hospitalization Efficiency Change 1.081 0.975 1.071 1.021 1.037 Technological Change 0.928 1.029 0.945 0.967 0.967 Total Factor Productivity 0.991 0.994 1.003 0.982 0.992 Without Hospitalization Efficiency Change 1.258 0.984 1.069 1.009 1.080 Technological Change 0.887 0.968 0.990 0.982 0.957 Total Factor Productivity 1.025 0.946 1.050 0.983 1.001 Total Efficiency Change (Mean) 1.106 0.968 1.074 1.014 1.041 Total Technological Change (Mean) 0.918 1.029 0.950 0.971 0.967 Total Factor Productivity (Mean) 0.994 0.987 1.012 0.979 0.993 presented in the upper and lower panels of both Figs. 1 and 2 would With reference to Law 100 (1993), the results reflect deficient suggest that the paths followed by different hospitals to achieve parti- performance in public hospital efficiency. Taking into account that the cular levels of performance differ greatly, and the efficiency gains of reform was designed to trigger competition in order to achieve uni- some hospitals contribute to offset the overall negative impact on versal coverage based on interaction among insurers, healthcare service performance of best practice change. providers, and healthcare system users, the organizational autonomy the new social state companies (ESEs) gives to public hospitals has not had a conclusive effect in consolidating a positive tendency in pro- 5. Conclusions ductivity and efficiency. Compared with the growth in demand created by replacing supply subsidies due to the payment of capitation units to After the series of reforms introduced in the year 1993, this paper insurers, public hospitals continue to face difficulties in their personnel assessed the evolution of the efficiency in the Colombian public health and medicine expenditures, items in which the results reveal potential sector. More specifically, one of our main interests was to determine to for considerable improvements in resource management. On this point, what extent the excessive amount of patients referred by primary care and echoing the healthcare statute of 2015, it is important to highlight centers to high level hospitals influenced their level of efficiency, the relevance of institutional environment factors such as a clearly having into account the existent capacity to provide services with good defined national pharmaceutical policy (Art. 23) coordinated with quality. public healthcare policy (Art. 20) and the obligation to guarantee ef- The static analysis of productivity showed an average level of effi- ficient availability of healthcare services in marginalized areas (Art. 6 ciency of 0.441 during 2009–2013. The highest levels of efficiency were and Art. 24) aimed to provide favorable conditions for public hospital achieved by hospitals with operating rooms, while the highest level of management. Likewise, internal management tools and efficiency in- inefficiency was found in hospitals with inpatient beds but no operating dicators must be in place in accordance with the challenge of market rooms. In addition, the inputs with the highest reduction potential were competition, which include standard institutional practices within the those associated with personnel and medicines. Likewise, the results framework of a quality model for service aimed at the user. Suitable also suggest a reduction in patient referrals to more complex hospitals information systems must be created for hospital administrations, and of 44.1%. The public hospital system may therefore be bearing more any profits should be reinvested in improving structural capacity, with costs than it should, which also affects the effectiveness and quality the resulting positive effects on hospital efficiency. This is congruent further up the health system. In turn, the temporal analysis established with related findings in the literature calling for guaranteed contractual that productivity for the period fell by 1%, with a notable reduction for designs in which the objectives of a market reform are linked to the hospitals with no inpatient capacity. Our evaluation of the components aims of public sector hospital administration. of productivity determined that the best practices frontier worsened, There is an asymmetrical spatial concentration of public hospitals in although the detailed analysis for the periods 2011–2012 and the country which amplifies the negative effects of having a great 2012–2013 showed a slight recovery. Considering the elevated levels of number of hospitals with weak networks of health providers, and weak inefficiency identified, as well as the small changes in productivity local governments with a high and medium risk of corruption. A de- found in the temporal analysis, there is no clear tendency toward im- partment with a great number of public hospitals poorly connected in a provement in either productivity or its components, but rather, a con- network of health providers, and with private interests capturing public solidation of inefficiency levels in the public hospitals studied. institutions that allocate demand subsidies to low income individuals, The analysis by geographical location showed that the most efficient will likely have a lower level of inefficiency for a given level of outputs. hospitals are located in the departments of Cauca and Guaviare, while This seems to be the case of departments of Antioquia, Santander and the most inefficient are in the departments of Antioquia and Chocó. Bogotá which have a greater number of hospitals, and the case of Likewise, hospitals with a lower potential reduction in spending are Chocó, Huila and Casanare that have a relative high risk of corruption, Cauca and the Atlantic, while the departments with the highest excess compared to the others department in the sample. An extension of this in costs are located in the department of Chocó. The evolution of pro- research will test how the existence of public health networks and lack ductivity shows that the hospitals in the departments of Guaviare and of public institutions transparency allocating demand subsidies affect Cauca are the same as in the static analysis, and are therefore the most efficiency scores. active in improving productivity. The hospitals with the poorest evo- For the policy making, useful implications can be deduced from lution are located in the departments of La Guajira, Bolívar, Cesar and these results. Firstly, compared with the prevalent situation before the Boyacá. Finally, the hospitals located in Bogotá, the capital, have clear reform, the new regulatory framework tried to increase coverage, potential to improve their efficiency levels, even when they register quality and efficiency by introducing more market competition. The improvements in their productivity evolution. 31 V. Giménez et al. Socio-Economic Planning Sciences 65 (2019) 20–35 Fig. 1. Kernel density plots of the bipartite decomposition of hospital performance improvement, DEA, 2009–2013 (global bandwidth). Notes: All figures contain densities estimated via kernel smoothing for the different components of the bipartite decomposition in expression (9), considering sequentially and in both directions how each component (EC or BPC ) contribute to the change in hospital performance ( gml ). The vertical lines in each plot represent the average for each component of the decomposition. Densities were estimated using a Gaussian kernel and the Sheather and Jones [32] plug-in bandwidth (global bandwidth). problem is that the supposed increase in competition has not been efficiency score estimation to control for asymmetric spatial con- completely achieved because of the lack of a good design model of centration of health providers around the country. control of the EPSs, as the poor quality in the service does not imply any penalty in the incomes recognized for these organisms. Moreover, the excessive concentration in specific areas has limited in a substantial Acknowledgements way the real competition. Summing up, there are issues to be solved from the design of the contracts as well as from the geographical reach This paper is part of a wider research project founded by the Inter- of the organisms to enhance the level of competition and, as a results of American Development Bank (IDB) entitled Impactos de los obstáculos this, the improvement of the efficiency. institucionales para incrementar la eficiencia, eficacia y transparencia de la The main limitation of this work is that it analyzes only level 1 of gestión de la inversión pública en Colombia (project reference ATN/ Colombian public hospitals. A useful line of future research would be to Fr12361-CO). The authors gratefully acknowledge financial support expand the sample to include higher level and private hospitals so as to and collaboration from the IDB and the Ministry of Health and Social provide a more transversal analysis of the Colombian healthcare sector. Protection of the Republic of Colombia, which provided access to the Specifically, a network-DEA model could be used to assess the effect of database used in this research. We also thank the helpful comments by inefficiency at one level on higher levels. An additional extension of this Mario Loterszpil, which contributed to improve the overall quality of research could also include network effects and corruption risks on the article. 32 V. Giménez et al. Socio-Economic Planning Sciences 65 (2019) 20–35 Fig. 2. Kernel density plots of the bipartite decomposition of hospital performance improvement, DEA, 2009–2013 (local bandwidth). Notes: All figures contain densities estimated using kernel smoothing for the different components of the bipartite decomposition in expression (11), considering sequentially and in both directions how each component (EC or BPC ) contribute to the change in educational performance ( gml ). 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