‘Cyclic syndrome’ of arrears and efficiency of Indian judiciary

Abstract

One of the four pillars of democracy in India is the judiciary, which in the recent past has experienced the ‘cyclic syndrome’ of arrears. There are 3.5 crore cases pending in the Indian judicial system that has a bearing on contract enforcement. A burgeoning stream of literature has reported the role of the judiciary in economic growth and development. In the wake of a given potential economic multiplier of the judicial system, examining the factors affecting the performance of the judiciary should merit attention. The present study juxtaposes jurisprudence and production theory, not frequently examined in the same gust by employing Data Envelopment Analysis (DEA), Malmquist Productivity Index (MPI), Stochastic Frontier Analysis (SFA), and regression for High Courts and Subordinate Courts. Employing the dataset for the years 2014–19, we investigate the technical efficiency and productivity of the High Courts and their Subordinate Courts and examine the factors influencing the dissolved cases. Furthermore, we examine the impact of COVID-19 on the cases instituted and cases disposed of. To sum up, the paper, thus, touches upon two basic dimensions of justice for High Courts and Subordinate Courts in India: Timeliness in the disposal of cases and the proportionate use of the state’s resources. The study confirms the role of judges, judicial staff, and demand for justice on the supply of justice. Shreds of evidence point toward the need to introduce a “cocktail-based” approach instead of a “one-size-fits-all”.

Supplementary Information

The online version contains supplementary material available at 10.1007/s43546-022-00377-1.

Introduction

“Inclusive economic institutions require secure property rights and economic opportunities not just for the elite but for a broad cross-section of society” (Acemoglu and Robinson 20121).

A technically efficient judiciary subtly not just emboldens the faith of people in the justice delivery system but empirical studies have also confirmed its growth effects (Feld and Voigt 2006; Dam 2006; Chemin 2009). An efficient adjudication contributes to ease of doing business and with timely resolution of disputes, property rights are also safeguarded. The efficiency analysis of the judiciary is based on the utility-maximizing, rational behavior of judges (Posner 1993; Cooter 1983; Beenstock 2004). Where the judiciary maintains fiscal balance, the underperformance of the same jeopardizes the ease of doing business and shakes the confidence of citizens. Studies have also confirmed the labor-intensiveness of the judiciary, which often suffers from the bottlenecks caused by the number of judges (Beenstock and Haitovsky 2004). Ceteris paribus, judges have the tendency to improve the outcomes of courts (reduction in backlogs and dispute resolution rate); however, the physical and procedural constraints slow the work of judges (Djankov et al. 2003).

Understanding the need for an impartial and efficient judiciary in fostering public trust and economic growth we build on the theoretical and preliminary findings to consider the case of the Indian judiciary. Indian judicial system is in the throes of a crisis and is currently experiencing a cyclic syndrome of delay2 of arrears and pendency (Ghosh 2018) as is evident from 3.53 crore cases pending among different levels of Courts in India (PIB 2019; Economic Survey of India 2019). Under Article 21 of the Indian constitution, a speedy trial is a fundamental constitutional right.3 Reviewing the arrears in the Indian Judiciary and the number of working days, the 230th Law Commission Report (2009) and Justice Malimath Committee (2000) recommended cutting down the holidays. Based on the data collected from the official website of the High Courts for the year 2020 (excluding the number of personal leaves taken by the judges), we found that on average the working days are 234 (Refer to Appendix Table 2 on Working days and vacancy for the year 2020). As per the EODB (Ease of Doing Business) report, in 2020 though India’s overall ranking improved to 63, in contract enforcement, it stands at 163rd position and 154th in property registration. Additionally, India ranks 98 in Civil Justice and 78 in Criminal Justice out of 128 countries (World Justice Project 2020).4 Circumstances have brought us to a long overdue moment of reckoning to deepen our understanding of the Indian judicial system and determine where the greatest opportunities for change lie. In Fig. 1, we present a schematic chart explaining the structure of the Indian Judiciary with the Supreme Court as the apex court followed by High Courts and their respective subordinate Courts.

Fig. 1.

Structure of the Indian Judiciary.

Source: Author’s calculation

India follows a Common law system where laws are not codified in contrast with Civil law jurisdictions. To identify obsolete laws and examine the repealing of 1382 acts recommended in the year 1988, the Prime Minister Office formed Ramanujan Committee in 2014 which further recommended repealing 1741 such old statutes.5 Reminiscent of what Tacitus wrote in his book, “Corruptissima re publica plurimae leges” (greater the number of laws, the rampant is corruption), India is over-legislated and under-governed. The Law Commission of India in its 248th report recommended repealing 72 enactments. It is worth mentioning here that the Commission has in total recommended the repeal of 288 archaic laws to date through four of its interim Reports. In Appendix Table 1 we report some of the archaic laws still functional in India and their status across the world.

To assess the performance of the judiciary, the India justice report, 2019 has employed an indicator methodology to rank the courts in India which is subject to criticism on the grounds of methodology because the rankings were constructed by quantifying indicators and then aggregating them by a weighted average method. It confuses and deludes policymakers (Akande et al. 2019). Nonetheless, the empirical evidence sheds no light on the kind of reform that should be adopted to bridge the inefficiency gap in the judicial system. Little research has been done in the Indian context that incorporates production theory to assess the performance of courts in India other than Gupta and Bolia (2020). Any kind of assessment should take into consideration multiple inputs and outputs. Thus, methods which come to our rescue are Data Envelopment Analysis (DEA), Stochastic Frontier Analysis (SFA), and Malmquist index. These three methods have been widely used to assess the performance of public administration. However, the application of the Malmquist index in the present context is limited to an analysis of Italian tax judiciary by Kittelesen and Forsund (1992) and Falavigna et al. (2018). The present study, thus, juxtaposes jurisprudence and production theory, not frequently examined in the same gust by utilizing DEA, SFA and MPI for High Courts and Subordinate Courts. The purpose is, with the assistance of economics, to throw new light on basic issues construing the efficiency of the Indian judicial system (Fig. 1).

There are some noticeable characteristics that discern the present study from the literature construing courts. A study done by Gupta and Bolia (2020) in the case of the Indian judiciary using Data Envelopment Analysis (DEA) noted that there is a gap in terms of analyzing the performance of different levels of the Indian judiciary. Their study is the first to use DEA to rank the performance of 24 High Courts for the years 2015–18. Our study has distinctive features over the earlier studies such as the usage of DEA, SFA, and MPI over the period of 2014–19 in the case of High Courts and their Subordinate Courts. Where Gupta and Bolia (2020) considered judges, staff, instituted cases, caseload, and cases disposed of as inputs and outputs of High courts our study in addition to these variables also incorporates the budget allocated to examine the technical efficiency of High Courts and Subordinate Courts. Moreover, this study delves into developing a different framework to compare the courts—both High Courts and Subordinate Courts in India which are here viewed as production units. Moreover, to contextualize our study, we have attempted to examine how the courts have performed in COVID-19.

Taking a cue from the literature, we endeavor to address the following questions—how technically efficient are the High Courts and their Subordinate Courts of India? Has the productivity of the courts gone up in the last 5 years? What factors influence the dissolved cases in High Courts and Subordinate Courts? How has COVID-19 impacted the caseload and cases disposed of? To sum up, the paper, thus, touches upon two basic dimensions of justice for High Courts and Subordinate Courts in India: Timeliness in the disposal of cases and the proportionate use of the state’s resources.

Literature review

There is a substantial body of literature construing the efficiency of institutions. To gain deeper insights into the working of courts and improve their performance, scores of articles have used the concept of the ‘Judicial Production function’ (Voigt 2016). The clear rationale behind the present study is to explain how the efficiency of courts is impacted. Pursuing the set of explorations indicated earlier, we strive to construct the literature in three aspects—theoretical background, empirical studies, and research gap. Below, we review relevant studies and point out the gap in the literature.

Theoretical background

Noting the influence and the supporting role of law on the exchange, Stigler (1992) underscored two fundamentally different roles of economics in law. First, in offering expertise requested by lawyers and second, in the study of legal institutions and doctrine. Economic analysis provides an arduous framework for assessing the trade-offs policymakers face when restructuring legal institutions (Shavell 1999). Therefore, attention needs to be paid to the judiciary and its operation to expose its role in making the institutional ecosystem effective (Marciano et al. 2019). Posner (1985) considered the invocation of fairness and justice and due process of judicial decision-making as proxies for wealth maximization. However, a large part of economic theory assumes efficient courts that administer contracts both perfectly, fair, and freely (Chemin 2009; Botero et al. 2003). Judiciary like any other organization of society is an institution which sets the “rules of the game” and in turn impacts the process of economic development (North 2008). It might be tempting to preclude the poor performance of the criminal and civil justice system from any direct consequence on economic development; however, studies have shown that the trust of society is a form of informal institution that act as social capital, in addition to physical and human capital (Wang et al. 2019). It is this trust of society in rule of law that has the potential in reducing the cost of information collection (Zaheer et al. 1998) and is further deemed as a channel impacting economic growth. Drawing a distinction between developing and developed countries, Wang et al. (2019) reported that in a developing country where rule of law (considered as a proxy for the formal institution) is weaker, social trust (informal institutions) plays a significant role. Their evidence supported the new institutional economics theory of the prevalence of informal social norms when the formal legal rules fail new institutional economics (Williamson 2000). Judicial inefficiency severely impacts poor societies by impeding productive exchanges between private individuals (Botero et al. 2003). The Economic Survey of India (2018–19) in its chapter titled “Ending Matsyanyaya: How To Ramp Up Capacity In The Lower Judiciary” underscored that a culture of rule of law cannot be understated and should be pervasive as governance cannot be improved in isolation. Where the judiciary maintains fiscal balance, the underperformance of the same jeopardizes the ease of doing business and shakes the confidence of citizens. Marciano et al. (2019) reported that efficient rules will not operate effectively if not properly enforced. This ‘chicken or the egg dilemma’ as claimed by Posner (1988) states that without an established “justice” people might not have the means to afford a fast judiciary and without timely decisions, no judiciary can afford to deliver fair justice. A fast judiciary acts as a fundamental deterrent against economic agents’ willingness to deviate from previously signed contracts (Melcarne et al. 2021). Acemoglu and Robinson (2012) have discussed that the well-performing judiciary could also turn into an “extractive” institution following systematic violations of the rule of law. Building on this ambiguity Melcarne et al. (2021) investigated the renowned legal maxim “justice delayed is justice denied” empirically and suggested that countries that have fast judiciaries enjoy high levels of quality of justice (World Bank’s judicial quality index and the rule of law).

Deyneli (2012) conveys that there is a dearth of studies in both legal and economic literature, that model and analyze the efficiency of courts, judges, and other judicial staff and noted that generally the literature has been limited to the demand side of justice service (Rosales-Lopez 2008). The supply side of justice service is dependent on the budget allocated for courts, the number of courts, judicial staff, working hours and technology, administration of the courts, management techniques, the system of legal education, the methods for licensing lawyers and selecting judges, education of the public about the legal system, the means of access to justice, the availability of alternative dispute resolution (ADR), judicial independence, and procedural reforms (Buscaglia and Ulen 1997). Drawing a caution on the expansion of courts beyond a point Posner (1988) stated that, unlike the way the economic system can add factories, courts cannot be added to meet the rising demand for justice, otherwise, it becomes difficult to synchronize the judgements of a large number of courts. Posner6 further argued that the crisis of overload in courts could be addressed with a simple but powerful tools of economic analysis like legislative reform and expansive interpretation of the nature and functioning of federal courts (Shapiro 1987).

Staats et al. (2005) have provided five levels to measure the performance of the judiciary- independence, efficiency, accessibility, accountability and effectiveness. These parameters are key to the functioning of the judiciary and, thus, to the economic performance of any country. Both Efficiency and effectiveness which are used to gauge the performance of the judiciary are indistinctively used synonymously however, there is an underlying difference between the two. Efficiency or technical efficiency as defined by Marciano et al. (2019) draws a parallel with the concept of production theory of judicial activity implying the optimal utilization of resources/inputs to attain the output and places focus on the dispute resolution technology whereas, effectiveness (efficacy) measures the ability of the judiciary to deliver the demand of justice and inspects the equilibrium in the “justice market”. The effectiveness of an institution if considered as “humanly devised constraints” is directly impacted by de facto institutions that implement these rules (Marciano et al. 2019; Bubb 2013; Safavian and Sharma 2007; Williamson 2009; Williamson and Kerekes, 2011; Hodgson 2006; Voigt and Gutmann 2013).

Empirical studies

Espinosa et al. (2017) in their study reported that the Demand for litigation is affected by both, the distance and burden that the courts take on and the average productivity of courts falls with the transfer of judges. To deduce further, the courts are demand driven (Beldowski et al. 2020). Falavigna and Ippoliti (2020) investigated how judicial delays produce social costs which tend to affect the demand for justice. Talking about the role of judges literature is still ambiguous about the role of judges in improving court outcomes (reduction of backlogs and dispute resolution rate) where Falavigna et al. (2018) employing DEA confirmed the clear role of judges whereas, another study by Beenstock and Haitovsky (2004) and Dimitrova-Grajzl et al. (2012) by employing regression analysis proved how reveals that the disposition of cases does not depend on the number of judges. In line with the studies assessing the role of judges on judiciary Dayneli (2012) adopted a two-stage DEA to prove that there exists a positive and significant relationship between the salary of judges and efficiency scores. Schneider (2005) revealed using two-stage DEA that the qualification of judges and their career incentives impact the efficiency and the confirmation rate of courts. Additionally, employing SFA, Antonucci et al. (2014) showed that the efficiency of courts in Italy depends upon the vacancies and per capita expenditure. Moreover, considering the legislative reforms, a study in the context of Sweden by Agrell et al. (2020) provided evidence of how merging the district courts, on average, made the whole sector more efficient. The impact of judiciary on the firm in Indian context was probed by Chakraborty (2016) which reported how the judicial quality is a significant factor in determining firm’s performance (especially for contract-intensive) both international and domestic.

From the methodological point of view, there have been various methods adopted to analyze the performance of courts like DEA and SFA. Metafrontier approach, Conditional DiD model, DEA (Output-Oriented with the assumption of VRS) with Bootstrap, Regression and Malmquist Productivity Index (MPI), FGLS (Feasible Generalized least square) among others (Beldowski, Dabros, and Wokciechowski 2020; Agrell, Mattson, and Mansson 2020; Espinosa et al., 2017; Falavigna et al. 2018; Antonucci et al. (2014); Deyneli 2012; Yeung and Azavedo 2011; Schneider 2005; Lewin et al. 1982). DEA is a linear programming and non-parametric approach to measuring the technical efficiency of firms. Technical efficiency is expressed as a ratio of actual to potential output and based on the technical efficiency scores one can compare and rank the firms in a sample. The studies comparing the courts by using DEA have either relied on output-oriented DEA with Variable Returns to Scale assumption (Falavigna et al. 2018; Schneider 2005) or DEA with Constant Returns to Scale assumption (Falavigna et al. 2018; Yeung and Azavedo 2011). The application of DEA with CRS assumption is not just a strong assumption but is also restrictive in nature in contrast with VRS. Additionally, there is a strand of literature that have performed two-stage DEA to examine the factors influencing the technical efficiency of Courts (Deyneli 2012). It is also worth mentioning here, that there is a burgeoning stream of literature that have ascertained not just the technical efficiency but also the productivity of courts like Kittelsen and Forsund (1992). Productivity is a descriptive measure expressed as a ratio of output to input, technical efficiency is a normative concept explaining the optimal conversion of inputs into output. Thus, a technically efficient decision-making unit (DMU) can still increase its productivity by making use of its scale economies (Coelli et al. 2005). Considering the deterministic nature of DEA there are studies that have adopted Bootstrap-DEA to obtain robust results like Falavigna et al. (2018) and SFA to overcome the limitation of DEA for being incapable to test hypothesis like the studies by Beldowski et al. (2020) and Antonucci et al. (2014).

Apart from the methodology adopted to compare the performance of courts the selection of variables also deserves attention. The studies that have concentrated on the production function approach have broadly included Office areas, law clerk, other staff, Number of Judges, Demand for justice (pending and instituted cases) and in some cases expenditure allocated on judiciary as inputs; whereas, the choice of output in cases of courts has remained more of less the same i.e., cases resolved by courts in a year. From the literature reviewed so far, the category of courts that have been examined is Labor courts (Espinosa et al. 2017), Tax courts (Falavigna et al. 2015), magistrate courts, and district courts (Agrell et al. 2020; Beenstock and Haitovsky 2004). The studies examining the performance of based on technical efficiency of courts have been limited to developed countries like Poland (Beldowski, Dabros and Wokciechowski 2020), Sweden (Agrell, Mattson and Mansson 2020), France (Espinosa et al. 2017), Italy (Castro & Guccio, 2018; Falavigna et al. 2015; Antonucci et al. 2014), Brazil, Norway, Israel, Germany among others.

Research gap

Based on the literature reviewed so far, we found that though studies have been conducted with respect to advanced nations, to the best of our knowledge there is a dearth of studies in the context of developing economies (Ash et al. 2021). Additionally, DEA has been adopted by most of the studies to ascertain the technical efficiency but, its deterministic nature has been criticized and thus lately, the studies have corroborated the empirical findings with a stochastic approach (SFA). For the reasons stated in the above section on the limitation of non-parametric approaches, there are other robust parametric methods like two-step DEA-OLS analysis, panel least squares regression and SFA to examine the variables explaining the court performance (Beldowski et al. 2020). Moreover, the judiciary, like any other institution requires budget for its smooth functioning but, there are very less studies that have considered Expenditure on the judiciary as a key variable. The literature presents us with an immediate paradox on the role of judges as clearly explained in the Literature Review section. Their productivity increases when they are flooded with cases but, this hypothesis needs to be tested given the cyclic syndrome of arrears in the courts of developing countries. Additionally, the gap in the literature in the Indian context pertaining to both the levels of judiciary, i.e., High Courts and Subordinate Courts is also prominent.

Methodology

DEA model

The requisite hallmark of a well-functioning judiciary is its ability to dispose of cases speedily. But, as far as measuring the performance of the court is concerned, due to the involvement of resources of multiple dimensions, it becomes a difficult task. DEA is one such method which can be used here. The origin of DEA dates to 1978 with the seminal work by Charnes and Cooper. DEA resembles the concept of production possibility frontier studied in economic theory. DMUs with efficiency scores of 1 form a frontier and all the other inefficient DMUs fall under that.

DEA is a non-parametric data-driven method in which due care needs to be exercised while choosing appropriate returns to scale (RTS). CRS (Constant Returns to Scale) also called CCR (Charnes, Cooper, and Rhodes) and VRS (Variable Returns to Scale), also termed BCC (Banker–Charnes–Cooper) are the two types of models of RTS. In the CRS-type model, output changes by the same proportion as input and VRS both increasing and decreasing returns to scale are encompassed. This study uses the VRS model because of the reason that “in most sectors the true technology experiences variable returns to scale” (Berbegal-Mirabent, Lafuente and Sole 2013). Fare, Grosskopf and Lowell (1994) mentioned that O–O model is “very much in the spirit of classical production function defined as the maximum achievable output given input.” For the present study output-oriented model is found to be suitable because judges aim at maximizing the output (cases disposed of) given the inputs available. The output-oriented DEA7 model is formulated as follows. Assume that there are n DMUs (courts). Each court $\left(DM{U}_{j,}j=1,2\dots .n\right)$ consumes m types of inputs and s types of outputs which in vector form can be expressed as $x_j=\left(x_{1j},x_{2j},\dots \dots ,x_{\mathit{mj}}\right)$ and $g_j=\left(g_{1j},g_{2j},\dots ..g_{\mathit{sj}}\right)$ for court j. Following connotations are brought in for DEA and the related examination of efficiency:

$$v_j={\left(v_1,v_2,\dots .,v_m\right)}^T\text{is the input weight vector,}$$

$$u_j={\left(u_1,u,\dots .,u_s\right)}^T\text{is the output weight vector,}$$

$$y_j={\left(y_{1j},y_{2j},y_{3j},\dots .,x_{\mathit{sj}}\right)}^T>0,\left(j=1,2,3\dots ..,n\right){\text{the output vector of DMU}}_{\text{j}},$$

$$x_j={\left(x_{1j},x_{2j},x_{3j},\dots .,x_{\mathit{mj}}\right)}^T>0,\left(j=1,2,3\dots ..,n\right){\text{the input vector of DMU}}_{\text{j}}.$$

Computation of DEA comprises of three efficiencies: Technical efficiency (TE) is a measure of resource allocation efficiency ascertained in case of CCR model; Pure technical efficiency (PTE) is the indication of utilization level of inputs in BCC model; Scale efficiency (SE) is expressed as the ratio of TE and PTE. The dual and primal form of the output-oriented BCC model can be illustrated as:

Basic form of BCC followed in the analysis.

Dual $\left(D_{\mathit{BCC}}^0\right)$	Primal $\left(P_{\mathit{BCC}}^0\right)$
$Maxz=z^0$	$Min(w^T{x}_0$+${\mu }_0)=z^0$
${\sum }_{j=1}^n{x}_j{\lambda }_j\le x_0$	$w^T{x}_j-{\mu }^T{y}_j+{\mu }_0\ge 0,j=1,2,3\cdots ..,n$
${\sum }_{j=1}^n{y}_j{\lambda }_j\ge {\mathit{zy}}_0$	${\mu }^T{y}_0=1$ $w\ge 1,\mu \ge 0$
${\sum }_{j=1}^n{\lambda }_j=1$
${\lambda }_j=\ge 0,j=1,\cdots .,n$

Source: Based on the review of literature

Here, $w^0,{\mu }^{0}and{\mu }_0^0=optimalsolutionsof{P}_{\mathit{BCC}}^0$. For our analysis n = 24, m = 4(3) and s = 1. Like statistics or any other empirical oriented methodology, sensitivity (stability or robustness) analysis is also important in DEA. Efficiency or inefficiency of DMU becomes questionable if the Degrees of freedom are inadequate. A general rule of thumb is (Cooper, Seiford and Tone 2007) $n\ge max\left\{m\times s,3\left(m+s\right)\right\}$

Malmquist index

Malmquist index summarizes the change in productivity into technical efficiency change, pure technical efficiency change, scale efficiency changes and total factor productivity change (Tone 2004). MPI shows the intertemporal change in productivity at t based on productivity of previous period (t-1). Thus, for the $j^{\mathit{th}}$ court MPI at period t is:

$$MP{I}_j^t=D_j^t\left(x_j^{t+1},y_j^{t+1}\right)/D_j^t\left(x_j^t,y_j^t\right).$$ 1

$D_j^t\left(x_j^{t+1},y_j^{t+1}\right)$ and $D_j^t\left(x_j^t,y_j^t\right)$ are the distance functions of $j^{\mathit{th}}$ court with level of period t as reference. $MP{I}^{t,t+1}$ indicate the status quo between period t and t + 1. $MP{I}_j^{}=1$ is interpreted as the state of no change in total factor productivity,$MP{I}_j^{}>1$ implies gain in efficiency and $MP{I}_j^{}<1$ corresponds to the loss in efficiency. The general form of MPI is derived from the geometric mean of $MP{I}_j^t$ and $MP{I}_j^{t+1}$ (Fare et al. 1994; Fare et al. 1998) which can be:

$${\mathit{MPI}}_j=\left[\frac{D_j^{t+1}(x_j^{t+1},y_j^{t+1})}{D_j^t(x_j^t,y_j^t)}\right]\times \sqrt{\frac{D_j^t(x_j^{t+1},y_j^{t+1})D_j^{t+1}(x_j^t,y_j^t)}{D_j^{t+1}(x_j^{t+1},y_j^{t+1})D_j^{t+1}(x_j^t,y_j^t)}},$$

$${\mathit{MPI}}_j=EFCH\times TECH.$$

In variable returns to scale (VRS), $EFFCH=PECH\times SEC,$

$${\mathit{MPI}}_j=\left[\frac{D_j^{t+1}\left(x_j^{t+1},,,y_j^{t+1}\right)}{D_j^t\left(x_j^t,,,y_j^t\right)}\right]\times \frac{D_j^t\left(x_j^t,,,y_j^t\right)D_j^{t+1}\left(x_j^{t+1},,,y_j^{t+1}\right)}{D_j^t\left(x_j^t,,,y_j^t\right)D_j^{t+1}\left(x_j^{t+1},,,y_j^{t+1}\right)}\times \sqrt{\frac{D_j^t\left(x_j^{t+1},,,y_j^{t+1}\right)D_j^{t+1}\left(x_j^t,,,y_j^t\right)}{D_j^{t+1}\left(x_j^{t+1},,,y_j^{t+1}\right)D_j^{t+1}\left(x_j^t,,,y_j^t\right)}}.$$

All the measures have been explained concerning movement from period t to t + 1. Table 1 provides a brief account of the decomposed measures of Malmquist Productivity Index (MPI). Finally, one needs to understand that MPIs are ascertained using the efficiency scores of DEA and frontiers are computed through DEA with output orientation. We have used DEAP version 2.18 for the analysis.

Table 1.

Summary of decomposed measures of MPI

Decomposition	Description (period t to t + 1)	Cases (change in efficiency)
$\mathrm{EFFCH}=\left[\frac{D_j^{t+1}\left(x_j^{t+1},,,y_j^{t+1}\right)}{D_j^t\left(x_j^t,,,y_j^t\right)}\right]$	Shows the change in technical efficiency on account of CRS. It indicates how well the production is close to PF	EFFCH = 1: on the PF (invariable) EFFCH > 1: close to PF (efficiency gain) EFFCH < 1: away from PF (efficiency loss)
$\mathit{TECH}$=$\sqrt{\frac{D_j^t\left(x_j^{t+1},,,y_j^{t+1}\right)D_j^{t+1}\left(x_j^t,,,y_j^t\right)}{D_j^{t+1}\left(x_j^{t+1},,,y_j^{t+1}\right)D_j^{t+1}\left(x_j^t,,,y_j^t\right)}}$	It measures the magnitude of shift in PF for DMU	TECH = 1: no change in technology TECH > 1: technical progress TECH < 1: technical backslide
$PECH=\left[\frac{D_j^{t+1}\left(x_j^{t+1},,,y_j^{t+1}\right)}{D_j^t\left(x_j^t,,,y_j^t\right)}\right]$	It accounts for technology level change in VRS	PECH = 1: no change in technology PECH > 1: increasing technology level PECH < 1: decreasing technology level
$SECH=\frac{D_j^t\left(x_j^t,,,y_j^t\right)D_j^{t+1}\left(x_j^{t+1},,,y_j^{t+1}\right)}{D_j^t\left(x_j^t,,,y_j^t\right)D_j^{t+1}\left(x_j^{t+1},,,y_j^{t+1}\right)}$	It represents the role of scale change in change in productivity	SECH = 1: scale change brings no productivity change SECH > 1: scale change promotes productivity change SECH < 1: scale change reduces productivity change

PF production frontier, DMU decision-making unit, CRS constant returns to scale

Source: Based on the review of literature

Stochastic frontier analysis

To measure the performance of DMUs, aimed at converting inputs into output(s), Aigner et al. (1977) and Meeusen and Van den Broeck (1977) put forward a parametric technique called the SFA model independently. The general form of which in panel data can be written as:

$$ln{q}_{\mathit{it}}=x_{\mathit{it}}^{{}^{\prime }}\beta +v_{\mathit{it}}-u_{\mathit{it}}$$

Or

$$q_{\mathit{it}}=exp\left({\beta }_0+{\beta }_{1}ln{x}_{\mathit{it}}+v_{\mathit{it}}-u_{\mathit{it}}\right)$$

Or

$$q_{\mathit{it}}=\text{exp}\underset{\mathit{Deterministiccomponent}}{\underbrace{\left({\beta }_0+{\beta }_{1}ln{x}_{\mathit{it}}\right)}}\times \underset{\mathit{Noise}}{\underbrace{\text{exp}\left(v_{\mathit{it}}\right)}}\times \underset{\mathit{inefficiency}}{\underbrace{\text{exp}\left(-u_{\mathit{it}}\right)}},$$

$$U_{\mathit{it}}=U_{i}exp\left(-\eta \left(t-T\right)\right),$$

$${\text{U}}_{\text{i}}\ge 0\sim \text{iid}\left(\text{truncated at zero of the N}\left(\mathrm{\mu },{\mathrm{\sigma }}_{\text{U}}^2\right)\text{distribution}\right),$$

$$\eta \text{is the paramter to be estimated,}$$

where in the first equation $q_{\mathit{it}}$ is the number of disposed of cases of the i-th high court; $x_{\mathit{it}}$ is the vector of inputs such as judges, staffs, pending cases and expenditure allocated by i-th court; $\beta$ stands for the vector of parameters to be estimated; $v_{\mathit{it}}\sim iidN\left(0,{\sigma }_v^2\right)$ random errors, independent of the $u_{\mathit{it}}$; $u_{\mathit{it}}\ge 0$ are associated with technical inefficiency.

TE of the $i^{\mathit{th}}$ country can be estimated as:

$$T{E}_i=\text{exp}\left(-u_i\right).$$

SFA uses the MLE procedure to estimate the technical efficiency of the network readiness across countries. The variance parameter is:

$${\sigma }_U^2={\sigma }_u^2+{\sigma }_v^2,$$

$$\lambda =\frac{{\sigma }_u^2}{{\sigma }_v^2}.$$

$$\gamma =\frac{{\sigma }_{\mu }^2}{{\sigma }_{\mu }^2+{\sigma }_{\nu }^2},\text{where}0\le \gamma \le 1.$$

This method differs from other parametric techniques like OLS or IV-SLS in the sense that here, the theoretical value of a dependent variable, is treated as “expected maximum value” instead of treating it as average value. Apart from this, SFA residuals include iid random error and non-positive inefficiency terms (incapacitated to reach the frontier) rather than the assumption of zero mean and constant variance in OLS (Beldowski et al. 2020). The benefits of using panel data are the increase in the number of observations and more efficient estimators of the unknown parameters. Panel data come with some other added utilities like allowing the user to relax some strong distributional assumptions, to obtain consistent predictions of technical inefficiencies and estimate changes in technical efficiencies over time (Coelli 2005)

Data and variable selection

Identification of inputs and output is an integral part of DEA and SFA. The selection of variables is done through two mechanisms (1) by solving mixed-integer linear programming (MILP) primarily employed when there is no heuristic decision-making or expert judgement, proposed by (Peyrache et al. 2020) and (2) previous research on efficiency (Mattson and Tidana 2019). Courts are Labor-Intensive, and all the previous research has incorporated at least one measure of labor but has not considered the input on capital (Mattson and Tidana 2019). Given the context and constraints, to assess the efficiency of courts following factors should have been gauged in financial and Human Resources, diversity, infrastructure, and workload. The data for the present study on High Courts and Subordinate Courts has been extracted from Annual reports of the judiciary for the period 2015–20 on civil and criminal cases. This is the longest period for which the data are available in Annual Reports. Although data on civil and criminal cases pending, judges, judicial staff, and the budget can be extracted from the Annual Report Of Indian Judiciary, for the capital aspect of input in the judiciary, data on completely constructed court halls and residential accommodations are only provided for the year 2018–19 by “Nyaya Vikas” a portal and mobile app for monitoring of projects under the CSS for development of infrastructure facilities for the district and subordinate judiciary (Department of justice Handbook on Revised Guidelines 2018–19, GOI). It is worth mentioning here that the pending cases of a particular year have been derived by summing up the new cases instituted and the pending cases at the beginning of that year.

Empirical results

High Courts and Subordinate Courts

To understand the status quo of 24 High Courts9 and their respective Subordinate Courts, in Appendix Table 3, we report the descriptive statistics in 5 dimensions for the period 2015–2020. From Fig. 2, we can see that on average the number of pending cases and disposed of cases in Subordinate Courts has been higher than in the High Courts which coincides with the observations from Fig. 3 where the number of judicial staff in subordinate courts seems to be higher than in the High Courts. Overall, there has been a surge in the workforce in both High Courts and Subordinate Courts.

Fig. 2.

Average number of pending and resolved cases in High Courts and Subordinate Courts.

Source: Author’s calculation

Fig. 3.

Average Strength of workforce in High Courts and Subordinate Courts

Source: Author’s calculation

To be specific, judges in HC, other judicial staff in High Courts and the judicial officers in Subordinate Courts increased by 11%, 155 and 16%, respectively. Moreover, there has been a 60% surge in the expenditure allocated to High Courts in India (Refer to Fig. 4). Where on the one hand there has been an increase in the inputs employed in the courts, on the other hand there has been a growth of 18 and 17% in cases pending in the High Courts and Subordinate Courts.

Fig. 4.

Expenditure allocated to High Courts. Source: Author’s calculations

Source: Author’s calculation

Data envelopment analysis

In the current study, we have employed output-oriented DEA with the assumption of Variable returns to Scale. The output-oriented model is configured to allow a DMU (in our case Courts) to become efficient by proportionately increasing the output given the inputs. It is expressed as the ratio of maximum output to actual output. In the software DEAP, the output-oriented technical efficiency ranges between 0 and 1 (inverse of an output-oriented theoretical model). A value of 1 means that the DMU is on the production frontier and is the benchmark for all the other DMUs, on the other hand, a value less than 1 indicates that the DMU is technically inefficient. Let us say a DMU’s Technical Efficiency score is 0.78 in output-oriented DEA, this would signify that it is technically inefficient and can become efficient by increasing 22% (1–0.78) of its output, and keeping the inputs fixed. As stated earlier, the non-parametric nature of DEA allows us to incorporate multiple inputs and outputs to obtain the technical efficiency score and rank the DMUs accordingly.

For both levels of courts there is one output, namely Cases Disposed of, whereas the number of inputs for High Courts are Judges, Judicial Staff, cases pending and budgetary allocation, the inputs for lower courts are Judicial staff and cases pending. It is a pre-requisite to check for the isotonic relationship between inputs and outputs in DEA which is satisfied in our case (Refer to Appendix Table 4). It is worth mentioning at this juncture that we would be using the technical efficiency scores to rank the High Courts and Subordinate Courts and comment on the potential for change. Though the number of Technically efficient Subordinate Courts and High Courts went up between 2015 and 19, it went down in 2019–20. The results of Output-oriented DEA with VRS assumption are presented in Source: Based on author’s calculations Appendix Table 5 and Source: Based on author’s calculations Appendix Table 6 and the results are summarized in Figs. 5 and 6.

Fig. 5.

Ranking of High Courts based on the average VRSTE scores

Source: Author’s calculation

Fig. 6.

Ranking of Subordinate Courts based on Average VRSTE.

Note: The rankings are based on the average VRSTE scores over 2015–20

Source: Author’s calculation

On average, it can be observed that other than Allahabad, Sikkim, and Meghalaya High Courts (Benchmark courts with perfect unity technical efficiency score), all the courts are technically inefficient and are required to increase the cases disposed of by keeping the inputs fixed. The lowest performing High Courts are UT of J&K and Ladakh, Bombay and Calcutta which need to increase the cases disposed of by more than 50% to reach the efficiency level. Similarly, the subordinate courts under the jurisdiction of Tripura, Sikkim and Allahabad High Courts set the benchmark and the remaining courts are technically inefficient. Subordinate Courts under the jurisdiction of Patna, Jharkhand, Orissa, and Meghalaya High Courts have been the poorest performing courts which need urgent policy measures to improve the case disposal rate to reach technical efficiency. DEAP also gives the Scale efficiency scores of the DMUs which is the ratio of output-oriented TE scores based on CRSTE and the scores from VRSTE. Based on the Scale Efficiency Scores of both, High Courts, and Subordinate Courts we can infer that over the years number of High Courts and Subordinate Courts witnessing DRS has shot up. This points toward an alarming situation where the courts are oversized, having exceeded their optimal size. Thus, to reduce their average input consumption, these High Courts must decrease their size. Practically, this could be done either by internal decay (i.e., producing less output) or by splitting the Courts into two separate Courts (Refer to Appendix Table 7).

Malmquist productivity index

In this section, we would analyze the DEA-based Malmquist productivity index which decomposes the change in productivity into technical efficiency change (catching-up effect) and Technology change (Frontier-shift). MPI primarily shows the intertemporal change in TFP and if it is observed to be greater than 1 then is a sign of improvement in the productivity of a particular DMU and vice versa. In Appendix Table 8 and Appendix Table 9, average decomposed MPI scores have been shown, where the product of EFFCH (technical efficiency change-second column) and TECHCH (technology change in the third column) gives TFP (total factor productivity change-fifth column). It can be observed that on average the productivity of both High Courts and Subordinate Courts has deteriorated by 6 and 9%, respectively, and the reason is the downfall in technical efficiency despite an improvement in technological change. We can infer that the courts in India need to have a proper balance between inputs and outputs. On average, the productivity of 8 High courts and Subordinate Courts under the legislature of 3 High Courts has gone up and remaining all courts have experienced plummeting productivity. The overall productivity of UT of J&K and Ladakh High Court has deteriorated (Refer to Appendix Table 10). The reason stems from the clear imbalance between inputs and output despite technological progress. A constant work in progress is required in the High Courts and the Subordinate Courts to move up from the status quo of deteriorating technical efficiency through transparent financial management, periodical review of the performance and maintenance of the supply of inputs like judges, staff, and budget. Additionally, the study suggests an innovation-centric approach and the introduction of new technology. These courts experience continuous struggles to move up the ladder of efficiency. The fact that the none of Subordinate Courts have experienced productivity gains barring the Subordinate Courts under Tripura High Courts (where the productivity has remained unchanged) underscores the need to change internal managerial conditions (referring to better use of resources by the court). To sum up, we can infer that the reason for the average productivity of courts is the lackluster internal management of resources (inability to approach the frontier) and imply significant policy interventions. After performing some non-parametric tests, we have found a statistically significant difference between the productivity of High Courts established before independence and the ones established after 1947 (Refer to Table 2).

Table 2.

Analysis of productivity of High Courts based on year of establishment

Year of establishment	Average	Std. dev	Max	Min	Two-sample t test	Two-sample Wilcoxon Mann–Whitney rank-sum test (z-value).	Kruskal–Wallis test Equality-of-populations rank (chi-square value).	Two-sample Kolmogorov–Smirnov test For equality of distribution functions (D-value).
Before independence	0.873	0.055	0.94	0.772	− 2.8***	− 2.6***	6.7***	0.68***
After independence	0.99	0.153	1.505	0.839

Source: Based on author’s calculation

Stochastic frontier analysis

In Table 3, we report the results of the true fixed-effects model of SFA in which column 2 shows the results when pending cases were considered as independent variables explaining the frontier and in column 3 we have considered the pending cases as an inefficiency-causing variable. In the case of High Courts, we have found a statistically significant positive impact of demand for justice, judges, judicial staff, and budgetary allocation on the cases dissolved. Furthermore, we have also found that there has been a decline in technical efficiency over the years (the negative coefficient of year). In a separate setup when we considered Pending cases as a technical inefficiency-causing variable, it was found to be statistically significant along with the statistically significant positive impact of other explanatory variables in our analysis. This explains that pending cases hinder the technical efficiency of High Courts. When a similar exercise was performed for Subordinate courts, judicial staff was found to be positively (and significantly) impacting the cases dissolved and the pending cases were found to be insignificant in explaining the technical inefficiency of Subordinate Courts.

Table 3.

Stochastic Frontier analysis with log of dissolved cases as a dependent variable

	High Courts		Subordinate Courts
	(1)	(2)	(3)	(4)
log_pending	0.060*** (0.0004)	–	0.3814*** (0.122)	NA
log_judges	0.483*** (0.00001)	0.757*** (0.119)	0.616** (0.285)	1.12* (0.668)
log_staff	0.479*** (0.00001)	0. 7747*** (0.128)		NA
log_budget	0.020*** (0.00002)	0.1761*** (0.018)	NA	NA
Year FE	− 0.0420*** (6.08E-06)	− 0.057*** (0.016)	− 0.08*** (0.019)	0.67*** (0.067)
MU (technical inefficiency) log_pending cases	–	0.336*** (0. 0934)	NA	−0.6896 (4.17)
Usigma _cons	4.674*** (1.47)	–	− 7.37	2.98
Log-likelihood (SFA)-UR	34.936	− 3.3699	− 7319	− 298.89
Log-likelihood (OLS)-R	− 68.045	− 121.251		− 135.15
LR = − 2(LR(H0)-LR(H1))	205.964***	235.762***	214.750***	− 327.48

All the variables were taken log of Values in parenthesis show standard error

*p < 0.05, **p < 0.01, ***p < 0.001

Thus, based on SFA, we can infer that though demand for judges, Judges, judicial staff, and budgetary allocation improves case solvency, pending cases also cause technical inefficiency in High Courts. Thus, rising pendency is a matter of great concern for India’s High Courts and from the policy perspective, we emphasize not just judicious utilization of resources but also underscore the importance of infusing more resources (financial capital and manpower). Furthermore, we found no difference in the summary statistics of VRSTE scores of High Courts obtained from DEA and that from SFA (Refer to Appendix Table 11).

Panel regression analysis

To understand the average impact of demand for justice (pending cases), judges, judicial staff and expenditure with year and the court fixed effects dummy, we have performed panel regression analysis10, the results of which are reported in Table 4.

Table 4.

Panel LSDV (Robust) results for High Courts and Subordinate Courts

Variables	High Courts			Subordinate Courts
	(1)	(2)	(3)	(4)	(5)	(6)
log_pending	− 0.148 (0.395)	0.668*** (0.0711)	− 0.166 (0.387)	.0739 (0.173)	0.751*** (0.123)	− 0.0444 (0.149)
log_judges	0.580*** (0.194)	0.211*** (0.0722)	0.582*** (0.173)	0.314 (0.405)	0.180 (0.195)	1.042** (0.402)
log_staff	0.570*** (0.212)	0.398*** (0.111)	0.559*** (0.188)	NA	NA	NA
log_budget	− 0.0103 (0.158)	− 0.192*** (0.0644)	0.179 (0.158)	NA	NA	NA
Court FE	Yes	No	Yes	Yes	No	Yes
Year FE	No	Yes	Yes	No	Yes	Yes
Constant	7.504** (3.662)	3.635*** (0.983)	3.610 (5.349)	13.77*** (3.562)	1.874*** (0.536)	7.896** (3.023)
Observations	120	120	120	120	120	120
R-squared	0.980	0.944	0.982	0.980	0.897	0.986

Log of dissolved cases as dependent variable (All the variables were taken log of) Judges are judicial staff in cases of Subordinate Courts; Values in parenthesis show standard error

*p < 0.05, **p < 0.01, ***p < 0.001. Source: Based on the author’s calculations

It can be clearly seen that Judges on average have a significant positive impact on the cases disposed of in both, High Courts, and Subordinate Courts. The results refute the claim of the insensitivity of case disposition to the judicial staff revealed by Beenstock and Haitovsky (2004) and Dimitrova-Grajzl et al. (2012), and are in line with the emphasis placed on the recruitment of additional judges to clear backlogs in Economic Survey (2018–19). Furthermore, we find evidence of a direct positive impact of Cases pending on cases disposed of as was found in the case of Israeli courts by Beenstock (2004) and of Andhra Pradesh by Rabiyath and Rupakula (2010) confirming that the number of cases resolved depend on the demand for justice.The problem is not insurmountable, i.e., the disposal rate could be improved by filling up the vacancies and increasing the number of working hours (Refer to Appendix Table 2 on working hours in India’s High Courts in 2020). Interestingly, when we controlled for year-fixed effects, we found that Expenditure allocated to the judiciary has a negative impact manifesting the two dimensions of inequality.11 This signals a need to examine the budgetary allocation to the courts in India by the Finance Commission. There is a vicious cycle existing here in the sense that the judicial staff are occupied with disposing of cases, hence they devote very limited time to infrastructural deficits. Other aspects could be Red-Tapism and corruption. Mere allocation of funds does not guarantee an outcome, it needs to be at par with productivity. Thus, further research in this field could shed light as to why Budget has a statistically significant negative impact on cases disposed of.

Impact of COVID-19 on instituted cases and disposed cases

The problem of staggering pendency in Indian Courts was exacerbated by the unprecedented pandemic called COVID-19 which impacted each stratum of society. As India grappled with a health and economic crisis, the nationwide lockdown imposed on 24th March 2020, compelled the High Courts to function virtually. Consequently, the number of pending cases reached an all-time high but, in sheer contrast the number of fresh cases instituted, and cases disposed of plummeted (Refer to Fig. 7). In the Indian context, the prevailing literature is limited on the impact of COVID-19 (Rattan and Rattan 2021; Singh et al. 2022). To the best of our knowledge, the literature related to the pre-COVID-19 crisis period is scant and mostly pertains to the pre-COVID-19 crisis period and covers the government intervention with E-Courts and the process of digitization. Thus, to bring this study into the current context we also looked at the impact of COVID-19 and performed statistical tests the results of which are reported in Table 5.

Fig. 7.

Impact of COVID-19 on cases instituted and cases disposed of The first dotted vertical bar(gray) shows the first Case of COVID-19 which was found in Kerala and the second bar (Red) indicates the break due to nationwide lockdown on 24th March 2020. Source: Based on the author’s calculations

Table 5.

Statistical tests to understand the difference in cases instituted of and cases disposed of due to lockdown

Variables	Two-sample Kolmogorov–Smirnov test	Kruskal–Wallis equality-of-populations rank test	Two-sample Wilcoxon rank-sum (Mann–Whitney) test	Two-sample t test with unequal variances
Cases instituted	0.22***	31.95***	5.652***	5.68***
Cases disposed of	0.233***	36.530***	6.044***	2.82***

Source: Based on Author’s calculation

*p < 0.05, **p < 0.01, ***p < 0.001

Thus, to understand the impact of the Lockdown on the number of fresh cases instituted and cases disposed of we collected monthly data of High Courts between January 2019 and July 2021 (National Judicial Data Grid-NJDG) and performed some non-parametric and classical tests. Based on the results reported in Table 5, we find a statistically significant difference in the number of fresh cases instituted in High Courts and the cases disposed of due to the lockdown.

Conclusions and policy implications

One of the four pillars of democracy is the judiciary. De facto, a technically efficient judiciary subtly not just emboldens the faith of people in the justice delivery system, but empirical studies have also confirmed its growth effects. The present study provides a methodological alternative to evaluate the performance of the judiciary. Following the attempt of Gupta and Bolia (2020), the current study presents evidence in the context of a developing country like India by juxtaposing jurisprudence with production theory, not frequently examined in the same gust by employing output-oriented DEA, SFA, Malmquist productivity index, and panel regression for both the levels of courts—High Courts and the Subordinate Courts. The current study does not enquire into probing the quality of verdicts but, somewhat it endeavors to examine the relative technical efficiency of courts in India. We revealed how the supply of justice (cases disposed of) is determined by the demand for justice, serving judges and judicial staff and the expenditure allocated in both, HCs and Subordinate Courts. Employing a unique dataset spanning over 2015–19 facilitated us to infer that the High Courts and Subordinate Courts are technically inefficient, and their productivity has declined over the analysis period. Furthermore, we were able to infer that on average the High Courts established post-independence fared better in technical efficiency than the ones established before independence. From the Malmquist productivity index, we were able to suggest that a constant work in progress is required in the High Courts and the Subordinate Courts to move up from the status quo of deteriorating technical efficiency through transparent financial management, periodical review of the performance and maintenance of the supply of inputs like judges, staff, and budget. We have also found that the issue of pendency is not insurmountable, i.e., the disposal rate could be improved by filling up the vacancies and increasing the number of working hours. However, the evidence does not suggest a “one-size-fits-all” approach to bring reform in the Indian Judicial system. Each court should examine and practice different ways to improve efficiency. In SFA we have also shown that pendency leads to technical inefficiency in High Courts. Interestingly, when we controlled for year-fixed effects, we found that Expenditure allocated to the judiciary has a negative impact manifesting the two dimensions of inequality in fiscal federalism. Analyzing the monthly database, we found a statistically significant difference in the number of fresh cases instituted and the cases disposed of in High Courts due to the nationwide lockdown in India.

From the point of view of behavioral economics, the performance of the civil and criminal justice system has effects on human beings through a cultural spillover. Our study in the context of India’s judicial system by focusing on two levels—High Courts and Subordinate Courts could be a learning experience for lower-middle-income countries where the judiciary enjoys an important and powerful position and for the countries ranking low in the Rule of Law indices (World Justice Project). Our estimates confirm the role of judges, judicial staff, and pendency in the cases solved. Policy implications from the current study revolve around the increase in the number of judges and judicial staff, increasing the number of working days, and establishment of a separate professional body for the judicial administration (being prevalent in countries such as the UK, USA, and Canada) and technology deployment among others. These recommendations are pervasive for the global, South Asia regional peers, Lower Middle-income peers and poor countries that have fared low in the two sub-indices of the Rule of Law such as criminal and civil justice.

The study is also not devoid of any limitations. First, data limitation on environmental factors like corruption, the budget allocated to Subordinate Courts, court halls, representation of women, technological factors, and Police which ideally could have been included in the analysis. Second, it is important to also analyze the efficiency of fast-track courts and Lok Adalat in India and construct a model that incorporates a simultaneously operating intertemporal model. Third, from the methodological point of view Bayesian approach, Network DEA and the application of Artificial Neural Networks could be what future research could focus on. Fourthly, from the global perspective, the availability of panel data on all the inputs and outputs could give a better picture. Fifthly, as stated the current study does not enquire into probing the quality of verdicts which could be a potential topic for future studies. Moreover, it would be interesting to look at the impact of COVID-19 on the Indian judiciary, which was compelled to work digitally for a longer period.

Supplementary Information

Below is the link to the electronic supplementary material.

Author contributions

This is a study conducted by a single author.

Funding

No funding was received for the completion of the study

Data availability

The data are available and could be provided when required.

Declarations

Conflict of interest

There is no conflict of interest

Ethical approval

Ethics approval was not required for this study.

Consent for publication

I give consent for the publication of the manuscript.