Assessing Road Safety in Morocco’s Regions from 2014 to 2022: A DEA-MPI Benchmarking Analysis

Abstract

Assessing road safety performance in various regions of a country is crucial for improving overall road safety conditions and reducing the global mortality rate. This study employs the data-envelopment-analysis-based Malmquist productivity index (DEA-MPI) to comprehensively assess the progress of road safety performance in different regions of Morocco over time. Using a dataset spanning from 2014 to 2022, which contains data on road accidents, fatalities, injuries, the number of vehicles, and road traffic, this article evaluates the efficiency evolution across Morocco’s twelve regions. The study results show that the improvement of Morocco’s road safety performance during the studied period is unsatisfying and far from reaching the objectives of the current road safety strategy, which aims to reduce the number of fatalities by 50% by 2026. Moreover, the Malmquist productivity index (MPI) approach, which decomposes total factor productivity change into efficiency and technical changes, revealed that neither component shows a consistent trend throughout the studied period. This indicates that performance progress over time is insufficient and falls short of expectations, underscoring the immediate need for both technical and managerial improvements to address the current road safety challenges effectively.

1. Introduction

Growing recognition exists that road traffic accidents, with their attendant injuries and fatalities, are a preventable public health concern [1,2,3]. In accordance with guidance from the World Health Organization, many nations are actively working to improve their road safety conditions [4]. In October 2021, the World Health Organization (WHO) initiated the Second Decade of Action by introducing the Global Plan for the Decade of Action for Road Safety 2021–2030 [5]. The primary aim of this plan is to achieve a minimum 50% reduction in road traffic fatalities and severe injuries by 2030. Achieving this ambitious goal necessitates consistent and enduring efforts from every nation [5]. Consequently, there is a growing need for each country to evaluate the performance of its regions over time to ensure a comprehensive and equitable approach to improving road safety. Recognizing that road traffic accidents and their consequences vary from one region to another, this intra-country evaluation allows for a tailored response to address specific challenges in each area. By assessing regional disparities in road safety outcomes and identifying the underlying factors contributing to these differences, this analysis can trigger more effective resource allocation and enable policymakers to implement targeted interventions where they are most needed. This not only enhances the effectiveness of road safety measures but also ensures that every region is actively involved in the effort to reduce road traffic fatalities and severe injuries. Morocco is no exception to this global challenge; it is actively working to enhance its infrastructure and struggling to ensure the safety of its roads.

Morocco implemented its first national road strategy from 2003 to 2013 with the primary objective of sustainably reducing fatal crashes on Moroccan roads [6]. Although the strategy showed some progress, its effectiveness was not consistent throughout the entire duration. Consequently, an analysis of its impact led to the development of a more comprehensive second national road safety strategy, operational from 2017 to 2026 [6]. This ongoing strategy revolves around five primary elements: pedestrians, motorcycles, single-vehicle accidents, children, and professional transport. Its objectives include reducing the number of fatalities by 50% between 2017 and 2026. Hence, Moroccan decision makers must proactively monitor road safety performance by implementing intermediate action plans designed to facilitate the realization of the strategy’s objectives. Various approaches have been employed to assess road safety and assist policymakers in their decision-making processes. Data envelopment analysis (DEA) along with its variations is among the most used methods for performance evaluation in different fields [7]. It has become the principal method for road safety performance evaluation [8]. It is also recognized as a managerial tool that plays a crucial role in pinpointing the strengths and weaknesses of the decision-making units (DMUs) under evaluation, setting targets, and determining the ranking of the units being assessed [9]. Nevertheless, the application of the DEA model is primarily oriented towards comparing the status of multiple units at a single time point. Challenges arise when attempting to compare historical data and make judgments about future development trends [10]. To capture this variability and assess the dynamics of road safety performance, the data-envelopment-analysis-based Malmquist productivity index approach (DEA-MPI) emerges as a powerful tool [11]. The Malmquist productivity index (MPI) is a measure used in productivity analysis to assess efficiency changes over time [12]. It was first introduced by [13] and has been widely applied since then in different sectors, including assessing road safety, demonstrating the effectiveness of the DEA-MPI methodology.

The DEA-MPI methodology has emerged as a valuable tool for evaluating road safety performance over time. Presently, many researchers employ the DEA-MPI method to examine the temporal variations in road traffic performance [12]. For example, Ref. [14] employed DEA and Malmquist indices to evaluate the accomplishment of goals within the operational units of the Norwegian Public Roads Administration (NPRA) responsible for traffic safety services from 1996 to 1999. The findings indicate that technological advancements have been the primary drivers of safety improvements during this period. Ref. [11] developed a DEA-based Malmquist index model to assess the relative efficiency and productivity of U.S. states in decreasing the number of fatal crashes. They consolidated five input factors and a sole output, representing fatal crashes, into a unified road safety score. This composite score was then incorporated into the DEA-based Malmquist index mathematical model to assess the relative efficiency of 50 U.S. states from 2002 to 2008. Ref. [15] utilized the DEA-MPI methodology to assess road safety progression across 26 European countries from 2001 to 2010. The findings indicate substantial advancements in road safety within the majority of Member States over the decade, highlighting that their improvement was significantly achieved through the adoption of new technologies to enhance productivity. In their study, Ref. [16] employed the DEA-MPI methodology to assess the road safety performance of 31 Iranian provinces from 2014 to 2016. The findings reveal a consistent annual decrease in safety performance of 22.24%, suggesting that this decline in road safety was primarily attributable to technological regress. The study was intended to provide additional motivation for underperforming provinces to enhance their future performance. Ref. [12] employed the DEA-MPI methodology to assess the evolution of road safety performance from 2007 to 2016. They utilized three road risk indicators as inputs and four road accident outcome indicators as outputs. The findings indicate significant advancements in road safety across the majority of provinces during the past decade.

On this basis, the objective of this research is to assess the evolution of road safety performance in Morocco from 2014 to 2022. The analysis aims to offer valuable insights for decision makers and the road safety authorities in Morocco, with the intention of triggering improvements in underperforming regions and enhancing their future road safety performance. The subsequent sections of this article are structured as follows: In Section 2, we introduce a concise analysis of the data used to assess the road safety performance of the Moroccan regions. Section 3 offers a brief explanation of each technique employed in this study, specifically the DEA methodology and the DEA-MPI approach. The results of the proposed model are outlined and discussed in Section 4. Finally, we conclude by addressing the potential impact and significance of our work in Section 5, along with potential avenues for future research and extensions.

2. Data Description for Characterizing the Road Safety Performance of Moroccan Regions

To assess the road safety performance of Moroccan regions, seven metrics, namely, cars per region (number), road traffic (in millions of vehicle kilometers per day), non-fatal accidents (number), fatal accidents (number), fatalities (people), minor injuries (people) and serious injuries (people) are used to characterize the state of road safety in Morocco. The data for these metrics were sourced from accident and traffic data statistics in Morocco from 2014 to 2022.

The statistical data for the seven metrics used to characterize road safety in Moroccan regions from 2014 to 2022, along with the trend in their evolution, are presented in

Table 1. The statistical data for the seven metrics that characterize road safety in Moroccan regions between 2014 and 2022.

Metric	Cars per Region	Road Traffic	Non-Fatal Accidents	Fatal Accidents	Fatalities	Minor Injuries	Serious Injuries
Min	60,000	0.28	74	8	9	313	36
Max	2,366,865	22.15	38,416	746	819	53,664	2815
Mean	346,246	8.80	7313	264	295	10,161	839
Std.Dev	511,589	6.37	8006	195	218	11,270	606

and Figure 1.

Table 1 reveals significant variations in road safety metrics across various Moroccan regions over the analyzed years. The variation in the number of cars per region, spanning from 60,000 to over 2.3 million, underscores the diverse traffic conditions across different areas. Furthermore, the daily road traffic, ranging from 0.28 to 22.15 million vehicle kilometers per day, demonstrates substantial regional differences in transportation activity. The considerable variability in non-fatal accidents, fatal accidents, and fatalities underscores the necessity for targeted safety measures. The wide standard deviations across all metrics indicate significant disparities among regions, highlighting the complexity of road safety dynamics.

The COVID-19 pandemic lockdowns and restrictions in 2020 led to a significant reduction in human activity, which had a clear impact on road safety. With fewer cars on the road and reduced travel overall, there was a noticeable decrease in road accidents, fatalities, and injuries. As shown in Figure 1, the number of traffic incidents dropped sharply compared to previous years. The unique circumstances of the pandemic unexpectedly resulted in safer roads during that period.

Based on the findings (see Figure 1), it is evident that there is a positive correlation among road safety metrics related to accidents, fatalities, and injuries in Morocco. To better understand this correlation, we generated a correlation matrix using the available data on the seven road safety metrics, and the results are shown in

Table 2. Correlation between the seven metrics that characterize road safety in Morocco.

	Cars per Region	Road Traffic	Fatalities	Non-Fatal Accidents	Fatal Accidents	Minor Injuries	Serious Injuries
Cars per region	1	0.991187	−0.36247	0.903282	−0.00149	0.890483	0.160691
Road traffic	0.991187	1	−0.36069	0.90446	0.03507	0.892734	0.138229
Fatalities	−0.36247	−0.36069	1	0.04879	0.815417	0.067109	0.790788
Non-fatal accidents	0.903282	0.90446	0.04879	1	0.337393	0.998869	0.503304
Fatal accidents	−0.00149	0.03507	0.815417	0.337393	1	0.344158	0.787169
Minor injuries	0.890483	0.892734	0.067109	0.998869	0.344158	1	0.510747
Serious injuries	0.160691	0.138229	0.790788	0.503304	0.787169	0.510747	1

.

As all the correlation coefficients in the lower part of the correlation matrix (indicated by a darker color) are positive, the metrics—fatalities, non-fatal accidents, fatal accidents, minor injuries, and serious injuries—move in the same direction. When one metric increases, the others also increase, albeit with different intensities. This analysis reveals a strong positive correlation between ‘minor injuries’ and ‘non-fatal accidents’. Additionally, there is a strong positive correlation among ‘fatalities’, ‘fatal accidents’, and ‘serious injuries’. We also observed a strong correlation between the number of cars per region and road traffic, which makes sense as traffic levels typically rise with the number of vehicles.

Based on the data description provided below and following several discussions with decision makers, we have decided to use four key metrics—number of cars per region, road traffic, fatalities, and injuries—to define the inputs and outputs for the upcoming DEA-MPI methodology. This will facilitate cross-regional benchmarking of road safety performance across various Moroccan regions. To convert a minimization metric Ii into a maximization metric Ii’, a simple trick is employed. We substitute Ii with Ii’ such that Ii’ = 1/Ii. The inputs and outputs used in the DEA-MPI methodology are illustrated in Figure 2.

The entities called decision-making units (DMUs) to be evaluated across time by the used DEA-MPI methodology are the different regions of Morocco, namely:

Region 1: Béni Mellal-Khénifra

Region 2: Casablanca-Settat

Region 3: Dakhla-Oued Ed Dahab

Region 4: Drâa-Tafilalet

Region 5: Fès-Meknès

Region 6: Guelmim-Oued Noun

Region 7: Laâyoune-Sakia El Hamra

Region 8: Marrakech-Safi

Region 9: Oriental

Region 10: Rabat- Salé- Kénitra

Region 11: Souss-Massa

Region 12: Tanger-Tétouan-Al Hoceima

In light of the current road safety strategy’s objective to achieve a 50% reduction in fatalities by 2026, we will compare the trend of fatalities with that of road safety performance using the data-envelopment-analysis-based Malmquist productivity index methodology (DEA-MPI).

3. Research Methodology

This section offers a clear and concise explanation of each technique used in this study. It starts with an introduction to the basic DEA model, which is used to evaluate the performance of various decision-making units (DMUs). It then provides a brief overview of the DEA-MPI methodology, which is employed to assess the changes in total factor productivity and its components among DMUs over time.

3.1. Basic DEA Model

Data envelopment analysis (DEA) is a mathematical methodology based on linear programming and production theory, pioneered by [17] in 1978. In the standard version of DEA, the aim is to assess and compare different decision-making units (DMUs) based on their capacity to transform various inputs into numerous outputs. The rationale behind the use of DEA is to evaluate efficiency from the perspectives of either maximizing outputs or minimizing inputs through the application of linear programming methods. An output-oriented approach allows for maintaining the level of inputs and adjusting the output levels to maximize efficiency. An output-oriented specification appears more fitting for the road safety sector, given that the input data utilized by the DEA-MPI methodology, as outlined in Section 2, are beyond our control. DEA’s principal strength lies in its ability to benchmark similar units without relying on subjective weighting procedures. It allows the calculation of an overall performance score for a decision-making unit (DMU), known as “efficiency.” This efficiency metric quantifies how effectively inputs are employed to generate outputs within the predefined scope, without the need for subjective judgments in the process. Hereafter is the basic DEA model in its general output maximization form for calculating the road safety performance score (RSPS) (x_k, y_k) for DMUk or region (k) under evaluation:

$$\begin{array}{cc}\mathrm{RSPS} (x_k, y_k)=\max \mathrm{\theta }\mathrm{k}\hfill & \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\end{array}$$

Subject to

$$\begin{array}{cc}\mathrm{\theta }\mathrm{k}{y}_{rk}-{\sum }_{j=1}^n{\mathsf{\lambda }}_j{y}_{rj} \le 0 \hspace{1em}\hspace{1em}\mathrm{r} = 1,\dots ,\mathrm{s}\hfill & \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\\ x_{ik }-{\sum }_{j=1}^n{\mathsf{\lambda }}_j{x}_{ij} \ge 0 \hspace{1em}\hspace{1em}\hspace{1em}\mathrm{i} = 1,\dots ,\mathrm{m}\hfill & \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\\ {\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\mathsf{\lambda }}_j \ge 0 \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\mathrm{j} = 1,\dots ,\mathrm{n}\hfill & \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\end{array}$$

(1)

where θk represents the road safety performance score of regions (k) (the region under assessment), ${\lambda }_j$ represents the associated weighting of outputs and inputs of firm j, x_ik and y_rk refer to the ith input and rth output of region (k) under evaluation. x_ij and y_rj refer to the ith input and rth output of region (j).

3.2. DEA-Based Malmquist Productivity Index Methodology (DEA-MPI)

The research primarily uses the DEA-MPI proposed by [18] to examine the performance evolution of road safety in various regions of Morocco over time. The DEA-Malmquist methodology is capable of analyzing data with multiple inputs and outputs, allowing for an examination of the evolution of total factor productivity across decision-making units (DMUs) over time [12].

The total factor productivity change (Tfpch) can be decomposed into two distinct components, namely, efficiency change (Effch) or catch-up effect representing the capability of an inefficient DMU to catch up with the best-performing ones, and technical change (Techch) or frontier-shift effect to capture the progress or regress in frontier technology of the DMUs [19]. According to [20], efficiency change (Effch) can also be decomposed into two distinct efficiencies, i.e., pure technical efficiency change (Pech) and scale efficiency change (Sech). Hereafter, the global formula of total factor productivity change (Tfpch) is as follows:

$$\begin{gathered} \mathit{Tfpch}=\mathit{P}\mathit{e}\underbrace{\mathit{c}\mathit{h} \times \mathit{S}\mathit{e}\mathit{c}}\mathit{h} \times \mathit{Techch} \\ \mathit{Effch}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} \end{gathered}$$

(2)

Pure technical efficiency change (Pech) assesses the improvement or deterioration in efficiency when utilizing inputs to generate outputs, all while keeping the same scale of operations, whereas scale efficiency change (Sech) assesses the change in the overall scale of operations, reflecting the ability of a firm to adjust its size or scale of production relative to its optimal scale. Technical change (Techch) reflects changes in technology or the production frontier over time. The efficiency change (Effch) of a DMUk from period t to t + 1 can be determined by calculating the ratio of these two efficiency scores, presented in the following manner:

$$\frac{\mathrm{Effch}={\mathrm{R}\mathrm{S}\mathrm{P}\mathrm{S}}^{t+1}({\mathrm{x}}_k^{t+1},{\mathrm{y}}_k^{t+1})}{{\mathrm{R}\mathrm{S}\mathrm{P}\mathrm{S}}^t({\mathrm{x}}_k^t,{\mathrm{y}}_k^t)}$$

(3)

RSPSt $(x_k^t,y_k^t)$ represents the road safety performance score of DMUk at period t and can be derived from Equation (1) as expressed below:

$$\begin{array}{cc}\mathrm{RSPSt} ({\mathrm{x}}_k^t, {\mathrm{y}}_k^t)=\max \mathrm{\theta }\mathrm{k}\hfill & \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\end{array}$$

Subject to

$$\begin{array}{cc}\mathrm{\theta }\mathrm{k} y_{rk}^t-{\sum }_{j=1}^n{\mathsf{\lambda }}_j{y}_{rj}^t \le 0 \hspace{1em}\hspace{1em}\mathrm{r} = 1,\dots ,\mathrm{s}\hfill & \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\\ x_{ik}^t -{\sum }_{j=1}^n{\mathsf{\lambda }}_j{x}_{ij}^t \ge \hspace{1em}\hspace{1em}\mathrm{i} = 1,\dots ,\mathrm{m}\hfill & \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\\ {\hspace{1em}\hspace{1em}\hspace{1em}\mathsf{\lambda }}_j \ge 0 \hspace{1em}\hspace{1em}\hspace{1em}\mathrm{j} = 1,\dots ,\mathrm{n}\hfill & \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\end{array}$$

(4)

Effch > 1 signifies progress in the relative road safety performance score of DMUk from period t to t + 1. A value of 1 denotes a status quo, and a value lower than 1 indicates a regression in the relative road safety performance efficiency from period t to t + 1.

• Technical change (Techch) of DMUk reflects changes in the technology frontier from period t to t + 1 and can be determined by calculating the geometric mean of Techch $(x_k^t,y_k^t)$ and Techch $(x_k^{t+1},y_k^{t+1})$ as expressed below:

$$\mathrm{Techch}=\sqrt{\mathrm{T}\mathrm{e}\mathrm{c}\mathrm{h}\mathrm{c}\mathrm{h}\left({\mathrm{x}}_k^t,{\mathrm{y}}_k^t\right)\times \mathrm{T}\mathrm{e}\mathrm{c}\mathrm{h}\mathrm{c}\mathrm{h}\left({\mathrm{x}}_k^{t+1},{\mathrm{y}}_k^{t+1}\right)}$$

(5)

$$\begin{array}{cc}\mathrm{With}\hspace{1em}\hspace{1em}\hspace{1em}& \{\begin{array}{l}\mathrm{Techch}({\mathrm{x}}_k^t,{\mathrm{y}}_k^t)=\frac{{\mathrm{R}\mathrm{S}\mathrm{P}\mathrm{S}}^t({\mathrm{x}}_k^t,{\mathrm{y}}_k^t)}{{\mathrm{R}\mathrm{S}\mathrm{P}\mathrm{S}}^{t+1}({\mathrm{x}}_k^t,{\mathrm{y}}_k^t)}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\mathrm{(6)}\hfill \\ \hspace{1em}\\ \mathrm{Techch}({\mathrm{x}}_k^{t+1},{\mathrm{y}}_k^{t+1})=\frac{{\mathrm{R}\mathrm{S}\mathrm{P}\mathrm{S}}^t({\mathrm{x}}_k^{t+1},{\mathrm{y}}_k^{t+1})}{{\mathrm{R}\mathrm{S}\mathrm{P}\mathrm{S}}^{t+1}({\mathrm{x}}_k^{t+1},{\mathrm{y}}_k^{t+1})}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} \mathrm{(7)}\hfill \end{array}\end{array}$$

RSPSt + 1 $({\mathrm{x}}_k^t,{\mathrm{y}}_k^t)$ and RSPSt $({\mathrm{x}}_k^{t+1},{\mathrm{y}}_k^{t+1})$ in Equations (6) and (7) can be derived from Equation (1) as expressed below:

$$\begin{array}{cc}\mathrm{RSPSt} ({\mathrm{x}}_k^{t+1}, {\mathrm{y}}_k^{t+1})=\max \mathrm{\theta }\mathrm{k}\hfill & \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\end{array}$$

Subject to

$$\begin{array}{cc}\mathrm{\Theta }\mathrm{k} y_{rk}^{t+1}-{\sum }_{j=1}^n{\mathsf{\lambda }}_j{y}_{rj}^t \le 0 \hspace{1em}\hspace{1em}\mathrm{r} = 1,\dots ,\mathrm{s}\hfill & \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\\ x_{ik}^{t+1} -{\sum }_{j=1}^n{\mathsf{\lambda }}_j{x}_{ij}^t \ge 0 \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\mathrm{i} = 1,\dots ,\mathrm{m}\hfill & \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\\ {\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\mathsf{\lambda }}_j \ge 0 \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\mathrm{j} = 1,\dots ,\mathrm{n}\hfill & \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\end{array}$$

(8)

$$\begin{array}{cc}\mathrm{RSPSt}+1 ({\mathrm{x}}_k^t, {\mathrm{y}}_k^t)=\max \mathrm{\theta }\mathrm{k}\hfill & \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\end{array}$$

Subject to

$$\begin{array}{cc}\mathrm{\theta }\mathrm{k} y_{rk}^t-{\sum }_{j=1}^n{\mathsf{\lambda }}_j{y}_{rj}^{t+1} \le 0 \hspace{1em}\hspace{1em}\mathrm{r} = 1,\dots ,\mathrm{s}\hfill & \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\\ x_{ik}^t -{\sum }_{j=1}^n{\mathsf{\lambda }}_j{x}_{ij}^{t+1} \ge 0 \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\mathrm{i} = 1,\dots ,\mathrm{m}\hfill & \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\\ {\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} \mathsf{\lambda }}_j \ge 0 \hspace{1em} \hspace{1em}\hspace{1em} \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\mathrm{j} = 1,\dots ,\mathrm{n}\hfill & \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\end{array}$$

(9)

Techch > 1 signifies progress in the technology frontier of DMUk from period t to t + 1. A value of 1 denotes a status quo, whereas a value lower than 1 indicates regression in the technology frontier.

• Total factor productivity change (Tfpch) of DMUk from period t to t + 1 can then be expressed as the product of Effch and Techch, as follows:

$$\mathrm{Tfpch}=\sqrt{{\displaystyle \frac{{\mathrm{R}\mathrm{S}\mathrm{P}\mathrm{S}}^t({\mathrm{x}}_k^{t+1},{\mathrm{y}}_k^{t+1})}{{\mathrm{R}\mathrm{S}\mathrm{P}\mathrm{S}}^t\left({\mathrm{x}}_k^t,{\mathrm{y}}_k^t\right)}}\times {\displaystyle \frac{{\mathrm{R}\mathrm{S}\mathrm{P}\mathrm{S}}^{t+1}({\mathrm{x}}_k^{t+1},{\mathrm{y}}_k^{t+1})}{{\mathrm{R}\mathrm{S}\mathrm{P}\mathrm{S}}^{t+1}({\mathrm{x}}_k^t,{\mathrm{y}}_k^t)}}}$$

(10)

Tfpch > 1 signifies an improvement in the total factor productivity of DMUk from period t to t + 1. A value of 1 denotes a status quo, whereas a value lower than 1 indicates a deterioration in total factor productivity.

4. Results and Discussion

4.1. Road Safety Performance Evaluation of Moroccan Regions

The evaluation of performance has become a crucial strategy for enhancing road safety and facilitating the identification of best practices through benchmarking [14]. The road safety performance scores (RSPSk) for the Moroccan regions from 2014 to 2022 are illustrated in

Table 3. Road safety performance scores (RSPSk) for the Moroccan regions from 2014 to 2022.

Regions	2014	2015	2016	2017	2018	2019	2020	2021	2022
Region 1	0.149	0.139	0.264	0.122	0.097	0.106	0.111	0.129	0.098
Region 2	0.002	0.004	0.006	0.002	0.172	0.002	0.003	0.003	0.003
Region 3	1.000	1.000	1.000	1.000	0.004	1.000	1.000	1.000	1.000
Region 4	0.168	0.124	0.652	0.271	1.000	0.196	0.231	0.207	0.190
Region 5	0.058	0.028	0.057	0.025	0.342	0.019	0.026	0.025	0.022
Region 6	0.480	0.348	1.000	0.378	0.036	0.419	0.338	0.350	0.386
Region 7	0.741	0.496	1.000	0.606	0.485	0.502	0.449	0.375	0.560
Region 8	0.013	0.010	0.036	0.015	0.813	0.012	0.014	0.015	0.014
Region 9	0.072	0.076	0.229	0.081	0.021	0.061	0.079	0.087	0.075
Region 10	0.025	0.009	0.024	0.014	0.143	0.010	0.012	0.012	0.010
Region 11	0.026	0.023	0.067	0.033	0.016	0.028	0.026	0.026	0.025
Region 12	0.048	0.038	0.144	0.065	0.042	0.048	0.061	0.060	0.057

.

According to Table 3, the road safety performance score for Moroccan regions from 2014 to 2022 ranges from 0.002 to 1. Region 3 consistently demonstrated high efficiency throughout the analyzed period, being efficient in 8 out of 9 years. The number of DEA-efficient regions with road safety performance scores equal to 1 for each year from 2014 to 2022 is 1, 1, 3, 1, 1, 1, 1, 1, and 1, respectively. This indicates that only in the year 2016 were there three DEA-efficient regions. Specifically, for that year, regions 3, 6, and 7 serve as peer units, suggesting that inefficient regions can refer to these peer units as role models to enhance their efficiency. The minimum score for road safety performance was 0.001. Additionally, the average score was 0.23, suggesting substantial room for improvement among the various regions. On average, the outputs can be reduced by 77% while maintaining the same level of performance for each region. In other words, the original metrics used in the output formulation can be increased up to 4.34 times without changing the performance level. Figure 3 illustrates the average road safety performance scores for Moroccan regions throughout the study period.

The average scores could assist decision makers in comprehending and benchmarking the state of road safety within different Moroccan regions and offer recommendations for improvement. During the studied period, regions 3, 6, and 7 emerged as the top performers, each achieving scores surpassing 0.40. These regions can serve as role models for others, providing justification for the results obtained in Table 3. The average road safety performance scores for the remaining regions varied between 0.022 and 0.338. This indicates a substantial opportunity for these regions to improve their performance in the future by adjusting the level of their outputs for the same level of inputs. The dynamic nature of role model regions suggests that the DEA method may not be sufficient for comparing regions across different time periods, as the role model regions in one year could vary in the subsequent year. Hence, the importance of using DEA-MPI.

Figure 4 illustrates the average road safety performance scores by year for the 12 Moroccan regions.

It can be observed that the average scores for road safety performance range from 0.191 to 0.373 annually, which is comparatively low when compared to the road safety performance score of an efficient region. The year 2016 achieved the highest performance score compared to other years under study. According to decision makers, the improvement in the average road safety performance in 2016 is attributed to Morocco’s new territorial division in 2015, transitioning from 16 to 12 regions, as illustrated earlier. However, it is noticeable that progress was not consistent throughout the entire duration. Identifying the origins of underperformance and executing remedial action plans proves to be necessary. In fact, a multifaceted analysis encompassing the identification of underperformance origins, the assessment of specific initiatives, and a comprehensive evaluation of road safety trends is essential for formulating informed and impactful strategies moving forward. Therefore, it is crucial to analyze the efficiency change by calculating the evolution of total factor productivity along with its components within the studied period.

4.2. Efficiency Change of Moroccan Regions: Total Factor Productivity Change and Its Components

To assess the ongoing road safety developments in Moroccan regions during the studied period, four different metrics were utilized to define both outputs and inputs, as outlined in Section 2. The data for these metrics were sourced from accident and traffic data statistics in Morocco spanning from 2014 to 2022.

The DEA-MPI is currently employed to assess the extent to which the 12 regions have enhanced their road safety levels throughout the studied period. The evolution of total factor productivity change, as well as its components (efficiency change and technical change), is illustrated in Figure 5, accompanied by the trends in road fatalities over the same period.

The upper graph in the Figure 5 illustrates the trend of the average total factor productivity change for the 12 regions, as well as the averages of its components (efficiency change and technical change) from 2015 to 2022. It characterizes the divergence of the Effch and Techch indicators. The Tfpch indicator is the resultant of the combined effects of Effch and Techch and varies in a very small range of values, i.e., the scientific interest is primarily in understanding the dialectical contradiction between the Effch and Techch indicators. The absence of total factor productivity change data for 2014 is due to its calculation requiring information from 2013, which is not included in the study.

Observing the evolution of Tfpch, we note that, on average, the different regions of Morocco have experienced a slight improvement in road safety performance from 2015 to 2020, totaling approximately 25.5%. The year 2020 was characterized by the imposition of lockdowns in response to the COVID-19 pandemic, justifying the sudden decrease in fatalities. However, a significant decline in both Tfpch and Techch was observed in 2021. This decline is primarily associated with the post-COVID-19 period, marked by the lifting of lockdowns and the easing of health restrictions. Consequently, there has been an upturn in the number of fatalities. The observed decline in Tfpch, amounting to 31.35%, can be attributed to the inefficient utilization of technology due to the impact of lockdowns and various health restrictions.

By comparing the evolution of Tfpch in the upper graph of Figure 5 with that of road fatalities in the lower graph, we observe an almost inverse trend. This is expected because when Tfpch increases, indicating an improvement in efficiency, the corresponding road fatalities show a decline. The decrease in road fatalities was approximately 17% between 2019 and 2020, accompanied by a 7% increase in Tfpch. Conversely, the increase in road fatalities was around 22.62% from 2020 to 2021, and this was associated with a decrease in Tfpch of about 31.35%.

By examining the components of Tfpch, namely, Effch and Techch in the upper graph of Figure 5, it becomes evident that the improvement in road safety during the studied period is insufficient and far from reaching the objectives of the current road safety strategy, which aims to reduce the number of fatalities by 50% by 2026. Moreover, none of the components exhibit a consistent trend throughout the studied period. This underscores the immediate importance of implementing improvement measures, both technically and managerially, to address the situation effectively.

Substantial efforts are essential from Moroccan regions to achieve the goals outlined in the current road safety strategy by 2026. Each region should assess its own road safety performance in comparison to others. Consequently, regions with poor efficiency should draw inspiration from benchmark regions, employing them as role models for formulating their road safety strategies.

This work represents a substantial effort to assess the progress of road safety in Moroccan regions during the analyzed period. It provides an easy and accessible method for evaluating the efficiency of regions and assisting those that are less efficient in recognizing their opportunities. Initially, each region should clarify the factors that enable or hinder them from achieving higher road safety performance, based on the results obtained through the DEA-MPI approach. Following this, every region with inefficiencies should undergo a comprehensive comparison with the most pertinent benchmark regions.

Finally, the DEA-MPI approach demonstrates significant efficacy in assessing and improving road safety outcomes across diverse geographical contexts. Its adaptability makes it a valuable tool for decision makers to comprehensively evaluate and enhance road safety performance in regions worldwide. By offering a systematic analysis of road safety progress over time, our approach provides a foundation for evidence-based decision making on a global scale. Policymakers in various countries can leverage the insights derived from our methodology to trigger targeted action plans, fostering continuous improvement in road safety practices and ultimately contributing to safer transportation systems internationally.

4.3. Examining the Relationship between Road Safety Metrics and Tfpch

To better understand the link between the seven road safety metrics and Tfpch, we generated a correlation matrix using the available data. The results are presented in

Table 4. Correlation between the seven road safety metrics in Morocco and Tfpch.

	Cars per Region	Road Traffic	Fatalities	Non-Fatal Accidents	Fatal Accidents	Minor Injuries	Serious Injuries	Tfpch
Cars per region	1	0.991187	−0.36247	0.903282	−0.00149	0.890483	0.160691	0.350386
Road traffic	0.991187	1	−0.36069	0.90446	0.03507	0.892734	0.138229	0.372225
Fatalities	−0.36247	−0.36069	1	0.04879	0.815417	0.067109	0.790788	−0.73897
Non-fatal accidents	0.903282	0.90446	trigger	1	0.337393	0.998869	0.503304	0.017008
Fatal accidents	−0.00149	0.03507	0.815417	0.337393	1	0.344158	0.787169	−0.67297
Minor injuries	0.890483	0.892734	0.067109	0.998869	0.344158	1	0.510747	0.01948
Serious injuries	0.160691	0.138229	0.790788	0.503304	0.787169	0.510747	1	−0.5803
TFPCH	0.350386	0.372225	−0.73897	0.017008	−0.67297	0.01948	−0.5803	1

.

According to Table 4, total factor productivity change (Tfpch) reveals a range of relationships with road safety metrics, highlighting complex interactions. Specifically, Tfpch exhibits a moderate positive correlation with both the number of cars per region (0.35) and road traffic (0.37). This suggests that as the number of cars and the volume of road traffic increase, there may be a concurrent improvement in Tfpch. This could be due to increased economic activity and efficiency associated with higher traffic and vehicle presence.

In contrast, Tfpch shows a strong negative correlation with several severe road safety metrics: fatal accidents (−0.74), fatal accidents (−0.67), and serious injuries (−0.58). These negative correlations indicate that as the frequency of these severe incidents rises, Tfpch tends to decline significantly. This relationship highlights the detrimental impact of severe road safety issues on overall productivity, likely due to factors such as increased healthcare costs, reduced workforce productivity, and disruptions in economic activities.

Non-fatal accidents and minor injuries, however, display very weak correlations with Tfpch. This suggests that these less severe safety incidents have a minimal effect on productivity. Although these types of accidents are still important for safety and economic reasons, they do not appear to have a substantial impact on Tfpch compared to more severe incidents. Overall, these findings emphasize the importance of addressing severe road safety issues to support productivity improvements, whereas the impact of less severe incidents appears to be less significant.

5. Conclusions and Recommendations

The empirical research conducted in this study employed the DEA-MPI methodology to analyze regional road safety performance in Morocco from 2014 to 2022, highlighting the impact of events such as the COVID-19 pandemic. Our findings reveal that road safety improvements have been insufficient compared to the goals set for a 50% reduction in fatalities by 2026. The study also noted inconsistent trends in total factor productivity components, indicating a need for more effective technical and managerial measures.

The DEA model assessed the efficiency of 12 regions, identifying both efficient and inefficient areas. This analysis provides benchmarks for improving efficiency and highlights the potential for output reduction without affecting performance levels. Positive correlations among metrics suggest that improved road safety performance aligns with reductions in fatalities and injuries.

Based on the findings from the empirical analysis, the following recommendations could be suggested:

• Enhance internal organizational management to improve the coordination and efficiency of operational management, fostering effective operations.
• Promote service innovation and the use of new technologies to improve road safety management.

The outcomes of this benchmarking analysis provide valuable insights for policymakers, road safety authorities, and stakeholders in Morocco. However, there is an opportunity to enhance the study’s scope and interpretability by incorporating additional information. This could include factors such as financial resources and road user behaviors (e.g., seat belt use and adherence to speed limits) across different regions of Morocco. A comprehensive approach could significantly improve our understanding of road safety and refine decision-making processes for more effective management. It is important to note that obtaining this supplementary data will require dedicated efforts from decision makers, as a considerable amount of data is currently missing. Moreover, the methodology presented in this study can be applied to evaluate road safety performance in other regions or countries, facilitating cross-national comparisons and knowledge exchange aimed at achieving safer road systems globally. By contributing to this collective effort, this research aims to enhance road safety worldwide.