Working paper
2023-01
Statistics and Econometrics ISSN 2387-0303
Measuring efficiency of Peruvian universities:
A stochastic frontier analysis
Juan Carlos Orosco Gavilán, Helena Veiga, Michael Peter Wiper
Serie disponible en http://hdl.handle.net/10016/12 Creative Commons Reconocimiento- NoComercial- SinObraDerivada 3.0 España (CC BY-NC-ND 3.0 ES)
Measuring efficiency of Peruvian universities: A stochastic frontier analysis
Juan C. Orosco Gavilána,∗, Helena Veigaa,b,c, Michael P. Wipera,b
aDepartment of Statistics, Universidad Carlos III de Madrid
bInstituto Flores de Lemus, Universidad Carlos III de Madrid
cBusiness Research Unit, ISCTE-Instituto Universitário de Lisboa
Abstract
In comparison with other regions such as Europe or the USA, there have been relatively few studies of efficiency in the higher education sector in South America. The main objective of this paper is to examine the teaching efficiency of Peruvian, public universities over the period 2011-2018, using stochastic frontier analysis. Our results suggest that efficiency depends on both the operating time of the university and on the scientific production. We also show that the majority of universities studied maintain their efficiency levels over time, whereas, most of the young universities started off as very inefficient, but have improved their efficiency over time.
Keywords: Higher education, Peru, Efficiency, Stochastic frontier analysis, Exogenous variables
1. Introduction
Measuring the efficiency of universities is increasingly required by public institutions, as policy makers often rely on these estimates to evaluate higher education (HE) institutions in order to allocate funding, see Gralka (2018a).
The two techniques commonly used to measure efficiency are Data Envelopment Analysis (DEA) and Stochastic Frontier Analysis (SFA). Both techniques estimate a frontier function that represents either the optimal output that can be produced with a given set of inputs or the minimum cost of producing a given amount of output.
DEA was developed by Charnes et al. (1978) and is a nonparametric approach to estimating a deterministic frontier based on (linear) programming techniques, see for exampleCooper et al.(2006) for a general introduction. Most studies of efficiency in the context of HE have applied DEA, see e.g. Liu et al. (2013) where it is pointed out that education is among the top five application areas of DEA. For early applications of DEA in the context of HE, see for example: Bessent et al. (1983);
Tomki and Green (1988); Sinuany-Stern et al. (1994); Arcelus and Coleman (1997); Johnes (2006);
Johnes and Yu (2008);Furková (2013), among others.
∗Corresponding author.
Email address: [email protected]. (Juan C. Orosco Gavilán)
On the other hand, SFA was originally proposed byAigner et al.(1977) andMeeusen and van den Broeck (1977) and uses a parametric frontier function that allows the introduction of a stochastic component into the frontier. Applications of SFA in the context of higher education include: Johnes (1998);Robst (2001);Izadi et al. (2002);Mensah and Werner (2003); Chapple et al.(2005); Stevens (2005); McMillan and Chan (2006); Castano and Cabanda (2007); Fu et al. (2008); Horne and Hu (2008);Johnes et al. (2008); Kempkes and Pohl (2008); Kuo and Ho (2008); Lenton (2008); Abbott and Doucouliagos (2009);Johnes and Johnes (2009), among others.
One advantage of SFA over DEA is that SFA models allow for the incorporation of inefficiency heterogeneity. In e.g.Gralka(2018a), it has been shown that inappropriate treatment of heterogeneity can bias estimates of inefficiency. This can be addressed by including unobserved factors via random effects, as in Tsionas (2002) or by including observed variables in the inefficiency component the so- called “determinants of efficiency.” These variables do not affect the frontier, and are often outside the control of institutions, but are assumed to affect the institution’s efficiency. Battese and Coelli(1995) proposed one of the most important specifications in which the mean of the inefficiency distributions is a linear function of the exogenous variables. Some applications in the HE sector where exogenous variables are used are: Robst (2001); Chapple et al. (2005); Stevens (2005); Castano and Cabanda (2007);Kuo and Ho(2008);Johnes et al.(2008);Kempkes and Pohl(2008);Abbott and Doucouliagos (2009);Kempkes and Pohl (2010);Sav (2012);Bolli et al.(2016);Sav (2016). Good, general reviews of SFA and efficiency in the HE sector can be found in Witte and López-Torres (2017), Kaur and Singh(2019),Ferro and D’Elia (2020) and Gralka (2018b).
Apart from a few exceptions, where the DEA approach is applied to studying research quality, see e.g. Nunez and Cornejo Mesa (2018) and Tello and Flores (2021), there have been few studies of efficiency in HE in Peru. This paper contributes to the literature by applying SFA to assess the teaching efficiency of Peruvian universities. We also incorporate inefficiency heterogeneity related to exogenous variables and explore how efficiency of different universities has changed over time.
The rest of this paper is organized as follows. In section 2, we provide a brief literature review of the HE sector with a focus on Latin America. Then in section 3, we provide an outline of the HE sector in Peru and in section4, we describe the data we use for this study. We then explain the SFA models applied in section 5. Section 6 shows the empirical results and finally, in section 7 we draw some conclusions and consider possible extensions.
2. Literature Review
Compared to Europe and the USA, there have been far fewer published applications of efficiency analysis in the HE sector in Latin America, see e.g.Gralka(2018b). Most existing studies on teaching efficiency in Latin America have applied DEA, and some of the few papers using SFA are commented below.
Miranda et al.(2012) use both DEA and SFA to measure the efficiency of business administration courses offered by private institutions that focus only on education and are located in the same geo- graphic region in Brazil. Zoghbi et al.(2013) examine education production efficiency by comparing first year and final year of Brazilian universities.
Gónzales et al.(2017) analyze the evolution of the level of technical efficiency of public universities in Colombia. The results of this study show that university training and research indices are positively determined by financial resources and, in particular, the number of teaching staff.
D’Elia and Ferro (2021) studied the technical efficiency of undergraduate teaching in national (public) universities in Argentina using SFA. Their analyses suggested the existence of observed and unobserved inefficiency heterogeneity and that not including inefficiency heterogeneity leads to underestimation of efficiency.
To date, there are very few published studies that deal with the efficiency of universities in Peru, and most of them are dedicated to the study of research efficiency. In particular, Nunez and Cornejo Mesa (2018) use DEA to conclude that a small number of universities are efficient in research, but that there are large differences in the efficiency of Peruvian universities. Furthermore, Tello and Flores(2021) use DEA to classify public universities into four categories according to their strategic focus on educational research, and find that technical efficiency is not related to the age of the university or its quality.
3. HE in Peru
Peru has a long history of university education and, in particular, the first university in the Western hemisphere was established as shortly after the Spanish conquest of Peru in 1551. This university continues in operation today as the National University of San Marcos.
Peru has both public and private universities, and the number of universities has increased rapidly in recent years. In particular, the total number of universities increased from only 36 in 1980, to 74 in 2008 and 139 in 2018. This increase has been reflected most in private universities, with the number of public universities growing more slowly. In 2000, there were 32 public institutions and 42 private institutions, whereas in 2019, these numbers had increased to 48 and 91 respectively. University entrance also increased rapidly from 775,000 to 1.6 million between 2008 and 2019. See, SUNEDU (2019).
There has been evidence that this increase in supply has been accompanied by a fall in education quality, see e.g. Castro and Yamada (2013). This lead to the introduction of a new university law in 2014 and a new overseer of the sector called the Superintendencia Nacional de Educación Superior Universitaria or SUNEDU, which is responsible for quality assurance in the HE sector. One consequence of the new law was that a a small number of public but more, mainly private universities were forced to close shortly afterwards. However, it is not clear that these steps have improved the
university system, as, for example, the 2021 Times Higher Education ranking of Latin American universities includes only a single Peruvian university, (the Pontifical Catholic University of Peru) amongst the top 50 in Latin America.
Peru is divided into three major regions: coast, mountain and jungle, as indicated in the left hand side map of Figure 1. Until recently, the jungle region, where many of the non Spanish speaking population reside, has suffered from a relative lack of opportunities for university education and it has been suggested that educational success is lower in this area, see e.g. Gaentzsch and Zapata-Román (2020). There are many more universities in the coastal region, particularly near the capital, Lima.
However, a number of new universities have been constructed in the jungle region in an effort to improve the opportunities for HE in this area.
The right hand side of Figure 1 shows the average income of each department (a territorial unit smaller than the region and bounded with black lines) in Peru over the period of our study. The wealthier departments in the country are mainly located in the coastal region, and, in particular, the most wealthy zone is that centred around the capital, Lima, where many of the most important universities are located.
Figure 1: Maps of Peru showing the regions (left hand side) and the average wealth distribution in the different departaments (right hand side).
For a much fuller review of the education system in Peru, see Monroy and Mackie (2022)
4. Data
The database used in this research corresponds to panel data from 2011 to 2018 from a sample of 35 public universities in Peru. Most of the universities have been functioning for a long time,
although seven centres have been founded since 2000, most of these in the jungle region. A complete list of the universities included in our study is provided in Table 1.
Table 1: Peruvian Public Universities
University Acronym University Foundation Year Region
1 Univ. Nac. Mayor de San Marcos UNMSM 1551 coast
2 Univ. Nac. San Cristóbal de Huamanga UNSCH 1959 mountain
3 Univ. Nac. de San Antonio Abad del Cusco UNSAAC 1692 mountain
4 Univ. Nac. de Trujillo UNT 1824 coast
5 Univ. Nac. de San Agustín UNAS 1828 mountain
6 Univ. Nac. de Ingeniería UNI 1955 coast
7 Univ. Nac. Agraria La Molina UNALM 1960 coast
8 Univ. Nac. San Luis Gonzaga UNICA 1955 coast
9 Univ. Nac. del Centro del Perú UNCP 1962 mountain
10 Univ. Nac. de la Amazonía Peruana UNAP 1961 jungle
11 Univ. Nac. del Altiplano UNA 1961 mountain
12 Univ. Nac. de Piura UNP 1961 coast
13 Univ. Nac. de Cajamarca UNC 1962 mountain
14 Univ. Nac. Federico Villarreal UNFV 1963 coast
15 Univ. Nac. Agraria de la Selva UNAS 1964 jungle
16 Univ. Nac. Hermilio Valdizán UNHEVAL 1964 mountain
17 Univ. Nac. de Educación Enrique Guzmán y Valle UNE 1965 coast
18 Univ. Nac. Daniel Alcides Carrión UNDAC 1965 mountain
19 Univ. Nac. del Callao UNAC 1966 coast
20 Univ. Nac. José Faustino Sánchez Carrión UNJFSC 1968 coast
21 Univ. Nac. Pedro Ruíz Gallo UNPRG 1970 coast
22 Univ. Nac. Jorge Basadre Grohmann UNJBG 1971 coast
23 Univ. Nac. Santiago Antúnez de Mayolo UNASAM 1977 mountain
24 Univ. Nac. de San Martín UNSM 1979 jungle
25 Univ. Nac. de Ucayali UNU 1979 jungle
26 Univ. Nac. de Tumbes UNT 1984 coast
27 Univ. Nac. del Santa UNS 1984 coast
28 Univ. Nac. de Huancavelica UNH 1990 mountain
29 Univ. Nac. Amazónica de Madre de Dios UNAMAD 2000 jungle
30 Univ. Nac. Toribio Rodríguez de Mendoza de Amazonas UNTRM 2000 jungle
31 Univ. Nac. Micaela Bastidas de Apurímac UNAMBA 2000 mountain
32 Univ. Nac. Intercultural de la Amazonía UNIA 2000 jungle
33 Univ. Nac. Tecnológica de Lima Sur UNTELS 2001 coast
34 Univ. Nac. José María Arguedas UNAJMA 2004 mountain
35 Univ. Nac. de Moquegua UNAM 2005 mountain
Outputs in research on efficiency in the HE sector are classified by Ferro and D’Elia (2020) as research related, teaching related and extension or transfer related. Here, we use the number of successfully graduated students (graduates) as a proxy measure of teaching quality. This measure has been used in a number of previous studies, see e.g. Ferro and D’Elia (2020).
As inputs, we use the number of students enrolled (enrolled ); the number of lecturers officially hired by the university (lecturers); the ratio of the annual budget, in soles (the Peruvian currency) allocated to each university by the government to the number of students in the university (budget ), and the proportion of the total annual budget which is actually spent (expenditure), total assets (assets) and liabilities (liabilities) and the GDP per resident (GDP ) of the department in which
each university is situated (GDP ). Note that there are a number of studies indicating that poverty is strongly related to university dropout, see e.g. Tinto (1993) and Breier (2010). This variable has also been employed as a frontier variable in e.g. Bertoletti and Johnes (2021).
As possible exogenous variables, we consider the region, classified as coast, mountain or jungle, in which the university is sited (region), the age or operating time (oerating) of the university, classified into two categories: old for universities which have been operating for at least 25 years and new for universities which have been founded in the last 25 years, and the relative scientific production (scient. prod.), that is the number of articles produced by a university each year, divided by the number of permanent academic staff. It is important to note that, there have been a number of different studies examining the relationship between teaching efficiency and research quality with very diverse conclusions, see e.g.Marsh and Hattie (2002).
All data come from sources of Peruvian government institutions, such as the Ministry of Economy and Finance (MEF), which is responsible for planning, directing, and controlling matters related to the budget, treasury, debt, accounting, fiscal policy, public investment, and economic and social policy throughout Peru; the National Superintendency of Higher Education (SUNEDU); and the National Institute of Statistics and Informatics (INEI).
5. Stochastic frontier analysis
Koopmans(1951) says that a company is production efficient if it produces the maximum output given the available resources. The frontier function I(t, x, β) represents the maximum output that a firm with inputs x can produce at time t. The real output, Eit, of firm i, with inputs xit at time t satisfies Eit ≤ I(t, xit, β) and the output efficiency is defined as:
T Eit = Eit
I(t, xit, β), (1)
which reaches the maximum value of 1 when a firm is 100% efficient.
Under the SFA approach, it is assumed that the frontier function is stochastic, by introducing a multiplicative error term, so that, taking logarithms:
log I(t, xit, β) = f (t, xit, β) + vit
where f (·) is a particular functional form and the idiosyncratic error term, vit is typically assumed to be normally distributed: vit∼ N (0, σ2v).
Taking logarithms in (1), then gives:
yit = f (t, xit, β) + εit
where yit = log Eitand the composite error term, εit, satisfies εit= vit−uit, where uit = − log T Eit ≥ 0 is the inefficiency.
The most typical parametric functional form f (·) is the Cobb Douglas:
f (t, xit, β) = β0+
k
X
j=1
βjxijt
where xit = (xi1t, ..., xikt)0 and β = (β0, β1, ..., βk)0. Other forms such as trans-log have been reviewed in e.g. Battese and Brock (1997).
A number of different distributional assumptions have been proposed for the inefficiency term, uit. For examples, Aigner et al. (1977) assumes a half-normal distribution, Meeusen and van den Broeck(1977) propose an exponential distribution, Battese and Coelli(1988) use a truncated normal distribution.
One simplification of this model is to assume that a firm’s inefficiency does not change over time so that uit= ui for all t. One such model, which we shall refer to as M0, was introduced inPitt and Lee(1981). Under this model, it is assumed that ui follows a half normal distribution. An alternative model was proposed by Schmidt and Sickles(1984).
In most applicatons, it is sensible to assume that inefficiency can change over time. For example, in the HE sector it may be that new universities start off as inefficient but grow more efficient over time as they learn to optimize procedures, whereas well established centres may become inefficient after a long time as they stick with older systems and are slower to introduce new technology.
Battese and Coelli (1992) assumed that:
uit = g(t)ui with g(t) = exp (−η(t − Ti))
where positive (negative) η means that the units gain (lose) efficiency over time. In the following, models of this type will be referred to as M1.
None of these models account for inefficiency heterogeneity and a major concern in the HE context is the structural differences that exist between different centres. Institutions have different locations, research areas and scopes, and governance structures, leading to a high degree of heterogeneity.
Heterogeneity can be captured either by an unobserved random variable, as in e.g. Galán et al.
(2014), or by including exogenous variables in the inefficient component, as in e.g.Battese and Coelli (1995). In this case, uit follows a truncated normal distribution, where either the location parameter or the scale parameter (or both) are affected by the exogenous variables.
Here, it is assumed that if exogenous variables zit are available, then:
uit ∼ N+(µit, σit2) where, either µit= γ0+Pp
j=1γjzijtor log σit2 = δ0+Pp
j=1δjzijt, or some combination of both. Models of this type will be referred to as M2 in the following.
Finally, as we are comparing multiple models in this study, it is important to consider model selection. In order to do this, we use the Akaike information criterion (AIC). The AIC for a given
model is defined as
AIC = 2k − log ˆL
where k is the number of parameters in the model and ˆL is the maximum value of the likelihood function under this model. Lower values of this criterion indicate preferred models, see e.g. Burnham and Anderson(2004).
6. Empirical results
Under all models considered, we assume that the output is the logarithm of the number of graduates each year and that those input variables related to size or wealth of the a university or region (enrolled, lecturers, assets, liabilities, GDP) are also logged whereas ratio variables (budget, expenditure) are not. All models were fitted using Stata,StataCorp (2021).
We first ran models M0 and M1 for all possible combinations of variables in the Cobb-Douglas format, supposing time invariant efficiency and model M1 assuming time varying inefficiency without heterogeneity. The optimum model under M1 was strongly preferred to the optimal model under M0 by AIC which suggests that it is important to assume a time varying efficiency structure.
The optimal model M1 was:
yit = β0+ β1log enrolled + β2log lecturer + β3budget + β4log GDP + vit− uit. The estimated parameters under this model are shown in Table 2.
Table 2: Estimated parameters for the optimal M1
log(graduates) Coef. Std. Err. z p L 95% U 95%
Frontier log enrolled 0.699 0.092 7.620 0.000 0.519 0.879 log lecturer 0.421 0.084 5.020 0.000 0.257 0.585 budget 0.014 0.003 4.320 0.000 0.008 0.021 log GDP 0.051 0.029 1.760 0.078 -0.006 0.108 constant -2.652 0.591 -4.480 0.000 -3.811 -1.492
σu 7.673 6.074 1.260 0.207 1.626 36.21
σv 0.316 0.024 13.350 0.000 0.272 0.365
λ 24.32 6.074 4.000 0.000 12.41 36.22
AIC 340.9
From Table 2 and with respect to the stochastic frontier, all variables are statistically significant (at a level of 5%) except for the logarithm of GDP per person in each department, which is significant at 10%. The coefficients of all inputs are positive which should be expected. Larger univerisities
typically have more enrolled students, more teaching staff and higher budgets, which should lead to more graduates. Also, there is evidence in the literature that dropout rates are often higher amongst poorer students, see e.g. Breier (2010) so it should also be expected that universities in zones with higher GDP should have more graduates than universities located in poorer regions.
It is also interesting to see if there is any evidence that efficiency is related to any of the exogenous variables. Therefore,Figure 2shows scatter plots of the estimated average efficiency of each university under the optimal model M1 and these variables.
Figure 2: M1 efficiency versus exogenous variables
From Figure 2, we can observe that the lower the relative scientific production, the higher the variability of college efficiency. The variability of efficiency is also higher for new universities, which is to be expected since they still have room to improve all their services. It is less clear if there is a relationship between the region in which the university is located and the efficiency.
As there is some apparent evidence of an effect of the exogenous variables on the variability of the efficiencies, we fitted model M2, including these variables in the scale parameter. Model selection was carried out to see which variables should be included, and under the optimal model, only the relative research production and the age of the university were retained. Table 3 shows the results of the optimal model.
According to AIC, the optimal model M2 fits the data better than model M1. This suggests that it is important to include inefficiency heterogeneity. The frontier parameter estimates are quite similar to those under the optimal M1 model. All variables have the expected sign and are statistically significant at a 5% significance level.
Table 3: M2 estimation results
log(graduates) Coef. Std. Err. z p L 95% U 95%
Frontier log(enrolled) 0.585 0.082 7.170 0.000 0.425 0.744 log(lecturer) 0.426 0.076 5.620 0.000 0.277 0.574 budget 0.012 0.003 3.860 0.000 0.006 0.017 log(GDP) 0.066 0.028 2.390 0.017 0.012 0.120 constant -1.987 0.545 -3.650 0.000 -3.054 -0.919 umean constant -153.4 244.4 -0.630 0.530 -632.4 325.6
usigma scient. prod 26.36 7.278 3.620 0.000 12.09 40.62
operating 1.761 0.333 5.290 0.000 1.109 2.414 constant 2.179 2.163 1.010 0.314 -2.060 6.418
vsigma constant -2.274 0.139 -16.30 0.000 -2.548 -2.001
E(σu) 4.378 4.107 4.649
σv 0.321 0.022 14.34 0.000 0.280 0.368
AIC 278.2
umean corresponds to the mean of the truncated normal distribution in terms of a linear function of the exogenous variables, usigmacorresponds to the variance of the inefficient component expressed as a function of exogenous variables, vsigmacorresponds to the variance of the idiosyncratic error component expressed as a function of exogenous variables.
We also find that both the relative scientific production and the age of the university have a positive effect on the scale parameter of the distribution of this component, whereas the region in which the university is located is not included in the optimal model.
In the case of the relation between scientific production and teaching quality, different studies have produced opposing conclusions, see e.g. Marsh and Hattie(2002) for a good review. Our results add to this literature by suggesting that, in the Peruvian case, the variation of efficiency is somewhat higher in universities where more research is undertaken.
Our results also suggest higher variability in efficiency in the case of younger universities.
Although the region was not a significant variable, one reason for this may be that most of the younger universities are situated in the jungle or mountain regions of Peru, whereas the older universities are mainly in the coastal region. Therefore it is possible that regional effects are being masked by the age effects.
It is also interesting to compare the estimated mean efficiencies for each university under models M1 and M2. Figure 3 illustrates is a scatterplot of the efficiencies for each university each year estimated under both models. Although the efficiencies are similar, it can be observed that including the exogenous variables leads to slightly higher mean efficiency estimates for the majority of univer-
sities. This result is in line with the findings of D’Elia and Ferro (2021) in the case of Argentinian universities.
Figure 3: M1 and M2 efficiency comparison
Figure 4 graphs the effiencies every year for all universities under M2. Most universities show appear to show similar efficiencies in most years. However, the newer universities (at the right hand side of each graphic) illustrate increasing efficiencies over time.
Figure 4: M2 efficiency estimates
Figure 5 shows this more clearly by fitting regression models to the estimated efficiencies of each
university against time under both models M1 and M2. For most universities, it can be observed that efficiency varies slightly over time. The exceptions are UNIA, UNAMAD and UNTRM which start being very inefficient, but improve their performance over the years. These universities are characterized by being located in the jungle region and having been in existence for less than 25 years. There are also universities that have fairly high efficiency in the early years, but their efficiency declines over time. Often, these are universities that have a high reputation in Peru and have existed for more than 25 years, namely UNI and UNALM.
Although it is not explicitly illustrated in Figure 5, it is clear to see that there is no obvious difference in the estimated university efficiencies under model M2 (or M1) after the new university law of 2014. This may be due to the fact that this study is comprised only of public universities, whereas private institutions, with less control were much more affected by this law, seeMonroy and Mackie (2022).
Finally, it should be noted that for most universities there is a difference between the efficiency obtained with M1 and M2: M2 usually provides efficiency estimates that are higher than those of the M1 model.This result backs up the evidence of D’Elia and Ferro (2021) from Argentina, where it was also found that including inefficiency hetereogeneity leads to higher efficiency estimates.
Figure 5: M2 versus M1 estimates of efficiencies overtime
7. Conclusion and extensions
In this study, we have investigated the teaching efficiency of Peruvian universities.
Firstly, we have shown that teaching efficiency is varying over time. In particular, our results indicate that, although the majority of universities illustrate relatively constant, high levels of effi- ciency, many of the newer universities, mainly in the jungle region are relatively inefficient initially but show increasing efficiency, approaching that of the traditional universities, over time.
Secondly, our results also suggest that teaching efficiency is dependent on research. In particular, we find that the dispersion of teaching efficiency varies with respect to the amount of research produced. Previous studies have suggested that average teaching efficiency may be higher, lower or the same, depending on research quality: see e.g. Marsh and Hattie (2002). Our study unifies these results by suggesting that it is mainly the efficiency dispersion rather than the average efficiency which depends on research quality.
Thirdly, we have shown that it is important to include exogenous variables in efficiency estimation.
Efficiency is generally underestimated when these variables are not taken into account.
The rest of our results are similar to other studies: larger, richer universities graduate more students.
As an extension, it would be interesting to compare the efficiencies of both public and private universities. Given that the evidence of our results suggests that newer, public universities are more inefficient initally, we might speculate that this result also holds true for private universities, and this may be one of the causes of the closure of these centres after the introduction of the new laws in 2014.
Acknowledgements
Helena Veiga acknowledges financial support from the Agencia Estatal de Investigación, research projects PID2019-108079GB-C21/AIE/10.13039/501100011033 and PID2021-122919NB-I00, and from Fundação para a Ciência e a Tecnologia, grant UIDB/00315/2020. Michael Wiper acknowledges finan- cial support from the Spanish government through project PID2019-108311GB-I00/AEI/10.13039/
501100011033.
Disclosure statement
No potential conflicts of interest were reported by the authors.
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