Evaluating Productivity and Efficiency Contradictions of Metrorail South Africa

This study focusses on the efficiencies of subunits of South Africa’s Metrorail services. Over the period 2015/16 to 2018/19 Metrorail implemented its corporate plan to improve operations efficiency. This study applies the Malmquist Productivity Index (MPI) to compare the performance efficiency of the three Metrorail subunits over the study period. The results indicate the variation of productivity levels amongst Metrorail subunits. Furthermore, output-oriented scale efficiency scores are used to measure the optimal scale situation of each Metrorail subunit. It is concluded that largely the KwaZulu-Natal subunit seems to be more efficient when compared to the other two subunits over the full period under analysis. Therefore, in the cognition of the relatively large size of the Gauteng and Western Cape subunits and their concomitant inefficiency levels, the findings suggest that Metrorail management should focus on correcting their inefficiencies while also considering alteration of their size to optimize production.


Introduction
The recent reports on poor performance outcomes of South Africa's SOEs have heightened a national discourse on the governance of SOEs. In particular, the debate borders on the productive pursuit of SOEs in South Africa that are expected to involve business activities promoting growth and fair distribution of services through an effective and just administration system of SOE governance. Trust and confidence in SOEs as apparatus of governance and social order towards development dictate the creation of good governance and operational efficiencies. Effective management of Metrorail, a subsidiary of Passenger Rail Agency of South Africa (PRASA), is likely to demonstrate observed successes that entrenches a social contract of government with its people. Alternatively, incompetence, corruption and dysfunctional Metrorail services compromise the descriptive nature and role of an ideal SOE which operates rail passenger services. Most probably the dominant narrative of management capabilities would regrettably be ascribed to the character and business practices of a South African SOE.

Literature Review
In the literature efficiency and productivity, measurements are considered as main aspects to measure a firm's performance (Lovell, 1994;Coelli et al., 2005). Generally, in an organisation, the efficiency of operations is a result of the maximisation of resources and achieving optimal outputs. However, public administration suffers from inefficient production because of monopolistic practices and the social service imperative that results in poor measurements of outputs (Mihaiu et.al., 2010;Vavrek, 2018). The management and decision-making field is progressively improving the ways of measuring government services (Lovell, 1994). Førsund (2015) posits that public sector productivity activities are non-profit making and thus are best measured by the Malmquist Productivity index (MPI) which is based on data envelopment analysis (DEA). Empirical investigations in the use of DEA productivity models and MPI analysis in some cases within South Africa are more revealing.
Along this line, a study of South Africa's public sector hospitals in three Provinces using MPI revealed a variation of performance with most hospitals being inefficient at non-optimal scales of decreasing returns to scale (United Nations, 2000). Two input variables, annual total recurrent expenditure and bed-size were used for small sized hospitals, whereas only the former input variable was used for larger hospitals due to the small sample size. The results were based on models adopted from Farrell (1957) and Charness et al. (1978), applied by the non-parametric output technique of DEA for measuring relative technical efficiency. The study confirmed a successful application of MPI analysis with many hospitals performing at scale inefficiency levels given their relative difference in size and complexity.
Also, Brettenny and Sharp (2018) successfully conducted a study on the productivity of water services by South African municipalities through an evaluation of the service efficiency change over time using MPI analysis. The results show that the annual average decline of production over the three-year period was a product of technological change. The researchers capitalized on the use of multiple input and output variables as an advantage to use the DEA methodology. Their three inputs included annual operational expenditure, full-time personnel, as well as the physical length of main water lines. On the other hand, the two output variables were system input volumes and metered connections. The outputoriented MPI results indicate that technical change in a particular year improved/regressed the productive capacity of municipalities. The efficiency gains were in some cases deemed to be associated with scale efficiency.
Regrettably, in South Africa available literature on the use of DEA and the application of MPI of public transportation is scarce. However, there is a number of international studies on the evaluation of public transportation through the DEA methodology. Carvalho et al. (2015) evaluated public transport in the twenty-one largest cities of Brazil by the DEA technique to determine infrastructure efficiency and service effectiveness. The cities were regarded as Decision Making Units (DMUs) with input variables as Municipal Inhabitants and Number of Urban Buses. The output was the average daily passengers transported by busses. The researchers used secondary data on three performance indicators, that is, efficiency, service effectiveness, as well as effectiveness against efficiency score. In using the Super-Efficiency DEA model the results indicated that efficiency was the focal indicator of some cities. In contrast, other cities paid importance to the effectiveness of their services. With a particular focus on the city of Campinas, the researchers were able to determine a need for the city to increase the effectiveness of the bus fleet in the years 2005 to 2010. Alternatively, the required decrease in the number of passengers to effect maximum effectiveness was calculated. Barnum et al. (2007) have also successfully shown the application of DEA by comparing a set of subunits that perform similar activities within a public transportation agency as a parent company. Their research on pack-and-ride facilities of the Chicago Transit Authority (CTA) had two input variables, namely average Daily operating expenses and Parking capacity with outputs being average Daily revenue and average Number of Parked cars. In order to determine the efficiency of parking lots, Barnum et al. followed a two-stage method of adjusting efficiency scores to control environmental factors. Normally, a DEA procedure assumes that there is a homogeneous environment under which DMUs are assessed. However, the potential effects of environmental factors for different units should be constrained to validate the outcome (Cooper, Seiford and Zhu, 2004). Thus, in the study by Barnum et al. environmental influence on the demand for parking lots was identified as the distance from the nearest freeway / central business district. As a result, after having determined the efficiency scores from the raw data of true inputs and outputs, researchers applied regression analysis to control the environmental influence. The use of Stochastic Frontier Analysis produced adjustments for DMU inefficiency by converting environmental conditions into outputs (Barnum et al.,2007).
Other DEA-based studies on public transportation include the evaluation of efficiency of bus routes in Beijing for the period 08 March 2012 to 22 March 2012 (Li et al., 2013), and the measurement of efficiency of 19 multi-modal systems of publicly owned transport companies in cities of Czech Republic during 2010 to (Fitzová et al., 2018. The research by Li et al. (2013) amplified efficiency evaluation by the use of sensitivity analysis. On the other hand, the Czech Republic study factored correlation analysis to evaluate the strength of the relationship between the variables used in the research. The DEA-based MPI model has been used in several studies to analyze transportation production activities. Viverita and Kusumastuti (2013) applied it for measuring operational efficiency gains and productivity growth of 22 Indonesian Airports ascertained the increasing/decreasing return to scale of airports. Guner and Coskun (2013) evaluated the efficiency of four passenger ports of Turkey covering a seven-year period of the average efficiency score of each passenger port and the average efficiency scores for each year for all the ports. Both studies measured the Total Factor Productivity (TFP) using DEA-MPI analysis. The study on efficiency analysis of 31 railway firms worldwide by Kutlar et al. (2015) also followed the TFP approach with an output-oriented MPI analysis. The data set covered the period of 2000 to 2009 was analysed by CCR and BCC methods. The MPI results provided insight into the capacity of small and large firms relative to the TFP of each firm. Moreover, outcomes of efficiency change, technical change, pure efficiency change and scale efficiency change values were estimated. That also assisted Kutlar et al. to derive conclusions on efficiency changes of each railway firm in relation to the capacity level of each firm.

Research Methodology
This research applied a data envelopment analysis (DEA) model to evaluate the performance of Metrorail subunits assigned as decision-making units (DMUs). Researchers focused on measuring efficiency and productivity tend to use different models to evaluate productive efficiency of the mix of collected input data and produced outputs. DEA is a linear programming optimization-based technique that uses nonparametric methods for measuring relative efficiency and productivity of DMUs. Charnes, Cooper and Rhodes (1978) are credited as the creators of the basic DEA model denoted by CCR Model (Cooper, Seiford and Zhu, 2004). The use of a DEA model enables the evaluation of production efficiency since it has a small number of assumptions and it allows the combination of multiple inputs and outputs involved in DMUs (Ibid). Cooper, Seiford and Tone (2007) define the Malmquist Productivity index (MPI) as having features of comparative statics that represents Total factor productivity (TFP) growth as an outcome of a DMU. TFP growth of a DMU represents efficiency progress or inefficiency of the frontier technology over a time period given the inputs and outputs structures in use. As claimed by Tone (2004) the MPI is associated with the non-parametric framework of the DEA technologies evaluating the productivity change of a DMU between two time periods. Thus, MPI explains progress or regress in efficiency (i.e. catch-up or recovery) and the related technological changes experienced is associated with efficiency frontier or innovation measures over a time period. The computed efficiency and technological change produce TFP growth values. Accordingly, Färe et al. (1994) posit that when MPIo(optimistic) value is >1 that indicates productivity progress. Alternatively, an MPIo (optimistic) = 1 when indicating constant productivity between two time periods and MPIo (optimistic) score is <1 representing a regressed productivity level. The output-orientated Optimistic Malmquist productivity index defined on a benchmark technology satisfying constant returns to scale (CRS) is given by:

The Malmquist Total Factor Productivity Index
This study adopted the DEA-based MPI approach since it requires minimal suppositions in respect of the underlying technology and is able to measure the production growth of DMUs over set periods (Cooper, Seiford and Zhu, 2004). Additionally, in support of Førsund (2015) Metrorail provides public service, and as such, the use of MPI methodology is appropriate in the evaluation of its production. The catch-up score of a DMU is respectively represented by the efficiency improvement of each of the three Metrorail subunits. The frontier-shift values measure the technological change of each Metrorail subunit between period t and period t+1 while also defining the efficiency limits of the subunits.

Data Collection Procedure Followed
The data on Metrorail subunits were collected as secondary data mainly from PRASA's Corporate  Table  1 provides the original data collected.   In terms of inputs, a sizeable variation amongst Metrorail subunits is noticeable. Despite some variations in the performance of individual Metrorail subunits over distinct periods, it is important to also determine whether subunits altered their relative performance over the full period of the study.

Results of the Output-Oriented Malmquist Productivity Index Based on Constant Returns to Scale Model
The hypothesis of this research is based on constant returns to scale of Total Factor Productivity (TFP) changes between three decision-making units ( Table 2 explains the comparative evaluation measurements of the three Metrorail subunits over the set periods. The catch-up values in Table 3 show the sign of recovery with the effect being either growth or deterioration in the operations of a Metrorail Subunit. Thus, the catch-up effect scores of each subunit define the efficiency change of a subunit between current and previous financial year which in turn explains the effectiveness level of a respective subunit.
Following figures 1,2 and 3 depict the comparative analysis of productivity performance of Metrorail subunits. Figure 1 shows the efficiency change, Figure 2 shows the technological change, and Figure 3 shows the Total-Factor Productivity change.

Total Factor Productivity Change (Malmquist Productivity Index Scores)
Gauteng Wcape KZN As shown in Figure 3, the result of the MPI indicates that the productivity of the three Metrorail subunits from 2015/16 to 2018/19 remained below a score of ≤1. The exception of MPI score being >1 was realised in 2015/16 when Gauteng was at 1,057 MPI score. KZN experienced a significant increase at 1,223 in 2018/19 despite a 95% reduction in Train sets (input variable) and no change in Passenger trips (output variable) when compared to the previous financial year. Furthermore, because in the 2018/19 KZN subunit had efficiency changes at a score of 1,047 and technological change at a score of 1,168, its MPI value was the highest above the other two subunits and also over the full period under analysis. Notwithstanding the determination of the nature and level of productivity for each of the subunits of Metrorail, it is important to further ascertain comparisons of optimal outputs in relation to the size of each subunit. Therefore, the measurement of scale efficiency would reveal the optimization of scale size of each subunit over the horizon. Førsund and Hjalmarsson (2002) posit that within the production theory in economics studies, scale properties are a feature of an efficient production function. Hence, this study measures output-oriented scale efficiency that informs the required relative output expansion/contraction of Passenger trips for Metrorail subunits at an optimal scale. Simultaneously, marginal changes at a point in output relative to the proportional increase in inputs indicate a measure of returns to scale (RTS) or scale elasticity. Banker et al. (1984)'s concept of the most productive scale size is associated with the notion of returns to scale and the comparison of average productivity. To obtain a measure of scale efficiency (SE) the scores of CTRS efficiency (TE CRS ) are compared to VRTS efficiency (TE VRS ) scores. The resulting difference between the scores is either a scaling efficiency or a scale inefficiency that constraints operations to gain optimal scale situation, calculated by Coelli 1996 as:

Scale Efficiency of Metrorail Subunits
In which SEi = 1 point out full scale efficiency and SEi < 1 shows the presence of scale inefficiency.
In this study, the CTRS efficiency is only relevant when all Metrorail subunits are operating at an optical scale in each year. It is possible to avoid system inefficiency which may be the cause factor attributing to subunits not operating at optimal scales by management exercising prudence in the application of scale economies. Thus, the use of VRTS becomes appropriate in order to account for variable returns to scale circumstances (Banker et al., 1984). To further delineate the scale property this study has adopted the qualitative approach of categorising the nature of RTS. Hence, RTS also indicates possible capacity of output growth when inputs are increased/decreased given the three RTS types as (1) the increase returns-to-scale (IRS), (2) the constant returns-to-scale (CRS), and (3) the decrease returns-to-scale (DRS) (Banker et al., 1984;Førsund & Hjalmarsson, 2002). Table 4 indicates that the scale efficiency reveals that if the input quantity of all Metrorail subunits increases/decreases by a given proportion that results in: In a situation of IRS, it is expected that the SE increases with a concomitant increase in output (passenger trips) towards an optimal scale (Banker et al., 1984) Decreasing returns to scale (DRS) in Gauteng for the financial years 2017/18 -2018/19, Western Cape for the financial years 2016/17-2017/18 and Kwazulu-Natal for the full period of this study covering the financial years from 2015/16 to 2018/19. This implies that in the stated financial years in order to attain the optimal scale the three Metrorail subunits should have reduced their input size. Moreover, Kwazulu-Natal should have reduced its size for the full study period in order to attain the optimal scale. Li and Cui (2008) posit that the DRS plan should follow a route that contracts output in order to reach the optimal scale.

Conclusions and Further Research
This study shows that the optimistic DEA-based MPI is a useful tool to evaluate the efficiency of subunits of Metrorail of South Africa. The longitudinal data used is over the 4-Financial Year period from 2015/16 to 2018/19. The MPI decomposed the productivity of the three Metrorail subunits into efficiency change and technological change on the basis of two inputs and one output. The results mainly reflect TFP changes of each subunit with the MPI productivity of all subunits remaining at a score of ≤1. A deviation is observed when both efficiency change and technological efficiency change are comparatively high in any of the subunits. Hence, the Gauteng subunit has an MPI score of >1 from 2015/16 to 2016/17 while the KwaZulu-Natal subunit experienced the highest MPI score of 1,223 from the 2017/18 to 2018/19. Additionally, the comparatively KwaZulu-Natal subunit attained the highest average MPI value over the full period under analysis because of the combined high scores of its efficiency change and technological change.
The scale efficiency results provide insight into the relative capacity of each of the three Metrorail subunits given their difference in size. All three Metrorail subunits experienced different average variable returns to scale technical efficiency in particular periods. Notwithstanding, the KwaZulu-Natal subunit was in average able to maximise productivity, which is the level of passenger intake. However, the KwaZulu-Natal subunit should have maintained a reduced input size over the horizon to maximize its production. This is in line with Banker et al. (1984)'s notion of the most productive scale size since the KwaZulu-Natal subunit experienced comparative average productivity of prevalent decreasing returns to scale. In contrast, Gauteng and Western Cape subunits were on average performing below their optimal scales and thus are inefficient in the use of their capacity in relation to the size of their operations. Moreover, at certain periods these two subunits should have reduced their input size to achieve an optimal scale.
Measuring the efficiency of a State-Owned Enterprise is an important tool for management and decision-makers. The efficiency improvement of any of the three Metrorail subunits has a positive contribution to the overall efficiency of Metrorail. However, one way of correcting inefficiency is to pay attention to the inefficient subunits of Gauteng and Western Cape in relation to the performance efficiency of KwaZulu-Natal. The former two subunits appear to be operating below optimal capacity and are not capitalizing on their relatively large sizes. Therefore, in the cognition of the relatively large size of the two subunits and their concomitant inefficiency levels, management should consider modification of the size of their operations in order to optimise production. Thus, KwaZulu-Natal subunit is a close standard of reference against which productivity for Metrorail subunits may be compared. The main limitation of this study is the availability of data in relation to other factors of production which could have been used to evaluate efficiency performances of the three Metrorail subunits. Further research can be conducted on the determinants of other productive factors or/and environmental factors that impact on the productivity and efficiency of Metrorail and its subunits. Also, a study can be done on the reconfiguration of Metrorail and its subunits to advance operational efficiencies.