The Covid-19 pandemic caused an unusual population mortality rate. This paper aims to determine a causal relationship and its incidence between the Technical Efficiency (TE) of healthcare systems and the Covid-19 mortality rate. Using the Data Envelopment Analysis (DEA) methodology and the OLS, GLS and 2SLS adjustment methods, in 108 countries grouped according to per capita health expenditure, it was found that a 1% increase in the TE of the healthcare systems of the analyzed countries reduces the number of deaths from Covid-19 by between 61 and 127 per hundred thousand inhabitants, concluding that the efficiency of expenditure was transcendental in the prevention of mortality caused by the pandemic.

In early 2020, humanity faced the COVID-19 pandemic, one of the most significant challenges of recent decades, making it necessary to build resilient, flexible and adaptable structures with institutions that would provide an effective and efficient response while being able to overcome traumatic situations, such as the one generated by the virus, with the most negligible social impact. On March 11, 2020, the World Health Organization (WHO) declared a global pandemic when a highly dangerous transmission of the SARS-CoV-2 virus became evident (Pan American Health Organization [PAHO, 2021]). Control measures were the primary basis for prevention: reduction of its spread through hand hygiene and when coughing, standard contact and airborne transmission precautions, and establishing of isolation measures.

At the end of April 2020, more than 3.1 million cases and 217,132 deaths were reported worldwide. By August, these figures had reached 21.1 million cases and 750,660 deaths. In April 2021, the number of infections was 147.2 million and 3.1 million deaths. In May of the same year, the figures increased alarmingly, with nearly 176 million cases worldwide and almost 4 million deaths. These figures show a highly transmissible infectious process, easily transmitted by nasal or oral particles, which brought the planet to a standstill (see Table 1).

Against this background, there was widespread ignorance about the causes, consequences and, above all, how health institutions responded and offered the necessary reassurance to the population. The scientific community warned that the presence of pandemics will be more frequent and their consequences more devastating, with elevated levels of contagion and higher mortality (IPBES, 2020; Han et al., 2015 and 2016; Menachery et al., 2015; Allen et al., 2017). It is estimated that about 1.7 million undiscovered viruses exist, of which more than 850,000 are capable of human transmission (IPBES, 2020). A bleak future seems imminent, making it necessary to direct efforts towards prevention in the field of health.

The healthcare service understood as a right, has constituent elements that the State should guarantee in order to satisfy one of the basic needs, as well as social justice and equality (Vanhulst, 2015). In this respect, the WHO and the PAHO have developed a series of indicators that determine minimum thresholds for healthcare services to correspond with effectiveness in care. The most usual are current public expenditure on health per capita and out-of-pocket expenses.¹ It has also been found that for every thousand inhabitants, 2.28 health professionals and 2.4 beds are required in the health system in order to provide a minimum coverage of 80% of care (WHO, 2006).

Table 2 shows that Argentina and Brazil have the highest per capita health spending in South America. In contrast, Ecuador, Paraguay and Venezuela show a higher percentage of out-of-pocket spending, although this has decreased in Venezuela.

Nevertheless, efficiency parameters are not established; instead, inefficiencies of between 20 and 40% of the resources allocated to the health field have been identified (WHO, 2010).

Efficiency should be conceived as the capacity to produce with limited resources measured in the amount of goods and services that can be obtained for each unit of resource used (Mankiw, 2012). Meanwhile, Hurley (2000) indicates that it is essential to discuss the efficiency of a service, good or activity if an explicit objective has been articulated against which this efficiency can be evaluated.

Farrell (1957) states the need to measure production efficiency in a given industry to understand how much that production unit can increase its product simply by increasing its efficiency without absorbing more resources than it has available.

Hurley (2000) and Cid et al. (2016) define TE as that which is achieved by producing a given output with the minimum use of inputs, understood as the adequate and optimal use of resources in production, with various combinations of inputs to achieve a given output. Soto and Casado (2019) contribute by indicating that TE is achieved by obtaining the maximum result from given resources, or that these results are at least as high as the opportunity cost or, if producing the same results, a smaller amount of resources is consumed.

From a sample of 32 public hospitals in Chile from 2011-2013, Santelices (2017) found an average efficiency of 77%. Another sample of 40 units in 2012 reported an efficiency of 86%. In Colombia, Fontalvo (2017) indicates that 12 of the 17 units analyzed present optimal efficiency. Meanwhile, Meza (2018) observed that only 14.5% of the 29 Colombian entities studied were 100% efficient.

Rodriguez et al. (2015) measured the TE of four clinics specializing in neurological diseases in Cuba, finding a mean scale efficiency of 66.8% in 2012 and 78.7% in 2013. In Ecuador, Suin et al. (2021) found higher TE in the public rather than in the private health system. However, they warn that this could be due to the very nature of the private service reflected in the variables used.

Multinational studies, such as that of Maza and Vergara (2017), which analyze the efficiency of high-complexity hospitals and clinics in Latin America during the period 2010-2011, found that 65% of the units were totally efficient and 48% experienced growth in their productivity due to increases in their efficiency and technological improvements. Sanmartín et al. (2019) quantified the relative efficiency of total health spending in 62 countries in Latin America and the Caribbean (LAC) and the Organization for Economic Cooperation and Development (OECD), finding that in 2014, the most efficient countries in LAC were Chile, Cuba, the Dominican Republic, Venezuela and Jamaica, and in the OECD, Japan, Luxembourg and Turkey.

The Inter-American Development Bank (Banco Interamericano de Desarrollo [IDB], 2018), which measures efficiency levels of healthcare systems in LAC and middle-income OECD countries, found that Latin America shows significant variations in terms of efficiency, with Chile being the best-ranked country (eighth place), together with most OECD countries in the top 25%. Meanwhile, another 22 of the 27 countries are located in the bottom half of average efficiency. Bolivia, Ecuador, Guatemala, Guyana, Panama and Suriname were the lowest-performing countries.

Regarding the use of variables in table 3, different studies have employed Data Envelopment Analysis (DEA) in the analysis of TE. This methodology is used with diverse types of data because of its excellent versatility.

Against this background, this study aims to determine a causal relationship and the incidence of TE in healthcare systems in their response to and management of mortality caused by the worldwide presence of the COVID-19 pandemic.

In terms of formality, this document is divided into five sections. The first is the introductory section with a review of the literature. The second section explains the methodologies used and a complete reference of the data that served as the basis for the analysis. The third section presents the results obtained and their interpretation and contribution based on the research. The fourth section discusses the results and refers to the limitations and new research alternatives from other perspectives and methodological resources. Finally, the fifth section presents the conclusions of the research.

The TE of healthcare systems was measured using the DEA, which is a deterministic and non-parametric frontier method widely used due to its versatility in the use of variables, especially when information is scarce and incomplete (Peñaloza, 2003; García, 1997; Martín, 2008; Yates, 1983).

The methodology presented by Farrell (1957) proposes the existence of Decision-Making Units (DMU) and the use of inputs and outputs, creating an empirical production frontier and measuring the distance to the DMU to obtain a relative efficiency measure. Charnes et al. (1978 and 1997) construct ratios resulting from the ratio of the weighted sum of the outputs to the weighted sum of the inputs and, pursuant to Paretian criteria, obtain an efficiency value between 0 (zero) or not at all efficient and 1 (one) or totally efficient, giving rise to the DEA, which assumes Consistent Returns at Scale (CRS).

In addition, Charners et al. (1978) obtained two more versions of the DEA: the first minimizes the quantity of inputs to obtain the same output (input orientation), and the second, while maintaining the same quantity of inputs, maximizes the output (output orientation). Meanwhile, Banker et al. (1984) propose dual models and add a convexity constraint to obtain the DEA with Variable Returns at Scale (VRS). For the analysis in this study, CRS and VRS models were used, with input orientation, whose mathematical expressions are:

Where:

: slack variables

Ф: Objective function. Efficiency measure

Y_rj : i-th output of the j-th DMU

X_ij : i-th input of the j-th DMU

The information used comes from the open database of the World Bank (2021). Table 4 presents a total sample of 108 countries as DMU, making a distinction by their per capita health expenditure, divided into 40 and 68 countries, respectively, in order to locate each country within its production area. As far as the inputs and outputs are concerned, the variables used are based on those proposed by the IDB (2018) and Sanmartín (2019), highlighting the fact that the number used in each of the calculations considers the formula proposed by Banker et al. (1984) to guarantee correct discrimination between each DMU.

(3)

The mathematical models applying DEA are presented as follows:

dea i_gastsalpib = o_esvinacdi o_masesycina o_tassuperv, rts(CRS) ort(in) stage(2)

dea i_gastsalpib = o_esvinacdi o_masesycina o_tassuperv, rts(CRS) ort(in) stage(2)

dea i_gastsalpcap = o_esvinacdi o_masesycina o_tassuperv, rts(VRS) ort(in) stage(2)

Ordinary Least Squares (OLS), General Least Squares (GLS) and 2-Stage Least Squares (2SLS) were used to determine the relationship between the TE of the countries' healthcare systems and the mortality caused by the COVID-19 pandemic.

OLS -attributable to Carl Friedrich Gauss- is one of the most efficient and popular regression analyses due to its statistical properties and assumptions: homoscedastic variance, explanatory variables not sharing information, and errors not correlated with each other. However, if there is evidence of heteroscedasticity, it should be changed to GLS, which will help to correct the lack of efficiency of OLS estimators (Gujarati and Porter, 2009; Girón, 2017).

Meanwhile, suppose inconsistencies occur due to a probable correlation between the stochastic explanatory variable and the stochastic disturbance term. In that case, instrumental variables can be used and 2SLS, developed by Arnold Zellner and Henri Theil (1962) and Robert Basmann (1957), can be applied. Finally, it is important to mention that GLS will present results similar to those of OLS. 2SLS will do the same if the equation explains all the variability in the data around the mean (Gujarati and Porter, 2009; Girón, 2017).

The dependent variable will be the mortality rate caused by Covid-19 and the independent variable will be the TE index of the healthcare systems. In addition, control variables were used (see Table 5).

The mathematical models of the regression are presented as follows:

The models would be interpreted as the relationship between the number of deaths caused by COVID-19 and the technical efficiency of the healthcare systems of the sample countries. Control variables are used to ratify the results obtained.

The control variables used were selected based on what the WHO (2009 and 2017) defines as the Social Determinants of Health by referring to the set of social, political, economic, environmental and cultural factors that exert significant influence on the state of health, omitting those that allude to the health condition per se.

In the Appendix, tables A1 and A2 show the TE results of the healthcare systems of 40 and 68 countries, respectively, differentiated by per capita health expenditure, while table A3 shows the countries used as a sample. The first group includes Bangladesh, Djibouti, Samoa, Morocco, Honduras, the Solomon Islands and Vietnam, which maintain a TE of 100%, while Gabon and the Central African Republic are the least efficient.

In group 2, Singapore, Japan and Qatar are 100% efficient; the first two in the three scenarios considered. Meanwhile, Kuwait with 14%, South Africa with 25% and Namibia with 21% are the countries with the lowest resource use efficiency. The values depend on the inputs and methods used (CRS or VRS).

The results are presented in Table 6 and show an inverse relationship between TE and COVID-19 mortality, except for panel B, whose t-value indicates that the results are unreliable. In panel A, in all the proposed scenarios, the results have a significant t-value of less than 1%, and although the R2 barely reaches 22%, the relationship between the two variables is reliable. These results are supported and exhibit similar behavior in panel C, which uses the 108 observations; the inverse relationship between the variables is maintained. However, the value of the parameter of the independent variable changes: considering the absolute value, it goes from a minimum of 61.17838 to a maximum of 127.88 depending on the input used for the calculation of the TE and the model used: VRS or CRS.

These deductions were tested using control variables in two scenarios. The first used only three variables: Population Density, Out-of-Pocket Expenditures and GDP Growth. Meanwhile, the Malnutrition and Gini Indexes were added to the second (see Tables 7, 8 and 9). Countries with a per capita health expenditure of less than US$500 have been omitted as they exhibit unreliable results in the relationship between variables.

Table 7 shows the results of the model for the sample of countries with a per capita health expenditure of more than US$500 with the inclusion of the control variables. The dependent and independent variables maintain their inverse relationship, as well as for calculation using OLS, GLS and 2SLS. Panel A shows statistical confidence, although its R2 has been reduced to 15.54. Panel B maintains the inverse relationship between the dependent and independent variables, preserving its statistical significance, and its R2 increases to 29.84. It is important to note that the values of parameter β vary depending on the number of control variables included, with no differentiation between the regression models used.

This behavior is maintained when all observations are used and the TE is calculated with health spending as a percentage of GDP and health spending per capita, both with VRS. These values are observed in Tables 8 and 9. The results do not vary. The relationship between the slope and independent variables continues to be inverse and the values maintain their statistical significance in all the proposed scenarios. Finally, it is essential to note that the model's fit improves as the number of observations increases, ending with an R2 of 42.70.

The TE shows values with expected behavior. There is a more significant difference when the calculations are carried out using CRS or VRS models, although this difference is not greater. Likewise, when the input is changed, the results are not subject to significant alterations. In the sample of countries with a health expenditure of less than US$500, Bangladesh is the only one that maintains a TE of 100% in all the proposed scenarios. The same occurs with Singapore and Japan in the sample of countries with a health expenditure of more than US$500.

Meanwhile, in the regression analysis, the tests were performed for the three types of samples using OLS, GLS, and 2SLS, and the results are homogeneous and statistically significant. The independent variable Deaths due to Covid is inverse to the dependent variable TE. However, it is worth mentioning that, for countries with health expenditure below US$500, the deductions are not reliable.

The results finally translate into a 1% increase in the TE of the countries' healthcare systems taken as a sample, which would reduce deaths due to COVID-19 by between 61 and 127 per 100,000 inhabitants. These results are supported when all countries are sampled: the regressor of the independent variable maintains its inverse relationship and statistical significance, which indicates that the values and, above all, the deductions that can be obtained based on these results are statistically reliable.

The results also show the importance of maintaining high percentages of TE to meet the population's needs. Gómez et al. (2019) indicate that positive changes in the levels of TE will lead to productivity increases in the operational and financial factors of the national healthcare systems of 28 countries of the European Union.

Similarly, the IDB (2018) suggests that several Latin American countries could significantly improve health output indicators while maintaining their current budget stable. The analysis indicates that, if efficient, the region would lengthen its life expectancy by four years; under-five mortality could be reduced by 10 deaths per 1,000 live births; Disability Adjusted Life Years (DALY) lost due to all causes could be reduced on average by 6.1432 per 100,000 inhabitants; specialized care during childbirth could be improved by 4.4% and DTP² immunization rates could reach 96.9%.

Furthermore, the R2 is relatively low and the model cannot adjust to the dependent variable. However, although the model does not reliably explain the variability of the data, the causes of mortality are based on the specific health situations of each person, resulting in the logical value of the R2.

As for the control variables, when only three are used, Out-of-Pocket Expenditures show a direct relationship with deaths due to COVID-19 and their value is reliable. In this case, their behavior could be explained by the fact that a deficient health system causes higher Out-of-Pocket Expenditures. Finally, when five control variables are used, the Malnutrition Index maintains statistical significance, although with an inverse relationship to the dependent variable, which could be explained by health factors specific to each person and the relationship with COVID-19.

Given the lack of complete, updated and relevant data, the study has a major limitation given that there is no quality information available, especially in Latin American and African countries and, in some cases, even in first-world countries. This makes it challenging to work with a larger number of variables to compare results.

By its very essence, the DEA also presents the difficulty of contrasting hypotheses since it does not have statistical characteristics such as the presence of error, translating any deviation from the data into ineffective behavior of the DMU. However, it is a valid method used in scientific research.

As for the regression analysis, working with few observations results in an insignificant R2. The scarce knowledge and heterogeneous nature of the dependent variable means that the model cannot provide a reliable explanation. However, it must be understood that the explained variable will depend on medical factors, which have also failed to provide a conclusive explanation.

In terms of scope, the study does not perform a slacks analysis, so it does not know exactly which variables are a source of inefficiencies. Finally, mortality rates by age group have not been standardized in order to determine the level of response to this condition in each country and to be able to compare them.

The study established a relationship between deaths from COVID-19 and the TE of healthcare systems. The better the use of available resources, the more prepared countries will be to face situations such as those that occurred in the last two years. The study shows that a 1% increase in the TE of the healthcare systems of the countries analyzed would reduce deaths from COVID-19 by between 61 and 127 per 100,000 inhabitants.

It should also be noted that the diversity of the countries, the structure of the healthcare systems, the physical conditions of the people, the behavior and vertiginous mutation of the virus, as well as the structure and economic development of the States, played a dominant role in the effectiveness of the fight against the pandemic. The main challenge initially was to attenuate and contain the accelerated advance of the epidemic.

Extensive literature indicates that pandemics will continue. There is a high probability that humanity will again face other health emergencies, which are expected to be mostly catastrophic and devastating. Given this scenario, a new approach and orientation of public policies in the field of health economics is necessary, acting from a more proactive viewpoint, preparing and improving the response capacity of healthcare systems in order to face, with minimum impact, the consequences of these new epidemics.

It is important to provide policymakers with the technical tools to help them make decisions that can prevent and correct the consequences of situations such as the presence of COVID-19, especially in terms of the use and destination of capital. It is not only a matter of increasing or correctly allocating more resources to the health field -at least in the first instance-, but also of improving their destination and use.

Efficient spending is therefore essential, not only to guarantee people's right to free access and high levels of healthcare coverage but also to ensure that healthcare services and systems respond in an efficient and timely manner to the needs and requirements of the population, being resilient and managing to overcome adverse and highly vulnerable situations, such as the recent pandemic, with the least possible impact.

It is imperative to start thinking about a new way of taking action. The purpose is not to obtain more available resources but to obtain more of the resources available -especially because of their scarcity as opposed to unlimited needs- by being cautious, pragmatic and flexible in prioritizing spending and allocating resources.