Mustapha Ouladsine
email: mustapha.ouladsine@univ.u-3mrs.fr

Gérard Bloch
email: gerard.bloch@esstin.uhp-nancy.fr

Xavier Dovifaaz

Neural Modelling and Control of a Diesel Engine with Pollution Constraints

Keywords: Diesel engine, nonlinear modelling, neural networks, neural controller, pollution reduction

The paper describes a neural approach for modelling and control of a turbocharged Diesel engine.

A neural model, whose structure is mainly based on some physical equations describing the engine behaviour, is built for the rotation speed and the exhaust gas opacity. The model is composed of three interconnected neural sub-models, each of them constituting a nonlinear Multi-Input Single-Output Output Error model. The structural identification and the parameter estimation from data gathered on a real engine are described. The neural direct model is then used to determine a neural controller of the engine, in a specialized training scheme minimising a multivariable criterion. Simulations show the effect of the pollution constraint weighting on a trajectory tracking of the engine speed. Neural networks, which are flexible and parsimonious nonlinear black-box models, with universal approximation capabilities, can describe or control accurately complex nonlinear systems, with few a priori theoretical knowledge. The presented work extends optimal neuro-control to the multivariable case and shows the flexibility of neural optimisers. Considering the preliminary results, it appears that neural networks can be used as embedded models for engine control, to satisfy the more and more restricting pollutant emission legislation.

Particularly, they are able to model nonlinear dynamics and outperform during transients the control schemes based on static mappings.

Introduction

Neural techniques are used in various domains and particularly for system modelling and control [START_REF] Chen | Nonlinear system identification using neural networks[END_REF][START_REF] Narendra | Identification and control of dynamical systems using neural networks[END_REF][START_REF] Pham | Neural Networks for Identification, Prediction and Control[END_REF][START_REF] Nørgaard | Neural Networks for Modelling and Control of Dynamic Systems[END_REF]. Neural networks bring important benefits by suppressing theoretical difficulties that appear when applying classical techniques on complex systems. Including nonlinearities in their structure, they can describe or control accurately complex nonlinear systems, with few a priori theoretical knowledge. In [START_REF] Bloch | Neural networks for process control and optimization: Two industrial applications[END_REF], the advantages of neural models are summarized: they are flexible and parsimonious nonlinear black-box models, with universal approximation capabilities.

In this paper, neural techniques are applied to model and control a turbocharged Diesel engine. The objective is to build a model to be used to control the Diesel engine. The engine speed and the exhaust gas opacity that characterizes one type of pollution must be controlled. More precisely, the control should allow reducing the opacity peaks that occur during engine acceleration. Neural networks are used because they can approximate and replace the complex and nonlinear thermodynamical, mechanical and chemical equations that describe the Diesel engine [START_REF] Cook | Engine control systems[END_REF]. For Diesel engines control, neural networks have been already used [START_REF] Hafner | Fast neural networks for diesel engine control design[END_REF].

Other works use neural predictors to optimise Air-Fuel Ratio (AFR) control [START_REF] Majors | Neural network control of automotive fuel injection systems[END_REF][START_REF] Magner | Delta air charge anticipation for mass air flow and electronic throttle control based systems[END_REF]Bloch et al., 2003). The work presented here is application oriented, just as the papers cited above. It extends optimal neuro-control to the multivariable case and shows the flexibility of neural optimisers. Considering the preliminary results, it appears that neural networks can be used as embedded models for engine control, to satisfy the more and more restricting pollutant emission legislation. Particularly, they are able to model nonlinear dynamics and outperform during transients the control schemes based on static mappings. Section 2 presents the building of the neural model for the rotation speed and the exhaust gas opacity. The structure of this model is mainly based on some physical equations describing the engine behaviour. The final model is composed of three interconnected neural sub-models, each of them constituting a nonlinear Multi-Input Single-Output (MISO) Output Error (OE) model. The structural identification (i.e. the determination of the regressor structure and the internal architecture) and the parameter estimation from data gathered on a real engine are described.

Experimental results are then presented.

In section 3, the (direct) model obtained in the previous section is used to determine a neural controller of the engine, in a specialized training scheme based on the minimisation of a multivariable criterion. The simulation of a trajectory tracking of the engine speed with and without pollution constraints is finally presented.

Neural modelling

A neural model of a Diesel engine

A turbocharged Diesel engine can be decomposed into subsystems as presented in Figure 1. The atmospheric air goes through the turbocharger compressor, the air intake manifold, and the combustion chamber. The injection pump injects fuel in the combustion chamber while the valves are closed, and the mixture burns. The gases produced by the explosion pass through the exhaust manifold and turbocharger turbine and are ejected out away. Five states have been modelled: the engine speed , the intake manifold pressure , the inlet airflow , the fuel flow and the opacity of the exhaust gas. This work is mainly focused on the engine speed and exhaust gas opacity. The only control variable considered here is the position of the injection pump. The physical relations that describe the behaviour of an internal combustion engine are used to design the corresponding neural model. Among the different possibilities, the Diesel engine speed R, the intake manifold pressure P and the exhaust gas opacity Op can be described with the following formal relations:

€ dR(t) dt = f R R(t), P(t), T(t) ( ) dP(t) dt = f P R(t), P(t)
( )

Op(t) = f Op R(t), ˙ m (t), ˙ m f (t) ( ) (1)
It is worth noting that the speed dynamics is mainly due to the engine inertia and that the speed value naturally depends on the injected fuel rate and thus on the injection pump position . On the other hand, the opacity depends on the ratio between the air and fuel masses (AFR) used in the combustion, and then on the flows of air

€ ˙ m and fuel € ˙ m f .
These relations are used to construct the neural model used to estimate the speed, the pressure and the opacity. The first step consists in discretizing the previous equations, which gives: Some modifications of the opacity model are needed. First, the opacity is measured at the exhaust of the Diesel engine. This means that there is some pure delay between the opacity measurement and the other variables and that there are some dynamics due to the gas transportation. Secondly, the opacity depends on the injected fuel flow € ˙ m f . Some works [START_REF] Blanke | On modeling large two stroke diesel engines : News results from identification, bridge between control science and technology[END_REF] show that this quantity mainly depends on the engine speed R and on the injection pump position T:

€ R(k) = F R R(k -1),, R(k -n RR ), P(k -1),, P(k -n PR ), T(k -1),, T(k -n TR ) ( ) € P(k) = F P R(k -1),, R(k -n RP ), P(k -1),, P(k -n PP ) ( ) (2)
€ O P (k) = F Op R(k), ˙ m (k), ˙ m f (k) ( )
€ ˙ m f (k) = f R(k),T(k) ( ) (3)
The opacity can be then expressed as:

€ Op(k) = F Op Op(k -1),, Op(k -n Op ), T(k -d), R(k -d), ˙ m (k -d) ( ) (4)
where € d is the delay mentioned above and € n Op the order of the opacity model.

One objective of the modelling is to control the engine. However, the complete model obtained is not easy to use for control because of the interdependency of the speed and pressure models. Some simplifications have been thus carried out. On one hand, the speed at time k depends on the control variable T, the speed R and the pressure P, at previous times. On the other hand, this pressure P depends on speed R at previous times. It is then possible to express the speed as a function depending on the control T and speed R only. Finally, the engine speed, the pressure and the opacity are given by:

€ R(k) = F R R(k -1),, R(k -n RR ), T(k -1),, T(k -n TR ) ( ) P(k) = F P R(k -1),, R(k -n RP ), P(k -1),, P(k -n PP ) ( ) O P (k) = F Op Op(k -1),, Op(k -n Op ), R(k -d), T(k -d), ˙ m (k) ( ) (5)
The three unknown models To complete the models, the orders of the regressors (i.e. the lag space) and the number of nodes in the hidden layer must be determined for each sub-model. The neural structure selection used is presented on Figure 2. For each order value, the neural network is trained with a given node number, chosen large enough, and the Final Prediction Error (FPE) criterion is calculated. The optimal order corresponds to the minimal FPE value. The neural network is then trained with this order, but for several values of the node number in the hidden layer. Again an analysis of the FPE criterion gives the optimal node number corresponding to the minimal FPE value and thus the final network structure. This process is repeated for each network, leading to the final models of speed and opacity:

€ ˆ R (k) = NN R ˆ R (k -1), ˆ R (k -2), T(k -1) ( ) ˆ P (k) = NN P ˆ P (k -1), ˆ R (k -1) ( ) O P (k) = NN OP O P (k -1), T(k -4), ˆ R (k -4), ˙ m (k -4) ( ) (6)
The complete model consists then in three interconnected neural networks. Each neural network is a multilayer perceptron composed of several inputs, an output and a single hidden layer. One of them reconstructs the engine speed R from the control T. The external input of the pressure model is the speed model output. The opacity is estimated from the speed and airflow estimates and the control variable. These recurrent neural networks have been trained using data of the control variable T, the speed R, the airflow € ˙ m and the opacity € Op. The complete simulation model is then obtained by connecting the networks.

Experimental results

The following figures present some results obtained from a real Diesel engine.

Neural control

Introduction and theory

There is presently a vast literature on neuro-control and successive states of the art have been regularly provided (Hunt et [START_REF] Plumer | Optimal control of terminal processes using neural networks[END_REF] and adaptive control [START_REF] Chen | Adaptive control of a class of nonlinear discrete-time systems using neural networks[END_REF]. The control can be direct or indirect, depending on whether a neural model of the system is needed or not. In the presented application, the stability issue of the control scheme is not considered. The approach used for constructing the control is indirect since a neural network model of the engine is used. The controller is a neural network that has to be trained to satisfy the objective of speed tracking with opacity constraint. The training scheme used is the specialized training, generally credited to Psaltis [START_REF] Psaltis | A multilayer neural network controller[END_REF], detailed in [START_REF] Nørgaard | Neural Networks for Modelling and Control of Dynamic Systems[END_REF]. Its principle is displayed on Figure 9. The control parameters (neural controller weights) are generally learned to minimize the sum of squared errors between the reference and the system output. The main difficulty lies in the fact that the minimization algorithm requires the Jacobian of the system, i.e. the derivatives of the output with respect to the input, which, most of the time, is unknown. This problem is overcome by including a neural (direct) model of the system in the training scheme and estimating the Jacobian from this model.

This method was applied to control the engine with, as direct model, the neural model presented in the previous section. The criterion, adapted to include the engine speed and the opacity, is then a multivariable criterion. However, for sake of simplicity, the algorithm, applied in the multivariable case for engine control, is first detailed for a criterion containing only one variable.

To tune the neural controller parameters, a recursive algorithm is used, in an approach very close to adaptive control. The criterion is defined at discrete time t by:

€ J t (W ) = 1 2 e y (W ,k) 2 k=1 t ∑ (7)
where

€ e y (W ,k) = Y ref (k) -Y(W ,k), € Y ref (k) and € Y (k)
are respectively the desired output, i.e. the reference, and the actual output of the system, at time k.

The general rule used to update the weights is as follows:

€ W t = W t-1 -µ t [R t (W t-1 )] -1 J' t (W t-1 ) (8)
where € W t denotes the controller parameter vector

€ W = w 1 w 2 w n (
) T updated at time t, € µ t the step length. The gradient € J'(W ) of the criterion is defined by:

€ J'(W ) = ∂J(W ) ∂w 1 ∂J(W ) ∂w 2  ∂J(W ) ∂w n       T (9)
The matrix € R(W ) can be chosen in various ways. In the steepest descent algorithm, € R(W ) = I (identity matrix). This algorithm is the simplest, but it is rarely efficient and not compatible with the differences of scales that can exist between the parameters. In the Gauss-Newton algorithm,

€ µ t = 1
and € R(W ) is an approximation of the Hessian (or second derivatives) matrix. Some theoretical developments can be found in [START_REF] Ljung | Theory and practice of recursive identification[END_REF][START_REF] Nørgaard | Neural Networks for Modelling and Control of Dynamic Systems[END_REF].

The algorithm description needs to develop the first and the second derivatives of the criterion with respect to the weights. From ( 7):

€ ∂J t (W ) ∂w i = ∂J t-1 (W ) ∂w i + 1 2 ∂e y (W ,t) 2 ∂w i = ∂J t-1 (W ) ∂w i + e y (W ,t) ∂e y (W ,t)
∂w i [START_REF] He | Control of base-excited inverted pendulums using a neural inverse modeling approach[END_REF] and then:

€ J t ' (W ) = J t-1 ' (W ) + e y (W ,t)Ψ y (W ,t) (11)
where

€ Ψ y (W ,t) = ∂e y (W ,t) ∂w 1  ∂e y (W ,t) ∂w n       T ( 12
)
When applying the rule (8), the term

€ J t-1 ' (W t-1
) is considered to be zero since

€ W t minimize € J t at
every step [START_REF] Ljung | Theory and practice of recursive identification[END_REF]. Thus:

€ J t ' (W t-1 ) = e y (W t-1 ,t)Ψ y (W t-1 ,t) (13)
The second derivative is developed as follows:

€ ∂ 2 J t (W ) ∂w i ∂w j = ∂ 2 J t-1 (W ) ∂w j ∂w i + ∂e y (W ,t) ∂w j ∂e y (W ,t) ∂w i + e y (W ,t) ∂ 2 e y (W ,t) ∂w j ∂w i         (14)
Assuming that the error € e y can be considered as a white noise, not correlated with the second derivatives € ∂ 2 e y ∂w j ∂w i , the approximate Hessian of the criterion, at iteration t, € R t , can be written in a matrix form:

€ R t (W ) = R t-1 (W ) + Ψ y (W ,t)Ψ y T (W ,t) (15)
Finally, we have:

€ W t = W t-1 -[R t ] -1 e y (W t-1 ,t)Ψ y (W t-1 ,t) R t = R t-1 + Ψ y (W t-1 ,t)Ψ y T (W t-1 ,t)      (16)
To replace the matrix inversion with a scalar one, the classical matrix inversion lemma is used:

€ W t = W t-1 -P t e y (W t-1 ,t) Ψ y (W t-1 ,t) P t = P t-1 - P t-1 Ψ y (W t-1 ,t) Ψ y T (W t-1 ,t) P t-1 1+ Ψ y T (W t-1 ,t) P t-1 Ψ y (W t-1 ,t)      (17)
The vector € Ψ y , defined in [START_REF] Hunt | Neural networks for control systems -a survey[END_REF], contains the derivatives € ∂e y (W ,t) ∂w i that are developed as follows:

€ ∂e y (W ,t)

∂w i = - ∂Y (W ,t) ∂w i = - ∂Y (W ,t) ∂U(W ,t -1) ∂U(W ,t -1) ∂w i ( 18
)
where U is the input vector of the system, i.e. the neural controller output. Replacing the Jacobian of the system by the Jacobian of the neural model gives:

€ ∂e y (W ,t)

∂w i = - ∂ ˆ Y (W ,t) ∂U(W ,t -1) dU(W ,t -1) dw i ( 19
)
where € ˆ Y (W ,t) is the model output and where € dU(W ,t -1) dw i only depends on the controller structure.

The controller parameter learning method previously described is now applied to a multivariable criterion, involving two system outputs Y and Z. Defining

€ e y (W ,k) = Y ref (k) -Y(W ,k) and € e z (W ,k) = Z ref (k) -Z(W ,k
), the criterion can be written:

€ J(W ) = 1 2
η y e y (W ,k) 2 + η z e z (W ,k) 2 ( )

k=1 t ∑ (20)
where € η y and € η y are weighting factors. In this case, using the same notation as before and using the matrix inversion lemma twice, the final minimisation algorithm is given by:

€ W t = W t-1 -P t η y e y (W t-1 ,t) Ψ y (W t-1 ,t) + η z e z (W t-1 ,t) Ψ z (W t-1 ,t) ( ) M = P t-1 - P t-1 Ψ y (W t-1 ,t) Ψ y T (W t-1 ,t) P t-1 1+ Ψ y T (W t-1 ,t) P t-1 Ψ y (W t-1 ,t) P t = M - M Ψ z (W t-1 ,t) Ψ z T (W t-1 ,t) M 1+ Ψ z T (W t-1 ,t) M Ψ z (W t-1 ,t)            (21)
where

€ Ψ y (W ,t) = ∂e y (W ,t) ∂w 1  ∂e y (W ,t) ∂w n       T and € Ψ z (W ,t) = ∂e z (W ,t) ∂w 1  ∂e z (W ,t) ∂w n       T .

Application to the Diesel engine

This section describes the simulation of Diesel engine control, i.e. the control application where the actual engine is replaced by its model obtained in section 2, as presented on Figure 10. Since the objective is to control the engine speed and the opacity, the criterion is defined by: The controller output is then expressed by a neural function of the following form:

€ J(W ) = 1 2 R ref (k) -R(W ,k) ( ) 2 + η Op Op ref (k + d -1) -Op(W ,k + d -1) ( ) 2       k=1 N ∑ (22)
€ U(k + 1) = NN U R ref (k + 1), R(k), R(k -1), Op ref (k + d), Op(k + d -1) ( ) (23)
Training was carried out using the algorithm presented in [START_REF] Plumer | Optimal control of terminal processes using neural networks[END_REF].

Conclusion

In this paper, we presented a control scheme of Diesel engine speed with pollution constraints. This scheme used the specialized training of a neural controller using a neural direct engine model. To include pollution constraints, the criterion to minimise includes both the engine speed and the exhaust gas opacity. The work extends optimal neuro-control to the multivariable case and shows the flexibility of neural optimisers. The results highlight the interest of using neural networks both for engine modelling and control, despite strong dynamics and nonlinearities (opacity). Obviously, an important work must be done to implement neural controllers on real engines. However, considering the preliminary results, it seems that neural networks can be used as embedded models for engine control, to satisfy the more and more restricting pollutant emission legislation.

Particularly, they are able to model the nonlinear dynamics and outperform during transients the classical control schemes. They could constitute an interesting alternative to the methods employed for pollution control which are based on the use of set point cartographies.

Figure 1 :

 1 Figure 1: Turbocharged Diesel engine.

F

  Op were estimated from data by using neural structures, more precisely conventional MLP (Multi-Layer Perceptron) architectures with one hidden layer of sigmoidal units and linear activation function for the output unit (see[START_REF] Bloch | Neural networks for process control and optimization: Two industrial applications[END_REF], for example). The training (i.e. estimation of the parameters) was performed by minimizing the mean squared error function, with a batch Levenberg-Marquardt algorithm (see[START_REF] Nørgaard | Neural Networks for Modelling and Control of Dynamic Systems[END_REF], for example). Note that each neural model is identified in the form of a Multi-Input Single-Output (MISO) Output Error (or simulation) model, involving, among the regressors, delayed estimates, not delayed measurements, of the output.

Figure 2 :

 2 Figure 2: Structural identification process.

Figures 3 , 4 and 5 present

 35 the measurements and estimations respectively for the speed, pressure and opacity, for data used to train the neural models (identification data). In order to validate the model, another time sequence for the input T was applied to the real system and the neural model. The corresponding measurements and estimations of speed, pressure and opacity are given inFigures 6, 7 and 8.

Figure 3 :

 3 Figure 3: Measurements and estimates of speed (rpm), identification data.

Figure 4 :

 4 Figure 4: Measurements and estimates of pressure (kPa), identification data.

Figure 5 :

 5 Figure 5: Measurements and estimates of opacity (%), identification data.

Figure 6 :

 6 Figure 6: Measurements and estimates of speed, validation data.

Figure 7 :

 7 Figure 7: Measurements and estimates of pressure (kPa), validation data.

Figure 8 :

 8 Figure 8: Measurements and estimates of opacity (%), validation data.

Figure 9 :

 9 Figure 9: Architecture of training for control.

Figure 10 :

 10 Figure 10: Training applied to the engine model.

η

  where € R ref is the speed reference and where € Op ref represents the opacity constraint, defined such that the opacity is reduced during the transients.€ Op is the weighting factor of the opacity constraint. For instance, with € η Op = 0 , the control is a simple engine speed tracking without opacity constraint. The controller output U is calculated by a MLP with one hidden layer of sigmoidal units, from inputs which are the speed and opacity references and the speed and opacity system outputs.

€η€η

  Figures 11 and 12 show the simulation results obtained with the resulting neural controller for three values of the weighting factor, Op = 0, 0.2, 0.8 , for the speed and the opacity respectively.It is worth noting that, when € η Op = 0 , the neural controller performs a good tracking of the engine speed, since the speed output follows precisely the reference. On the contrary, when the opacity constraint is taken into account ( € η Op ≠ 0 ), a tracking error occurs during the transients (acceleration). The peaks of opacity are caused by an excess of injected fuel (depending on the injection pump position U) during engine acceleration. Naturally, to satisfy the opacity constraint, the neural controller calculates U such that less fuel is injected. This leads to a decrease of the acceleration and then to a speed tracking error during the transients. This error increases with the weighting factor Op while in the same time the peaks of opacity decrease.

Figure 11 :

 11 Figure 11: Engine speed (rpm) with respect to time (s).

Figure 12 :

 12 Figure 12: Opacity (%) with respect to time (s).


Rodrigo Freire Lins

Alice Erthal

Dom Fundação

Cabral

Palabras Clave

Supply chain sustainability reporting in the global south: the role of funding

Keywords: Sustentabilidade na cadeia de suprimentos, Transparência, Relato, Stakeholder, Global Reporting Initiative Supply chain sustainability, Transparency, Reporting, Stakeholder, Global Reporting Initiative RESUMÉN Sostenibilidad de la cadena de suministro, Transparencia, Informe corporativo, Stakeholder, Global Reporting Initiative

Companies deal with increasing pressure from multiple stakeholders to report not only their sustainable practices, but also their extended supply chain sustainability (SCS). However, how stakeholder pressures are shaped in the Global South characterized by institutional voids related to contracting, outsourcing, and weak legislation enforcement have received less attention from the literature. This study maps which stakeholder pressures are associated with SCS reporting analyzing an unbalanced panel data of 220 corporate sustainability reports from 2016 to 2018 by Brazilian publicly listed companies. Results show that long-term oriented shareholders and creditors, company size and adoption of GRI guidelines are all associated with higher levels of SCS reporting, while public and regulatory pressures are not, offering support to the institutional voids rationale. In the absence or weakness of regulatory pressures, long-term funding sources and access to resources seem to step-in as associated drivers to SCS reporting.

INTRODUCTION

Corporate sustainability reporting is on the spotlight. What has been labelled as the "Super Transparency Era" pushes companies to improve their reporting and amplifies the risks of miscommunicating and/or ignoring external pressures [START_REF] Austin | Leading in the age of super-transparency[END_REF] .

While corporate reporting addressing environmental and social concerns has become a core corporate activity, a plethora of sustainability-related incidents have showed that sustainability breaches often happens beyond the purview of the focal company, in the extended supply chain instead [START_REF] Marques | Sustainable supply network management: A systematic literature review from a knowledge perspective[END_REF]. Thus, corporate sustainability reporting must include information not only about the company's own activities, but also about their extended supply chain [START_REF] Yadava | Scoring Sustainability Reports Using GRI 2011 Guidelines for Assessing Environmental, Economic, and Social Dimensions of Leading Public and Private Indian Companies[END_REF]. Reporting issues related to supply chain sustainability (SCS) should become then an integral part of corporate sustainability reporting [START_REF] Marshall | What's your strategy for supply chain disclosure?[END_REF], although companies yet do not properly disclosure their actual and potential impacts along their supply chain.

The increased complexity of supply chain [START_REF] Wilhelm | Sustainability in multi-tier supply chains: Understanding the double agency role of the first-tier supplier[END_REF] imposes a significant barrier to SCS reporting. In many cases, ompanies may wish to report, but lack visibility of their own supply chains [START_REF] Sodhi | Research Opportunities in Supply Chain Transparency[END_REF]. Moreover, as the most relevant impacts of a supply chain take place at developing countries, different stakeholders with specific characteristicssuch as more permissive regulationswill influence the level of accountability, thus the level of transparency of a company.

As a response to the combined effects of transparency demands and the supply chain complexity, companies should map the stakeholders´ pressure in order to filter down what needs to be prioritized. The extent that companies can address and communicate environmental and social issues is a reflection of how they perceive the attention that their key stakeholders devote to these concerns [START_REF] Yadava | Scoring Sustainability Reports Using GRI 2011 Guidelines for Assessing Environmental, Economic, and Social Dimensions of Leading Public and Private Indian Companies[END_REF]. Successful companies must shift from a short-term/single-oriented economic focus to a longer-term/multiple-stakeholder approach that balances and incorporate multiple goals from multiple stakeholders [START_REF] Reimsbach | In the Eyes of the Beholder: Experimental Evidence on the Contested Nature of Materiality in Sustainability Reporting[END_REF]. The journey towards effective corporate sustainability reporting is hence a tough one, raising the importance of methodologies that support this process, such as the Global Reporting Initiative (GRI). The GRI offers guidelines to companies on the disclosure to stakeholders about how they deal with their material topics. Supply chains is an element of particular concern in the GRI framework (Islam et al., 2016). It is already known that stakeholders do play a key role in SCS reporting [START_REF] Sodhi | Research Opportunities in Supply Chain Transparency[END_REF]. And that front-runner companies tend to adopt frameworks such as the GRI. However, less is known about what types of stakeholders impose more pressure on SCS reporting [START_REF] Okongwu | The maturity of supply chain sustainability disclosure from a continuous improvement perspective[END_REF]. And even less is known regarding SCS reporting beyond the Global North. Most research on this topic has, firstly, not included supply chain-related issues, and secondly, has been focused on the Global North context [START_REF] Kuzey | Determinants of sustainability reporting and its impact on firm value: Evidence from the emerging market of Turkey[END_REF]. Thus, out study aims to fulfill a gap within research on SCS reporting focusing on the Global Southa core region when discussing environmental and social impacts while characterized by institutional voids that reshape how SCS can be addressed [START_REF] B3 | On the effectiveness of private transnational governance regimes-Evaluating corporate sustainability reporting according to the Global Reporting Initiative[END_REF][START_REF] Silvestre | Sustainable supply chain management in emerging economies: Environmental turbulence, institutional voids and sustainability trajectories[END_REF].

Institutional voids produce uncertainty that result from weak control over outsourcing contracts, untrained labor force, and lack of enforcement of existing legislation [START_REF] Marques | Inhospitable accessibility and blurred liability: Institutional voids in an emerging economy preventing supply network transparency[END_REF]. These institutional voids are all highly related to SCS and their existence allows companies to engage in poor supply chain practices without being punished [START_REF] Khanna | Why focused strategies may be wrong for emerging markets[END_REF]. Institutional voids can also reshape how stakeholder pressures co-exist. For example, while governmental pressures may be weaker, private pressure may become stronger. However, this is yet to be confirmed by research. The present study starts from the research question (RQ):

-Which stakeholder pressures are associated with higher levels of supply chain sustainability (SCS) reporting in the context of institutional voids?

In the following sections, this manuscript offers the theoretical background on corporate sustainability reporting SCS reporting and stakeholder pressures. In doing so, we develop hypotheses of stakeholder influences to SCS reporting in the context of institutional voids. Next, we delineate the research method while grounding our choice of Brazil as a representative of the Global South. Brazil is chosen due to two key reasons. First, previous research has showed that institutional voids influence SCS in the country [START_REF] Silvestre | Sustainable supply chain management in emerging economies: Environmental turbulence, institutional voids and sustainability trajectories[END_REF].

Second, the well-developed stock market allows robust data collection from publicly listed companies issuing annually corporate sustainability reports (In 2020, Brazil was the 14 th stock market in the world, and the 8 th among Global South countries1 ). We offer results on a mixedmethod content analysis of 220 corporate sustainability reports from the 2016-2018 period.

Finally, we present implications to theory and practice, highlighting two key roles of funding as driver of SCS reporting. While funding is represented by pressure from shareholders (via participation in a sustainability index) and creditors (via long-term debt profile), the complementary perspective of access to resources is represented by company size and adoption GRI guidelines which seem interconnected as adherence to standards demands funding and time for knowledge acquisition and implementation.

THEORETICAL BACKGROUND

Supply chain sustainability reporting

SCM has been defined by Mentzer et al (2001, p. 18) as "the systemic, strategic coordination of the traditional business functions and the tactics across these business functions within a particular company and across businesses within the supply chain, for the purposes of improving the long-term performance of the individual companies and the supply chain as a whole". The definition emphasizes the coordination of common goals between the focal company and their suppliers, but historically the goal has been restricted to economic performance. Yet, since 2008, the relationship between sustainability and SCM has been increasingly addressed, giving rise to the term sustainable SCM (SSCM) (Carter & Rogers, 2008, p. 368): "the strategic, transparent integration and achievement of an organization's social, environmental, and economic goals in the systematic coordination of key interorganizational business processes for improving the long-term economic performance of the individual company and its supply chains." The SSCM definition thus expands the notion of common performance to the intersection of environmental, social, and economic performance.

Complementarily, supply chain sustainability (SCS) reflects the company`s balanced efforts to make the extended supply chain comply with sustainability standards [START_REF] Bird | Coupling labor codes of conduct and supplier labor practices: The role of internal structural conditions[END_REF]. Effective SCS reporting can "prevent or reduce reputation damages caused by the public exposure of unacceptable supplier practices or undesirable supply provenance" [START_REF] Sodhi | Research Opportunities in Supply Chain Transparency[END_REF], p. 2950). Good practices related to supply chain sustainability include fair sourcing, transparent contracting conditions, collaboration with suppliers to support their adherence to sustainability standards, among others. [START_REF] Wilhelm | Sustainability in multi-tier supply chains: Understanding the double agency role of the first-tier supplier[END_REF] and [START_REF] Huq | Implementing Socially Sustainable Practices in Challenging Institutional Contexts: Building Theory from Seven Developing Country Supplier Cases[END_REF] discuss the challenges of diffusing such practices and standards in ever complex supply chains. The more complex the supply chains become, the higher the numbers of suppliers to impose new sustainability standards, and the wider the array of stakeholder pressures, that might be eventually conflicting. Therefore, companies find it hard to define exactly which social and environmental concerns they should prioritize.

The path commonly taken by firms to incorporate and prioritize social and environmental concerns along their supply chains has been listening to stakeholder demands. Thus, stakeholder pressures rise as a key driving force towards the adoption of SCS. In order words, companies map the sustainability risks they need to address according to the pressures they receive from multiple stakeholders [START_REF] Reimsbach | In the Eyes of the Beholder: Experimental Evidence on the Contested Nature of Materiality in Sustainability Reporting[END_REF]. In fact, misreading a stakeholder demand may be a source of risk in itself. Conversely, effective listening to and responding to stakeholder demands may companies communicate what they have implemented/ are in the process of implementing.

To ensure quality in their SCS reporting, companies have often resorted to standards such the GRI to reflect commitment to higher standards of public integrity (Islam et al., 2016). GRI guidelines emphasize the importance of reporting topics that are salient for stakeholders and their framework influences how companies respond to stakeholder pressures through reporting while ensuring credibility and comparability of information, making reporting more tangible [START_REF] Yadava | Scoring Sustainability Reports Using GRI 2011 Guidelines for Assessing Environmental, Economic, and Social Dimensions of Leading Public and Private Indian Companies[END_REF], reducing uncertainties, and helping financial analysts generate more accurate forecasts (García-Sánchez et al., 2019a). GRI emphasizes the importance of reporting supply chain related issues, but many companies still fail to provide both quantified and qualitative reporting of their supply chains [START_REF] Rashidfarokhi | Sustainability reporting in the nordic real estate companies: Empirical evidence from Finland[END_REF].

Limited information hinders data access both to researchers and the broader society [START_REF] Jia | Sustainable supply chain management in developing countries: An analysis of the literature[END_REF].

There is a third challenge to SCS reporting related to the Global South reality. In the Global South context, [START_REF] B3 | On the effectiveness of private transnational governance regimes-Evaluating corporate sustainability reporting according to the Global Reporting Initiative[END_REF] and [START_REF] Silvestre | Sustainable supply chain management in emerging economies: Environmental turbulence, institutional voids and sustainability trajectories[END_REF] state that companies face institutional voids that hinder and reshape SCS. Institutional voids mean lack of clarity and enforcement in outsourcing contracts, undeveloped labor market and weak enforcement of existing regulation all feed into turbulence and uncertainty that is less present in the Global North. These institutional voids allow companies to engage in corruption, informality and other poor supply chain practices without being punished [START_REF] Khanna | Why focused strategies may be wrong for emerging markets[END_REF]).

Understanding regional characteristics is thus key to understand SCS reporting more globally [START_REF] Gold | Sustainable Global Agrifood Supply Chains: Exploring the Barriers[END_REF]). Yet, despite the global reality of supply chains, the extant research has devoted more attention to the Global North [START_REF] Jia | Sustainable supply chain management in developing countries: An analysis of the literature[END_REF][START_REF] Kuzey | Determinants of sustainability reporting and its impact on firm value: Evidence from the emerging market of Turkey[END_REF]Silvestre, 2015a) and thus we face a lack of understanding of how companies translate stakeholder pressures into SCS reporting in a reality where institutional voids prevail.

Next, we turn our attention to unpacking the different types of stakeholder pressures that usually pressure companies to engage with SCS reporting.

Stakeholder pressures and SCS reporting

Corporate sustainability reports can support internal development, favoring alignment and helping companies to detect and correct poor supply chain practices (García-Sánchez et al., 2019b). But the key objective of reporting has been decreasing information asymmetry between the company and stakeholders, legitimizing response to their demands [START_REF] Fuente | The role of the board of directors in the adoption of GRI guidelines for the disclosure of CSR information[END_REF] and showing commitment [START_REF] Okongwu | The maturity of supply chain sustainability disclosure from a continuous improvement perspective[END_REF]. Key stakeholders may include customers, employees, regulators, investors, competitors and NGOs [START_REF] Miniaoui | The impact of country-level institutional differences on corporate social responsibility disclosure engagement[END_REF]) [START_REF] Hahn | Organizations, Climate Change, and Transparency: Reviewing the Literature on Carbon Disclosure[END_REF][START_REF] Tate | Corporate social responsibility reports: A thematic analysis related to supply chain management[END_REF]. Engagement with this wide array of stakeholder can decrease legal and financial risks and improve reputation [START_REF] Rashidfarokhi | Sustainability reporting in the nordic real estate companies: Empirical evidence from Finland[END_REF].

Anticipation towards stakeholders' demands via reporting can not only mitigate risks but also sustain competitive advantage responding to pressures [START_REF] Marshall | What's your strategy for supply chain disclosure?[END_REF].

Previous studies have aimed to establish connections between stakeholder pressures and corporate sustainability reporting. The majority has found a positive relation the two, covering pressures from customers [START_REF] Okongwu | The maturity of supply chain sustainability disclosure from a continuous improvement perspective[END_REF][START_REF] Vitolla | How pressure from stakeholders affects integrated reporting quality[END_REF], investors [START_REF] Chithambo | Corporate voluntary greenhouse gas reporting: Stakeholder pressure and the mediating role of the chief executive officer[END_REF][START_REF] Fernandez-Feijoo | Effect of Stakeholders' Pressure on Transparency of Sustainability Reports within the GRI Framework[END_REF][START_REF] Vitolla | How pressure from stakeholders affects integrated reporting quality[END_REF], and employees [START_REF] Fernandez-Feijoo | Effect of Stakeholders' Pressure on Transparency of Sustainability Reports within the GRI Framework[END_REF][START_REF] Vitolla | How pressure from stakeholders affects integrated reporting quality[END_REF]. Yet, research of stakeholder influence on reporting specifically focused on supply chain issues is limited [START_REF] Dubey | World class sustainable supply chain management: Critical review and further research directions[END_REF], as much as research focusing on specificities of the Global South, that might reshape those pressures.

The first key stakeholder group are the customers. Customers "seek information on the environmental impact of production, customer health and safety, marketing and labelling, and customer privacy" [START_REF] Vitolla | How pressure from stakeholders affects integrated reporting quality[END_REF](Vitolla et al., , p. 1596)). This is particularly important for companies which are known by their proximity to the end consumer [START_REF] Fernandez-Feijoo | Effect of Stakeholders' Pressure on Transparency of Sustainability Reports within the GRI Framework[END_REF].

Companies which are considered next to the end-consumers are more easily perceived and pressured by the consumer base. Previous research found a positive relation between customer pressures and reporting [START_REF] Okongwu | The maturity of supply chain sustainability disclosure from a continuous improvement perspective[END_REF][START_REF] Vitolla | How pressure from stakeholders affects integrated reporting quality[END_REF].

Supply chain research also found that companies closer the final consumers have more pressure to adopt SCS [START_REF] Schmidt | The supply chain position paradox: Green practices and firm performance[END_REF]). Yet, when turning attention to the Global South, research shows that customers may have limited or inhospitable access to information regarding companies in order to judge on their transparency [START_REF] Marques | Inhospitable accessibility and blurred liability: Institutional voids in an emerging economy preventing supply network transparency[END_REF]. Therefore, classifying companies according to their proximity to final consumers can serve as a proxy to investigate whether customer pressure is positively associated with SCS reporting.

H1: Customer pressure is positively associated with SCS reporting.

The second key stakeholder group is composed of non-governmental organizations (NGOs). The scenario where companies operate have decisively changed due to the emerging force of such entities. NGOs can focus on a plethora of priorities, and some are more influential to focal companies than others. These NGOs can be sub-grouped under the two main elements of sustainability: social and environmental concerns.

NGOs oriented towards environmental concerns aim to raise citizens' sensitivity to ecological issues [START_REF] Vitolla | How pressure from stakeholders affects integrated reporting quality[END_REF]. This pressure certainly affects different industries in different ways. It is reasonable to believe that the pressure for SCS reporting in regards with environmental impacts become more salient for companies perceived as the main contributors to problems like pollution and greenhouse gases emissions. Some studies have investigated the influence of NGOs focused on protection of the natural environment on sustainability reporting, exhibiting a positive relationship between the two [START_REF] Huang | Drivers of Environmental Disclosure and Stakeholder Expectation: Evidence from Taiwan[END_REF][START_REF] Vitolla | How pressure from stakeholders affects integrated reporting quality[END_REF].

Instead of environmental concerns, some NGOs are devoted to discussing social issues, and working conditions standout as a major issue related to supply chains [START_REF] Stevenson | Modern slavery in supply chains: a secondary data analysis of detection, remediation and disclosure[END_REF]. According to the Global Slavery Index (The Minderoo Foundation, 2018), 24.9 million people were working under forced labor conditions in 2016 globally. This results from suppliers around the globe that may prefer short-term economic gains in detriment of social improvements [START_REF] Huq | Implementing Socially Sustainable Practices in Challenging Institutional Contexts: Building Theory from Seven Developing Country Supplier Cases[END_REF], particularly among those under highproductivity incentives due to buyers' pressure [START_REF] Bird | Coupling labor codes of conduct and supplier labor practices: The role of internal structural conditions[END_REF]. Therefore, supply chains are at the core of modern slavery and poor working conditions. Buying firms impose productivity gains and 'close their eyes' to supplier malpractice and poor working conditions, often justifying with lack of visibility and control [START_REF] Marques | Inhospitable accessibility and blurred liability: Institutional voids in an emerging economy preventing supply network transparency[END_REF].

Sometimes, an industry sector improves while another deteriorates. In Bangladesh for example, after the Rana Plaza disaster, [START_REF] Huq | Implementing Socially Sustainable Practices in Challenging Institutional Contexts: Building Theory from Seven Developing Country Supplier Cases[END_REF] found that child labor was moved from the garment industry to other more harmful activities, such as construction. In Brazil, as another example, even though the partnership between the Public Ministry of Labor and ILO have been intensified in the last years, the challenge of irregular work is still a problem to overcome (SmartLab MPT/OIT, 2017). As pressure from NGOs grows, companies increasingly engage in processes to improve their transparency regarding their SCS [START_REF] Benstead | Horizontal collaboration in response to modern slavery legislation: An action research project[END_REF].

Hence, the hypothesize a positive association between both dimensions of NGO pressure and SCS reporting.

H2: Environmental NGO pressure is positively associated with SCS reporting. H3: Social NGO pressure is positively associated with SCS reporting.

Corporate sustainability reporting has been often a result of shareholder pressure.

Conscious shareholders, activist shareholders and long-term oriented shareholders are terms used to describe those that demand higher levels of compliance and who are increasingly interested in reinforcing a long-term investment strategy by funding companies that can provide evidence of sustainability/SCS [START_REF] Chithambo | Corporate voluntary greenhouse gas reporting: Stakeholder pressure and the mediating role of the chief executive officer[END_REF][START_REF] Fernandez-Feijoo | Effect of Stakeholders' Pressure on Transparency of Sustainability Reports within the GRI Framework[END_REF][START_REF] Vitolla | How pressure from stakeholders affects integrated reporting quality[END_REF]. Vittola et al (2019) for example, indicates a positive influence of shareholders on reporting quality, but measured in terms of shareholder concentration, in line with [START_REF] Chithambo | Corporate voluntary greenhouse gas reporting: Stakeholder pressure and the mediating role of the chief executive officer[END_REF]. An alternative perspective would be to consider the shareholders' long-term orientation, captured by sustainability-oriented stock market rankings.

By the same token that shareholders are sources of pressure, creditors may also pressure for SCS reporting [START_REF] Chan | Corporate governance quality and CSR disclosures[END_REF]. In more debt leveraged companies, creditors become more influential, calling for more monitoring on opportunistic behaviors and integrity, ultimately avoiding future penalties and fines [START_REF] Huang | Drivers of Environmental Disclosure and Stakeholder Expectation: Evidence from Taiwan[END_REF]. Previous research has found conflicting evidence: while Chithambo et al (2020) found a negative relationship, Chan et al 2014 found a positive one. Common to both studies, creditor pressure was measured in terms of the ratio between debt and equity. We turn our attention to two different angles. First, we look at long-term debt as a sign of creditor with a long-term orientation. Such creditors may tend to engage with the recipient companies through a strategic, rather than transactional approach, and this might lead to stronger pressures towards SCS reporting. Second, we focus on one single country to avoid uncontrolled institutional influences.

Taken together, shareholder pressure and creditor pressure represent the recent ESG trend (i.e., acronym for environmental, social and governance) in investment analysis oriented towards the long-term. Previous research has showed that different types of investors may impact reporting differently (García-Sánchez et al., 2020), therefore we hypothesize that both shareholders and creditors, when long-term orientated, are expected to be positively associated with SCS reporting.

H4: Long-term oriented shareholder pressure is positively associated with SCS reporting.

H5: Long-term oriented creditor pressure is positively associated with SCS reporting.

The fourth stakeholder group is represented by the Governments. Regulation can play a central role on the promotion of reporting practices, due to their power over companies [START_REF] Vitolla | How pressure from stakeholders affects integrated reporting quality[END_REF]. Government institutions may fine enterprises that violate socioenvironmental regulations or even impose them to cease activities. Research shows that higher levels of environmental disclosure are positively related to fines paid due to violations of environmental legislation [START_REF] Huang | Drivers of Environmental Disclosure and Stakeholder Expectation: Evidence from Taiwan[END_REF]. Because of that, it is expected that companies which are penalized by government agencies and under higher regulatory pressure are more prone to be active players on SCS reporting. As much as environmental requirements, companies which fail to attend regulatory social requirements such as working conditions may also face penalties and negative media [START_REF] Chithambo | Corporate voluntary greenhouse gas reporting: Stakeholder pressure and the mediating role of the chief executive officer[END_REF]).

Yet, when driving research attention to the Global South, it is expected that governmental pressures might be lower due to institutional voids related to weak contracting legislation and room for malpractice in outsourcing schemes [START_REF] Khanna | Why focused strategies may be wrong for emerging markets[END_REF].

Companies operating in the Global South can navigate in a context where regulation is weak, and even when existent, enforcement is limited, allowing corruption and informality [START_REF] Marques | Inhospitable accessibility and blurred liability: Institutional voids in an emerging economy preventing supply network transparency[END_REF]. Although we expect that there is less governmental pressure overall, for those sectors under specific regulatory scrutiny (such as mining, for example) we expect to see a positive effect on SCS reporting, on both the environmental and the social fronts.

H6: Environmental government pressure is positively associated with SCS reporting. H7: Social government pressure is positively associated with SCS reporting.

The last stakeholder group refers to the internal stakeholdersi.e., the employees.

Previous research has showed that employees can influence SCS [START_REF] Meixell | Stakeholder pressure in sustainable supply chain management: A systematic review[END_REF]. [START_REF] Vitolla | How pressure from stakeholders affects integrated reporting quality[END_REF] found that employee pressure affected the quality of integrated reporting among companies from different industries and regions. Same result was found by [START_REF] Huang | Drivers of Environmental Disclosure and Stakeholder Expectation: Evidence from Taiwan[END_REF], which state that workers have the power to make use of organized unions to "make sure their voices reach the managerial levels in the firm" (Huang & Kung, 2010, p. 440). In addition, Unions contribute to more coupled labor conducts and practices among suppliers [START_REF] Bird | Coupling labor codes of conduct and supplier labor practices: The role of internal structural conditions[END_REF].

Since previous empirical research cross-country or focused on the Global North have showed a positive influence of employee pressure related to Unionization, in countries were institutional voids prevail, the role of Unions tend to be fragile or incipient [START_REF] Khanna | Why focused strategies may be wrong for emerging markets[END_REF]. Therefore, although employee pressure may also be present, fragile regulation may hinder its effectiveness, hence further research is needed. We hypothesize that employee pressure will be positively associated with SCS reporting.

H8: Employee pressure is positively associated with SCS reporting.

In addition to the stakeholder pressures previously discussed, one final key driver is related to the adoption of GRI as a framework for SCS reporting. The adoption of GRI has been used as a tool to access good quality data and to homogenize the sample [START_REF] Fernandez-Feijoo | Effect of Stakeholders' Pressure on Transparency of Sustainability Reports within the GRI Framework[END_REF]. GRI adoption has been posited as an indicator of higher levels of reporting [START_REF] Tran | Does context matter for sustainability disclosure? Institutional factors in Southeast Asia[END_REF]. Indeed, higher levels of sustainability disclosure were found to be positively correlated to GRI adoption [START_REF] Kuzey | Determinants of sustainability reporting and its impact on firm value: Evidence from the emerging market of Turkey[END_REF]. Islam et al. (2016), for example, found a significant difference in the reporting levels after six large banks joined GRI. [START_REF] B3 | On the effectiveness of private transnational governance regimes-Evaluating corporate sustainability reporting according to the Global Reporting Initiative[END_REF] found that GRI promoted the dissemination of sustainability reporting globally, particularly in Asian and South American countries. Such evidence suggests a significant and positive impact of GRI adoption on SCS reporting. H9: GRI adoption is positively associated with SCS reporting.

METHODOLOGY

Research method

This research frames Brazil as exemplar of the Global South due to (a) extant research showing how institutional voids reshape SCS in the country, (b) the availability of corporate sustainability reports from publicly listed companies, and (c) the scale of adoption of GRI as a standard among these publicly listed companies [START_REF] Gri | Sustainability topics for sectors: What do stakeholders want to know?[END_REF]. To assess the level of SCS reporting, we conducted a mixed-method content analysis. First, specific keywords were defined to reflect how much attention each report had given to SCS. The selection of keywords reflects those words considered determinants of SCM, in line with previous literature reviews [START_REF] Marques | Sustainable supply network management: A systematic literature review from a knowledge perspective[END_REF] and thematic analysis [START_REF] Tate | Corporate social responsibility reports: A thematic analysis related to supply chain management[END_REF] on the topic. The sole different from lists used before, was the elimination of "supply network", as in Portuguese this term is not used, and the addition of "third-party", which by the same token in largely used in Portuguese to reflect suppliers. The final list was composed of: (in both English and the Portuguese counterpart): suppl* (fornec*), sourcing (suprimento), purchas* (compra*), procurement (contrata*), outsource* (terceiriz*), thirdparty/third party. The keyword search was followed by a qualitative assessment of the meaning of the words, to avoid misuse of the terms. Such qualitative cleanup of the data has eliminated words that were not related to SCS. For example, mentions related to "contrata*" were often associated with human resources hiring policies not related to SCM, therefore excluded. In case of doubt, the reading was expanded to paragraphs before and after the identified word for a better assessment. Some headings or subheadings, without further contextualization, were also ignored. The number of mentions on each report, after this laborious process was the one considered as company's wordcount of SCS issues.

In order to position ourselves from the stakeholder perspective, the most critical industries in terms of social, economic and environmental impact, according to the GRI Topics ( 2013) report were consulted. The GRI Topics ( 2013) was a study that involved 194 different organizations, representing all sort of stakeholder groups, listing 1,612 material topics for 52 business activity groups and was supported by over 600 documental sources [START_REF] Gri | Sustainability topics for sectors: What do stakeholders want to know?[END_REF]. Among the stakeholders included, the report mentions "business associations, labor representatives, civil society organizations, information users, and experts" (GRI, 2013, p. 8). This study helped to limit the number of industries covered by the present investigation.

Sample definition

The same keywords used to analyze sustainability reports were used to search the GRI Topics documents. In total, 159 out of 1,612 sensitive topics covered by the document were found to be related to SCS issues; nine of them were excluded because they did not deal with SCS directly (for example, materials management). Finally, 150 topics were computed. Industries with at least one topic related to SCS were initially considered, reducing the range of industry sectors from 52 to 33.

From those 33 industries initially considered, eight of them were excluded. Even though NGOs and Public Agencies industries, for example, had raised concerns from their stakeholders about SCS practices, they were excluded from the study as they do not trade shares and do not have the obligation to be fully transparent on internal information. The other missing cases were mainly due to the absence of reporting by companies (such as companies from media, software, and services industries). After that, an analysis was made to match the remaining 25 industries from the GRI topics' classification with the industry classification adopted by the Brazilian Stock Exchange. The procedure was made through the description of economic activities. This resulted in a potential sample of 275 listed companies.

The final step was the exclusion of companies from sensitive SCS industries but with no reporting, or without comprehensive SCS information, i.e., short statements that poorly covered SCS issues and did not configure corporate sustainability reporting. The final sample was composed by 220 reports. Those reports are originated from 88 different listed companies on the Brazilian exchange market (32% of the total 275). Both sustainability reports and annual/integrated reports were downloaded from companies' websites and/or the GRI Database. Data collection was conducted between May 25 th and Jun 7 th , 2020, with the intent of compiling three years of panel data. In May 2020 many companies had not yet released their reports since the COVID-19 outbreak delayed corporate reporting significantly in early 2020. Thus, the final dataset covers the years 2016, 2017 and 2018. Reports in both Portuguese and English were considered valid. Table 1 presents the demographics of the sample by industries and years.

[Table 1]

The sample was composed of an unbalanced short panel data. The most representative industry was Banks, Diverse Financials and Insurance, with the contribution of 45 sustainability reports from 17 different companies. Reports are reasonably balanced across the three years.

Variable definition

The hypotheses were operationalized by a multiple regression in order to know which stakeholder pressures influence SCS reporting.

The dependent variable, here labelled as supply chain mentions (SC mentions), consisted of the total number of citations of the predefined terms presented previously as keywords, with a further qualitative analysis if the words were indeed related to SCS. In a second step, the quantity of citations was transformed into a natural log scale to control for differences on the length of the reportsnaturally leading longer reports to have higher number of citations. This allowed the distribution of the dependent variable accommodates a possible influence of the variability on report length and be significantly less skewedon the descriptive statistics subsection (Table 3), it is shown that SCmentions presented almost the same mean and median values, added to a standard deviation close to 1.

Table 2 presents the independent variables and the control variables.

[Table 2]

Some variables are invariant through time -Customer, EnvNGO and SocNGO.

Another factor is the variation within companies (Shareholder, Creditor, EnvGov, GRI and Size) or only within industries (Customer, EnvNGO, SocNGO, SocGov and Employee).

Financial information, including long-term debt (LTDebt) and equity were collected at Economatica Database. We choose LTDebt instead of the whole debt structure (short + longterm debt), which is more prominent in the literature [START_REF] Chithambo | Corporate voluntary greenhouse gas reporting: Stakeholder pressure and the mediating role of the chief executive officer[END_REF][START_REF] Kalu | Determinants of voluntary carbon disclosure in the corporate real estate sector of Malaysia[END_REF][START_REF] Kuzey | Determinants of sustainability reporting and its impact on firm value: Evidence from the emerging market of Turkey[END_REF], because short-term debtholders do not necessarily have enough power and interest to change corporate policies regarding long-term sustainability actions. Some proxies had to be adapted to the Brazilian reality such as governmental pressure.

The obligation for companies to report their environmental/social performance is not applied for the Brazilian reality, as sustainability reporting is not enforced by law. Alternative measures were defined to evaluate the enforcement of the regulation on companies. For EnvGov pressure, a binary code was applied due to data dispersion (i.e. some companies had high amounts of fines while others have never been punished). The social perspective to the NGO pressure was considered relevant to be included as most of the studies just operationalize this specific stakeholder pressure on environmental sensitive industries.

FINDINGS & DISCUSSION

Descriptive results and statistical tests

The descriptive statistics for the variables included in the model are presented in Table 3.

[Table 3]

For Customer pressure median is 0.5, meaning half the companies are from industries that are close to the final customer. The mean for EnvNGO and SocNGO are below 0.5. This means that most companies are not under NGO pressureeither environmental or socially. In addition, most of companies did not receive any fine from IBAMA during the period searched -expressed by EnvGov pressure, which presented a median of zero with a mean close to the same number. Such finding may contradict the fact that most companies are classified as members of environmental sensitive industries. This leads to two possible interpretations: either companies have followed environmental regulations, or the monitoring/execution of fines have not been properly applied. Results from shareholder variable shows that, in general, companies are not involved in Brazilian voluntary best reporting practices -67 out of 88 companies did not join the ISE initiative. However, most of the sample adopted the GRI framework during the three-year period (183 out of 220 reports). Regarding creditors, some companies presented negative values. This is due to losses on net income for specific companies and years.

In order to run the regression model with no problems of multicollinearity, a Spearman correlation matrix with the respective correlations and significances among dependent, independent and control variables was produced (see Appendix A). At this stage, EnvNGO and SocNGO presented high correlation, and the former was dropped from the equation. As a result, H2 could not be verified in this study.

It is also interesting to notice that industries with major union membership rates (Employee) tend to have more people rescued from modern slavery work conditions (SocNGO), 0.35, p-value 0.00, and less fines applied due to labor legislation penalties (SocGov), -0.3, p-value 0.00. In conclusion, it seems that the pressure imposed by organized workers in Brazil have had a positive impact on the application of labor law. Even though, it is not possible to affirm that companies have stopped to violate labor laws in the reality of their SCs, regardless of legal punishments. Also, larger companies were found to be significant and positively correlated with environmental law violations (EnvGov), 0.26, p-value 0.00, and membership on ISE (Shareholder), 0.22, p-value 0.00. The latter, incidentally, is generally related to GRI adoption. In this regard, it is perceived a movement from the same companies applying best sustainability reporting practices simultaneously. It is possible to state that marginal costs on joining similar initiatives are lower for them, compared to less responsible companies.

Next, multiple regressions were performed, using the three main approaches to panel data. Pooled OLS, fixed effects and random effects methods were run and test to know which one would result best estimates for the model proposed. Statistical results in Table 4.

[Table 4]

Lagrange-Multiplier test was performed to know whether the model would consider effects and time variance. The null hypothesis was rejected (10.71, p-value 0.00), i.e., there is a significant effect to examine. Following, the Hausman test assessed what type of effect should be employed (fixed or random), resulting in a Chi-square value of 16.28 (p-value = 0.061), thus accepting the null hypothesis in favor of the Random Effects model. Finally, Breusch-Pagan test revealed that the random effects model was homoscedastic. The H₀ was accepted, with a value of 15.52 (p-value = 0.16). However, autocorrelation was detected in Breusch-Godfrey tests for first and second orders (41.94, p-value 0.00; 44.80, p-value 0.00, respectively). To correct the above problem and carry lower standard error levels, the study employed the robust covariance matrix estimation. Huber/White cluster robust method was applied, generating the results in Table 5. Random panel regression (Huber/White covariance robust matrix)

[Table 5]

Discussion of the results

At the final stage, customer pressure, previously significant, lost statistical significance when added to panel regression models (0.015, p-value = 0.93, thus rejecting H1). The fact that customer pressure has been previously associated with both SCS adoption [START_REF] Svensson | Developing a theory of focal company business sustainability efforts in connection with supply chain stakeholders[END_REF] and higher levels of reporting [START_REF] Okongwu | The maturity of supply chain sustainability disclosure from a continuous improvement perspective[END_REF] is a first evidence that institutional voids may be playing a role. In other words, in a context where there is lack of transparency regarding poor corporate practices, customers have either less accessibility or no accessibility to key information to support their judgement. Moreover, even when faced with information of poor practices, they lack tools to enforce change [START_REF] Marques | Inhospitable accessibility and blurred liability: Institutional voids in an emerging economy preventing supply network transparency[END_REF]. Also at the final stage, social government pressure, previously significant, lost statistical significance when added to panel regression models (0.017, p-value = 0.78 rejecting H7), and environmental government pressure remained not relevant (0.048, p-value = 0.52, rejecting H6). Taken together, the non-significance of both governmental pressures reinforces the argument that institutional voids are in place, characterizing weak law enforcement [START_REF] Khanna | Why focused strategies may be wrong for emerging markets[END_REF].

In line with the previous results (rejection of H1, H6 and H7), employee pressure was also not relevant (-1.573, p-value = 0.46, rejecting H8). This forth rejection completes a cluster of results that corroborate the presence of institutional voids in a Global South country.

Previous research has showed that employee pressure is present in the Global North. In Germany for example employees have been perceived as the most influential driver for SCS adoption [START_REF] Maas | Stakeholder Pressures, Environmental Practice Adoption and Economic Performance in the German Third-party Logistics Industry-A Contingency Perspective[END_REF]. However, voids related to weak professionalization and weak Unionization can hinder employee pressure and this lack of association is present in our study.

Regarding NGO pressure, while environmental pressure (H2) was dropped in the course of data analysis, social pressure was confirmed (0.378, p-value = 0.02, thus confirming H3). This may indicate the rising presence of NGOs in the corporate arena and aligns with recent research discussing the role of non-traditional stakeholders [START_REF] Tate | Corporate social responsibility reports: A thematic analysis related to supply chain management[END_REF].

Turning our attention to the remaining hypotheses, we see that shareholder pressure has been confirmed (0.415, p-value = 0.01, accepting H4). Shareholder pressure has been noted as positive to disclosure among German publicly listed companies [START_REF] Gamerschlag | Determinants of voluntary CSR disclosure: Empirical evidence from Germany[END_REF] and a sign of higher reporting quality in a multi-country study [START_REF] Vitolla | How pressure from stakeholders affects integrated reporting quality[END_REF].

Yet, these studies were looking at shareholder pressure from the perspective of shareholder concentration. This study conversely innovates by looking at shareholder long-term orientation. The fact that an association was found may indicate that within the context of institutional voids, long-term oriented shareholders rise as a key driver of SCS reporting. In fact, the correlation here was the stronger among all tested drivers.

In line with what was found in H4, creditor pressure has also been confirmed (0.007, p-value = 0.00, accepting H5). Creditor pressure was also found positive to SCS adoption and reporting. [START_REF] Kalu | Determinants of voluntary carbon disclosure in the corporate real estate sector of Malaysia[END_REF] found a positive relationship between voluntary carbon disclosure and creditor pressure among Malaysian companies. [START_REF] Yunus | Impact of stakeholder pressure on the adoption of carbon management strategies[END_REF] found that creditors' influence among Australian publicly listed companies drives carbon reduction strategies. Implication of these results are twofold. While [START_REF] Chithambo | Corporate voluntary greenhouse gas reporting: Stakeholder pressure and the mediating role of the chief executive officer[END_REF] have found a negative association between creditor and reporting, their focus was on credit leverage. In our study, the focus has changed to creditor long-term orientation. The fact that the study shows a positive association corroborates results from the shareholder long-term orientation and together indicate both sources of fundinginvestors and creditormay be associated with advancements in SCS reporting [START_REF] Chan | Corporate governance quality and CSR disclosures[END_REF]. This also reflects the recent trend on ESG funding analysis.

The two final hypotheses can also be discussed as a cluster. First, GRI adoption exhibited a positive association with SCS reporting (1.196, p-value = 0.00, accepting H9).

And the control variable for size (number of employees) was also confirmed (0.378, p-value = 0.02). Results are in line with [START_REF] Gamerschlag | Determinants of voluntary CSR disclosure: Empirical evidence from Germany[END_REF][START_REF] Chithambo | Corporate voluntary greenhouse gas reporting: Stakeholder pressure and the mediating role of the chief executive officer[END_REF] and [START_REF] Kalu | Determinants of voluntary carbon disclosure in the corporate real estate sector of Malaysia[END_REF], which have considered number of assets instead of number of employees as a proxy for size. While the adoption of the GRI framework is an indication of knowledge and maturity in SCS reporting, it is also costly, and thus it is expected that larger companies will more often subscribe to the GRI framework. Resource availability may explain these results.

The planning, preparation and execution of sustainability reports, alongside the adherence to GRI standards require human and financial resources that, are often not available for smaller companies [START_REF] Svensson | Developing a theory of focal company business sustainability efforts in connection with supply chain stakeholders[END_REF]. disclosure only "good news" [START_REF] Sodhi | Research Opportunities in Supply Chain Transparency[END_REF]. Moreover, mentions to supply chain issues does not guarantee the quality of the practices being reported. Our focus has been on reporting, rather than actual practice. Future studies complementing reporting data with primary data (interviews and other data collection methods) could better evaluate the quality of the SCS practices reported.

Our study looks only at GRI as a framework. GRI currently acknowledges the need to improve their focus on SCS. For example, [START_REF] Mancini | Social impact assessment in the mining sector: Review and comparison of indicators frameworks[END_REF] found that some health and safety aspects were not included in the G4 guidelines (active version in 2021); same case for poor working conditions. The increasing attention devoted to supply chains should serve as a signal to both GRI and companies of the importance of SCS reporting.

The absence of companies not publicly listed in the stock market is explained by the lack of information available. In most countries (and Brazil is no exception), a large share of small and medium companies is not publicly listed. Future studies should find ways to incorporate this share of companies in the data analysis, although this is a challenging endeavor.

Finally, the scarcity of studies on the Global South calls for further studies in other countries other than Brazil to allow confirmation of the role of institutional voids. The current paucity of studies focused on the region leaves question marks related to the adequate proxies for each stakeholder pressure and other issues that are particular to companies operating in the Global South. Proxies for regulation, for example, were particularly difficult to be defined, due to the absence of systematic enforcement.

See: https://www.theglobaleconomy.com/rankings/stock_market_capitalization_dollars/

CONCLUSION

Main contributions to theory and practice

This study offers complementary evidence to research by analyzing stakeholder pressures association to higher levels of SCS reporting [START_REF] Okongwu | The maturity of supply chain sustainability disclosure from a continuous improvement perspective[END_REF] and delineates contributions to theory and practice regarding the study of institutional voids and SCS.

Theoretical implications emerge from results showing that drivers associated with SCS reporting can be clustered in three angles. We found no association between pressures from customers, employees, and government to SCS reporting. This implies that in a context of weak law enforcement, weak professionalization and weak Unionization, pressure from these stakeholder groups may be hindered [START_REF] Khanna | Why focused strategies may be wrong for emerging markets[END_REF]. Future research should look further into these interactions between different stakeholder pressures and reporting which may lead refinement of stakeholder theory and the concept of stakeholder salience in the context of the Global South (Ali, 2015). Conversely, our study shoes that a positive association between pressures related to long-term funding (shareholders and creditors) and SCS reporting. The long-term perspective taking in these two variables show novel evidence regarding the association of funding and reporting, in line with recent research (Kim el al., 2019). Finally, the third angle relates to GRI adoption and company size, which may reflect access to resources. The profile of companies leading SCS reporting is associated with pressure from funding sources, adherence to standards, and access to resources.

Practical implications emerge from the association between SCS reporting and the long-term profile of funding sources. This provides an indication for companies that both investors and creditors with a long-term orientation may influence not only financial reporting but also sustainability reporting [START_REF] García-Sánchez | Do institutional investors drive corporate transparency regarding business contribution to the sustainable development goals?[END_REF]. It also corroborates the importance of adherence to standards. Ultimately, it calls attention to the fact that even in countries characterized by institutional voids, there may still be rising pressures for SCS reporting. When legislation fails, other pressures may eventually replace it. Further research is needed, but maybe companies not advancing on the road to better SCS even within the context of voids may face challenges market challenges.

Limitations and future research

Our study is based on self-reporting. However, it is plausible to believe that some companies may not report salient impacts of their activities as well as may not have mentioned strategic projects they do not want to make public. Companies may engage on selective reporting and

List of Tables