Gaoussou Diarra
email: gaoussou.diarra@u-clermont1.fr.

Sébastien Marchand
email: sebastien.marchand@u-clermont1.fr

Environmental Compliance, Corruption and Governance: Theory and Evidence on Forest Stock in Developing Countries

Keywords: Corruption, Environmental compliance, Forest Stock, Political Economy, Governance D73, Q23

We are sincerely grateful to Vianney Dequiedt for his helpful comments. We

"(S)ustainable development depends upon good governance, good governance depends upon the rule of law, and the rule of law depends upon effective compliance. None are sufficient alone, but together they form an indivisible force that is essential for survival and for sustainable development". Zaelke et al. (2005, p.29-30) 1 Introduction

Moving onto the path of sustainable development requires that human behavior change to address major environmental issues such as biodiversity loss and climate change. In this context, understanding factors of deforestation is relevant to improve sustainable environment for various reasons. For instance, the current global warming issue highlights the importance to reduce emissions from deforestation, forest degradations, and enhance forest carbon stocks in developing countries (REDD+) [START_REF] Angelsen | Realising REDD+: National strategy and policy options[END_REF]. Moreover the protection of biodiversity, particularly in pristine forested area, becomes a significant environmental issue in the current international development agenda. Thus, the depletion of forested areas in developing countries has drawn attention in order to improve sustainable development.

To respond to these issues, governance systems have to become more effective as it describes the available way to shape human actions towards its common goals as sustainable development. In this system, institutions, conceived as "rules of the game" [START_REF] North | Economic performance through time[END_REF] provide practices and guide economic, political and social human interactions. As noticed by (Zaelke et al., 2005, p.38), "all forces that can influence human behavior are potential tools of governance". In this context, good governance depends on rule of law which refers to a set of rules applied fairly, efficiently and predictably by independent institutions in a framework of public-private interaction process. Thus, a set of social norms comprising, rule of law, anti-corruption, and accountability have been put forward to enhance governance. In this context, compliance is a substantial element of good governance. Compliance with the law is related to the respect and the enforcement of legal system. As a result, compliance may be treated as an indivisible part of rule of law: rule of law cannot have meaning without compliance. The growing focus on compliance seems to be important to enhance the success of efforts to strengthen rule of law, which in turn will improve the achievement of efforts to promote good governance, and thereby allow the society to reach sustainable development. Indeed, in most studies on governance, emphasis is put on the supply side of reforms. The importance of taking into account the demand side of good governance reforms imply to be aware of factors driving stakeholder's compliance [START_REF] Young | Compliance and Public Authority: A Theory with International Applications[END_REF][START_REF] Odugbemi | Governance reform under real-world conditions[END_REF][START_REF] Mcneil | Demanding Good Governance: Lessons from Social Accountability Initiatives in Africa[END_REF].

This paper aims at bridging this gap by analyzing relationships between governance infrastructures and patterns of keys stakeholders' compliance with regulatory policies, notably in environmental field such as deforestation. The importance of compliance is nowhere more important than in the field of environment and sustainable development. For instance, in a poor legal and judicial system, in which non-compliance and corruption become pervasive and law are not enforced, the respect for the rule of law is lessened, environmental degradation is more likely to occur, and progresses towards sustainable development are weakened. In this context, improvements of governance infrastructures and more particularly norms enforcement and compliance have been widely recognized.

Thus, factors underlying actors' compliance concerned with regulatory policies allow to understand corruption phenomenon and functioning of governance infrastructures. Moreover, the literature on regulatory compliance has focused on whether a firm complies with existing regulations, and on effects of enforcement on a firm's compliance behavior [START_REF] Magat | Effectiveness of the EPA's regulatory enforcement: The case of industrial effluent standards[END_REF][START_REF] Deily | Enforcement of pollution regulations in a declining industry[END_REF][START_REF] Laplante | Environmental inspections and emissions of the pulp and paper industry in quebec[END_REF]. Nonetheless, in these studies the role of bribery and other political economy aspects of enforcement and compliance were under-investigated. While compliance with regulations was treated in terms of compliance versus non-compliance [START_REF] Deily | Enforcement of pollution regulations in a declining industry[END_REF], compliance level [START_REF] Laplante | Environmental inspections and emissions of the pulp and paper industry in quebec[END_REF] or duration of non-compliance episodes [START_REF] Nadeau | EPA effectiveness at reducing the duration of Plant-Level noncompliance[END_REF], studies on corruption have been focused on analysis of factors dealing with selection and incentives of actors taking policy decisions in a State with some interests on bureaucratic or political institutions structures. Besides, some evidences are also found about over-compliance of firms in manufacturing sector.

Then, many firms are likely to comply with environmental regulations even when these regulations are weak or non-existent, well known as the Harrington paradox [START_REF] Harrington | Enforcement leverage when penalties are restricted[END_REF].

Analyzing sustainability of governance reforms implies to know why is there too few demand for good governance in some economies, or to understand the persistence of some bad institutions such as those self-sustaining corruption. For instance, bureaucratic corruption can be attributed to a lack of sufficient political will while political corruption can be attributed to lack of adequate political competition. As good governance reforms are gradual processes and necessitate investment in legal and administrative infrastructures, political instability is likely to create an environment under which corruption becomes more pervasive and tends to persist [START_REF] Damania | The persistence of corruption and regulatory compliance failures: Theory and evidence[END_REF][START_REF] Mishra | Persistence of corruption: some theoretical perspectives[END_REF]. Therefore, governments will be constrained in its abilities to enforce compliance with chosen policies while being vulnerable to lobbying activities. Hence, corruption is conceived along different dimensions which are interlinked: grand versus petty corruption. Grand corruption which involves higher decision-levels in a country, is conceptually quite different from petty corruption. It includes cases when politicians or high-ranking civil servants manipulate a country's management or regulation of infrastructure industries to gain exclusive benefits [START_REF] Knack | Measuring corruption in eastern europe and central asia: A critique of the Cross-Country indicators[END_REF][START_REF] Kenny | Grand corruption in utilities[END_REF]. A main contrast between petty and grand corruption is related to monitoring mechanisms, which can be far better organized when petty corruption is the main issue. With grand corruption, elected politicians are often directly or indirectly controlling supposed monitoring mechanisms, including media as well as judicial system.

In this perspective, the fundamental rationale for giving special attention to corrupt actions in forestry highlights how these actions undermine the government's apparatus. This is critical in a sector such as forestry that generates many social and environmental impacts that call for a strong and clean intervention from State. If government is corrupt, there is little hope that illegal operations by other actors in the economy will ever be controlled [START_REF] Contreras-Hermosilla | The underlying causes of forest decline[END_REF]. Anti-corruption policies limited to forestry are unlikely to work in countries with high corruption levels, which require systemic institutional changes. Corruption may matter for deforestation through design and implementation of land use plans. Indeed, grand corruption is likely to influence land use planning because decisions are made at high levels of government and large sums of money (or political support) are required to manipulate involved people. Petty corruption is likely to occur when local officials allow illegal encroachment on forest areas [START_REF] Angelsen | Realising REDD+: National strategy and policy options[END_REF]. Strategy for combating forest crime rests on an assessment of governance situation of the country, the streamlining of policy framework, and the focus on operational activities around a prevention, detection and suppression framework. However, since forestry does not operate in complete isolation from other sectors, enhancing compliance with forest law will depend on actions by judiciary and law enforcement agencies (FAO, 2005). Hence, this article examines interrelationships between governance, environmental compliance and forest cover in developing countries.

Positioned on the same lineage as [START_REF] Damania | The persistence of corruption and regulatory compliance failures: Theory and evidence[END_REF] but without being primarily interested by the channel of political instability as the way through which corruption may affect environmental compliance, we develop a theoretical model that explains how (i) petty corruption and environmental compliance interact belong to the extent of governance infrastructure and (ii) environmental compliance and governance infrastructure interact to reduce environmental damages as loss of forest stock.

More precisely, a two-stage model is adopted where a profit-maximizing representative harvester selects the optimal amount of harvested land to be cleared given the available technology in forestry. In the second step, the logging firm is inspected by a bureaucrat (inspector) and she might be willing to bribe this inspector in case of non-compliance. Firm-inspector interactions are shaped by judicial efficiency and authorized harvest quota previously set. Indeed, the first step presents a model of policy-maker corruption, following [START_REF] Grossman | Protection for sale[END_REF]. Policy maker designs the forest policy i.e the maximum harvest. The logger acts as a lobby so that policy-maker maximizes a weighted sum of social welfare and received bribes.

We have drawn some positions predicting the relationships between firm's environmental compliance, petty corruption, governance infrastructures and environmental outcomes. Proposition 1 states that firm's environmental non-compliance and petty corruption are positively correlated (firminspector relation) and conditioned to the efficiency of the legal and regulatory framework. This proposition relies on two results concerning the negative effect of judicial efficiency and the positive effect of a less stringent harvest quota on both environmental compliance and petty corruption. Proposition 2 states that environmental compliance is a substitute of low judicial efficiency or a complement of high judicial efficiency to strengthen forest stock. Empirical estimations, using cross section data for 59 developing countries, are supporting main theoretical predictions. First, we find that (i) environmental compliance and corruption are positively correlated but conditioned to judicial efficiency and (ii) that judicial efficiency lessens both corruption and compliance. Second, we find empirical evidences on the substitutability and complementarity of environmental compliance and judicial efficiency to preserve the forest stock.

The paper is organized as follows. Section 2 presents a political economy model. Section 3 provides econometrical evidence in support of the predictions of the model. Section 4 concludes and discusses policy implications.

The Baseline Model

A three-tier hierarchy agency model is used: firm-harvester/inspector/government [START_REF] Tirole | Hierarchies and bureaucracies: On the role of collusion in organizations[END_REF] 1 . We assume that all parties are risk neutral. The representative harvester has right to cut timber in a given public forested land (like a concession). The harvester decides the volume to harvest knowing that an inspector will monitor his production.

We first define the time sequence of actions and specify our model. Then, firm-inspector interactions are studied to determine harvesting and reporting decisions as well as optimal bribe. Finally, policy decisions are investigated.

Time Sequences of Decision

The model is a sequential finite-period stage game. The timing of events is given below:

• At date t = 0, the harvester determine its political contributions offered to the incumbent government. The level of these contributions is linked to the forest policy.

• At date t = 1, the incumbent government selects the forest policy to maximize his pay-off.

• At date t = 2, the harvester determines his harvest and reported effort.

• At date t = 3, the inspector controls firm's production and an optimal level of bribe is determined with a probability to be discover depending on the level of judicial efficiency i.e the quality of the audit agency.

A backward induction process is used for the resolution of the game. Hence the forest and legal policy is given for the harvester and inspector in the second stage.

Firm-Inspector Interaction

The policy-maker designs a forest policy in order to reduce deforestation, to preserve biodiversity or to implement a durable forestry management. This policy consists to set the maximum harvest effort, e required i.e a harvest quota. We assume that the harvester tends to produce more than the quota and to set e > e implying a positive level of non-compliance v = (e -e). Given that harvest production results in environmental damages, the government has to control harvest effort and imposes a bureaucrat (for instance an inspector) who monitors the firm. Moreover, the harvester has a private information on his harvest production so that the principal has to use an inspector to monitor firm's reported information.

However, the harvester may propose a bribe B to inspector in the case of non compliance. This corrupt behaviour is defined as petty corruption because it occurs between the firm and inspector2 .

Then, the harvester's bribe incites inspector to declare that the quota is respected. In the model, inspection is not probabilized because we suppose that the harvester is alone which makes obvious the inspection. In other words, given that the inspector is risk-neutral, he could accept or refuse the bribe if the amount of this contribution is not enough to optimize his pay-off. If the inspector accepts bribe, he reports harvest effort e ≤ e. Moreover, we assume that the inspector receives from the regulator (government) a fixed wage (w) and a variable wage (R). This last component of inspector's remuneration, R, is considered as a reward for reporting the true harvester's effort. Then, R depends positively on the level of non compliance (v, ∂R/∂v > 0) but as public resources are scarce, R should not increase indefinitely with v ( ∂ 2 R ∂v 2 > 0). This award is a positive incentive used as a regulatory tool by the incumbent government to persuade the inspector to comply with his original purpose i.e to report the true harvest production.

However, knowing that the inspector could be bribed by harvester, the regulator implements an audit of the harvest effort. The audit uncovers the true harvest effort with a probability λ ∈ (0, 1).

Therefore, the level of λ could be an indicator of the efficiency of auditing process as noticed by [START_REF] Damania | The persistence of corruption and regulatory compliance failures: Theory and evidence[END_REF]. If e > e, a fine f(v) is imposed to the harvester (f H ) and inspector (f I ). Thus, the fine for corruption is increasing and convex in non-compliance f (v)( ∂f ∂v > 0; ∂ 2 f ∂v 2 > 0). Hence, the harvest effort will depend on the forest policy (e) and the efficiency of the audit (λ), built for penalties in the case of non compliance. Thus, harvest effort will be e = e(e, λ) in the cheat/bribe strategy and e S = e(e, λ) in the safe strategy (where e S = e).

Let H(e) be the net harvest function of the harvester from its harvest effort, with the land-holding cost and timber prices integrated. We assume that this logger is price taker given that he trades on international market. The net harvest function depends on the logging effort (which is the logger's choice variable), and takes the form H(e), with standard properties: H e > 0, H ee < 0. The net harvest function is H(e) in the safe case and H(e) in the cheat strategy. Consequently, the strategies and their related pay-off are given in the following table 1.

(e) w + R(v) Cheat H(e) -[B + λf H (v)] w + B -λ[f I (v) + R(v)] Net Ψ H (e, e) Ψ I (e, e) = H(e) -[B + λf H (v)] -H(e) = w + B -λ[f I (v) + R(v)] -w -R(v) = B -(1 + λ)R(v) -λf I (v)
Following [START_REF] Damania | The persistence of corruption and regulatory compliance failures: Theory and evidence[END_REF] and [START_REF] Wilson | Corruption, political competition and environmental policy[END_REF], we begin by determining the optimal level of bribe and effort intensity. The process of this game can be divided in two stages. First, the logger sets the effort level to maximize the joint pay-off (Ψ J ≡ Ψ H + Ψ I ). Then, the inspector and logger share the surplus through a Nash equilibrium process.

Therefore, taking the policy parameters as given (e, λ,

f H v , f I v , R(v))
, the harvest effort is chosen to maximize the joint net pay-offs of the logger and the inspector.

max e Ψ J ≡ Ψ H + Ψ I = [H(e) -[B + λf H (v)] -H(e s )] + [B -(1 + λ)R(v) -λf I (v)] (1)
The first order condition is:

Ψ J e = H e -λf H e -λf I e = 0 (2)
The logger's optimal harvest effort e * (e, λ,

f H v , f I v , R(v)
) is implicitly given by equation 2. In equilibrium, this equation ( 2) specifies that the actual effort is set such that the marginal revenue from production equals the marginal expected penalty.

The equilibrium bribe is determined by a Nash bargain between the harvester and bureaucrat. In this process, both parties share equally the benefit of the bribe strategy (non compliance) i.e they have the same bargaining power. To be successful, the bargaining has to respect the reservation values of the bureaucrat and logger. By the harvester's net pay off (

B > (1 + λ)R(v) + λf I (v) ≡ B.
Therefore, the optimal bribe is determined by the following Nash bargain

max B (Ψ H Ψ I ) (3)
The first order condition is

∂(Ψ H Ψ I )/∂B = [H(e) -H(e S ) + (1 -λ)R(v) -λ(f H -f I ) -2B] = 0 (4)
Hence, the optimal bribe is

B * = 1/2[H(e) -H(e S ) + (1 -λ)R(v) -λ(f H -f I )] (5)
The optimal bribe resulting of this process has to lie between [B, B] so that the global benefit of the bribe strategy is higher than the global loss of this strategy.

Having defined the firm-inspector equilibrium of the model (e * (e, λ) and B * (e, λ)), we now turn to analyse the comparative static properties of the equilibrium to examine interrelationships between forest policy (e), judicial efficiency (λ), petty corruption (B * ) and non-compliance (v = e * -e).

First, to ensure that higher fines (f ) reduces the optimal level of bribe (B * ), the term f H -f I must be positive. This assumption implies that the fine paid by the recipient (inspector) is lower than that paid by the bribe giver [START_REF] Damania | The persistence of corruption and regulatory compliance failures: Theory and evidence[END_REF][START_REF] Delacote | Systemic corruption, scale effects and forest harvesting[END_REF]. The intuition is as follows: if the regulator punishes more severely the bribe-taker than the bribe-giver, the inspector would incite the harvester to increase the bribe to compensate for the inspector's expected fine. Hence, as suggested by Mookherjee and Png (1995, p.151), "one way to reduce the bribe is to raise the penalty [...] on the bribe-giver (factory), while reducing the penalty [...] on the bribe-taker (inspector)".

Second, the bribe raises if the inspector's emoluments (rewards, R) increase [START_REF] Mookherjee | Corruptible law enforcers: How should they be compensated?[END_REF]. Intuitively, the opportunity cost of cheating for the inspector raises, so the inspector demands and receives a bigger bribe. The idea leans on the inspector's weight in negotiations which increases with the level of rewards received. The inspector could ask a more important bribe to compensate rewards knowing that the probability of detection of the cheat is very low.

Result 1 The harvest quota (e) increases the effective harvest effort (e * ) but decreases the level of non compliance as well as the level of bribe payments (B * ) (see proof A.1.1).

Firstly, the intuition for the positive effect of harvest quota on effective harvest effort is as follows:

higher will be the harvest quota (increase of e), lower will be the fine paid by the logger for a given harvest effort, higher will be the over harvest production. Put differently, a less stringent harvest quota reduces the extent of the potential fine because of the decrease of the extent of non compliance.

Moreover, the marginal effect of the quota on harvest production is less than one implying that the increase of harvest production is less important than the raise of the harvest quota (see proof A.1.1).

Thereby the level of non compliance decreases with a rise of harvest quota. Secondly, a less stringent harvest quota (an increase of e) reduces the level of bribe payments. The intuition is as follows: an over indulgent harvest quota decreases the probability and the extent of non compliance which implying a diminution of potential corrupt activities and so bribe payments.

Result 2 Judicial efficiency (λ) decreases the effective harvest effort (and so non compliance for a given level of harvest quota) and bribe payments (see proof A.1.2).

Firstly, an increase of the judicial efficiency reduces the harvest production and so the level of non compliance. The intuition is as follows. An improvement of the audit agency (increase of λ) increases the probability for the logger to pay a fine for a given harvest effort and so reduces his incentive to over harvest i.e to non comply. Put differently, a more efficient audit agency strengthens the extent of the potential fine. Secondly, an increase of the judicial efficiency leads to a decrease of the level of bribe payments. The intuition is as follows: knowing that the probability of the detection and sanctions of the cheat raised, the expected fine paid by the firm increases the cost of the cheat strategy implying that the harvester prefers to not bribe the inspector. More precisely, the firm knows that his non compliance behaviour will likely be detected with or without bribe, as judicial efficiency is high, and so will prefer to spare the amount of bribe. Thus, in a country with efficient judicial institutions, this leads to reduce opportunities of petty corruption.

From the marginal effects of the harvest quota and judicial efficiency, we have the proposition 1.

Proposition 1 The covariance of non compliance and petty corruption is positive (see proof A.1.3) conditioned to judicial efficiency.

Policy Determination

We now turn to the political process after having described the harvester-inspector interactions process.

Remind that we proceed backward so that the political process, which determines the forest policy takes place before harvester-bureaucrat outcomes. The incumbent government has to draw the policy but the logger act as a lobby. Consequently, the threshold level of harvest quota (e) is influenced by the harvester's lobbying.

Following [START_REF] Grossman | Protection for sale[END_REF], the incumbent government i receives political contributions S defined as grand corruption from the logger. We assume that the firm's political contributions depend on its level of non compliance, hence S(v) with S v > 0. In fact, a non compliant firm could have a trade off between the cost to bribe the incumbent government or the cost to bribe the inspector in the following stage. However, we assume that an optimal strategy for the firm would be to try to influence the government to have a well set harvest quota.

Thus, the government derives utility from political contributions and also from the welfare of voters (W ). The incumbent government draws the level of forest policy in order to maximise its payoff considering S as given. Consequently, the current utility of the policy-maker is a weighted sum of S and W :

U = (1 -α)βS(v) + αW (H(e), e)
Where β measures the degree of environmental compliance in the economy. More compliance increases the weight of corruption in the government's utility because the rent seeking government is more incited to deal with a compliant firm than with a non compliant one. α measures the weight of social welfare in government's utility. Social welfare represents the sum of utility of all agents in the economy in a given period. It is decreasing in the harvest effort (W e < 0; W ee < 0) which is associated to environmental damages (biodiversity losses,...) and increasing in the total harvested volumes (W H > 0; W HH < 0).

Following [START_REF] Grossman | Protection for sale[END_REF] and [START_REF] Dixit | Common agency and coordination: General theory and application to government policy making[END_REF], the equilibrium in a common agency model maximises the joint surplus of all parties. From lemma 2 of [START_REF] Bernheim | Menu auctions, resource allocation, and economic influence[END_REF], the forest policy (e) has to satisfy two necessary conditions, which are

CI : e * ∈ arg max U (6a) CII : e * ∈ arg max Π + U (6b)
The expected profit Π of the logger is

Π = H(e) -B -λf H (v) -S(v)
Condition 6a states that the incumbent government determines the forest policy to maximize its own welfare (U ), given the offered political contribution schedules (S). Condition 6b denotes that the equilibrium of the forest policy maximizes the joint welfare of harvester and government.

The optimal forest policy (e * ) maximizes (i) CI (equation 6a) and (ii) CII (equation 6b). Thereby, the first order conditions satisfy

(1 -α)βS v + αW H H e + αW e = 0 αW H H e + αW e + H e -λf H v -αβS v = 0
Thus, e * is implicitly given by:

H e + α β(1 -α) W H H e + α β(1 -α) W e -λf H v = 0 (7)
Having defined the political equilibrium of the model, we now turn to analyse the comparative static properties of the equilibrium to examine interrelationships between forest policy (e), judicial efficiency (λ) and environmental non-compliance (β).

Result 3 An increase of judicial efficiency (λ) reduces the forest quota i.e the forest policy becomes more stringent. (see proof A.2.1).

This result implies that an improvement of judicial efficiency is a condition to weaken environmental damages. In fact, a more efficient audit agency suggests that the costs associated to the bribe strategy increase implying less petty corruption and finally less opportunity to non comply with the forest policy. Thereby, the principal, here the government, could implement a more stringent forest policy to reduce environmental damages because he knows that the logger will be less incited to not comply with the forest policy. Thus, judicial efficiency allows to promote sustainable environmental policies.

Result 4 Conditioned to the level of judicial efficiency, an increase of compliance (a rise of β) tends to reduce the harvest quota i.e the forest policy becomes more stringent (see proof A.2.2).

These results implies that in countries with low judicial efficiency, an improvement of environmental compliance allows to reduce environmental damages as deforestation i.e forest quota. Moreover, in high judicial efficiency country, the effect of environmental compliance decreases harvest quota only if fines paid by firm are nil. Moreover given that judicial efficiency is high, firm has to be compliant to not pay fine (because the probability to be detected increases with judicial efficiency). Given that we have the following proposition concerning the effect of both environmental compliance and judicial efficiency on forest stock.

Proposition 2 Environmental compliance is a substitute of low judicial efficiency or a complement of high judicial efficiency in order to reduce harvest quota (see proof A.2.3).

Thereby, environmental compliance is a good substitute of weak governance infrastructure or a good complement of strong governance infrastructure to reduce environmental damages.

3 Econometric Framework

Econometric Approach and Data

Econometric Specification

The theoretical model has highlighted interrelationships between environmental compliance, petty corruption, governance infrastructures (here judicial efficiency) and environmental damages (here losses of forest stock). The econometric approach consists in testing whether: (i) environmental non compliance and petty corruption are positively correlated and conditioned to judicial efficiency (Proposition 1) which lessens both petty corruption and environmental compliance (Result 2) (ii) environmental compliance and judicial efficiency are complementary or substitutable to preserve the forest stock (Proposition 2).

To test our model, a cross-country data is used with a three equation econometric model of petty corruption (equation 8), environmental non compliance (equations 9) and forest stock (equation 10).

Petty Corruption Equation

To test the proposition 1, results 1 and 2, we run the following regression:

Corruption i = ∂ 0 + ∂ 1 Compliance + ∂ 2 F orest i + ∂ 3 Judicial i + k ∂ k W i + υ i (8)
where Corruption i is the inverse of the level of corruption in the country i, Compliance i is the degree of environmental compliance, F orest i is the level of forest stock and Judicial i is the quality of the legal framework. W i are control variables, ∂ k are coefficients vector to estimate and υ i is the error term.

Proposition 1 states that ∂ 1 should be positive and significant without judicial efficiency as control variable. Result 1 states that ∂ 2 should be positive and Result 2 states that ∂ 3 should be positive.

Following the literature, we divide factors of corruption (W i ) into four main categories: (i) economic factors, (ii) political and legal determinants, (iii) social structure and (iv) geographical features.

First, on economic factors, Log GDP per capita is introduced to control for development process which lessens the level of corruption . The presence of potential rents is often associated to corruption [START_REF] Tanzi | Corruption around the world: Causes,consequences, scope, and cures[END_REF]. A variable of Trade openness is used because it is assumed to reduce corruption by depressing the presence of potential rents [START_REF] Ades | Rents, competition, and corruption[END_REF].

Second, on legal factors, [START_REF] Treisman | The causes of corruption: a cross-national study[END_REF] and [START_REF] Damania | The persistence of corruption and regulatory compliance failures: Theory and evidence[END_REF] argue that democratic regime lessens corruption. Thus, a Democracy variable, measuring the extent to which there is a societal consensus supporting democratic principles, are introduced. Legal origins of the law and regulations are introduced to control for differences between major family of law (Legal origins dummy). La [START_REF] Porta | The quality of government[END_REF] show that English common law countries have less-corrupt societies than French civil law ones often characterized by an important government ownership and regulation which are associated with many adverse impacts on markets such as corruption. In our sample, countries are of fourth different legal origins, namely English, French and Socialist.

Third, we include Latitude because temperate zones with healthier climate and more agricultural productivity could develop their economic activities and their institutions and so lessens the potential opportunity of corruption (La [START_REF] Porta | The quality of government[END_REF].

Environmental Compliance To test the proposition 1, results 1 and 2, we run the following regression:

Compliance i = β 0 + β 1 Corruption + β 2 F orest i + β 3 Judicial i + k β k W i + υ i (9)
where Compliance i is the degree of environmental compliance in the country i, Corruption i is the inverse of the level of corruption; F orest i , the level of forest stock and Judicial i , the quality of the legal framework. W i are control variables, β k are coefficients vector to estimate and υ i is the error term.

Proposition 1 states that β 1 should be positive and significant without judicial efficiency as control variable. Result 1 states that β 2 should be positive and Result 2 states that β 3 should be positive.

Among control variables, Log GDP per capita is used to control for structural differences as economic development progresses. To capture the extent of pollution damages which may influence the degree of compliance with environmental regulations, we use the percent of urban population in a country (Urban) and the population density. More pollution exposure is assumed to lead to greater political pressure for compliance i.e both variables have a positive sign [START_REF] Damania | The persistence of corruption and regulatory compliance failures: Theory and evidence[END_REF]. We introduce legal origins to capture institutional persistences and major differences in the legal system La [START_REF] Porta | The quality of government[END_REF]. In our sample, countries are of fourth different legal origins, namely English, French and Socialist. A latitude variable as well as region dummies are also used to control for non observed differences.

Forest Stock Equation

To test proposition 2, we run the following regression:

F orest i = α 0 + α 1 Compliance i + α 2 Judicial i + α 3 Compliance i × Judicial i + k α k Z i + ε i (10)
where F orest i is the growing forest stock in the country i, Judicial i is the quality of the legal framework, Compliance i is the level of environmental compliance, Z i are control variables, α are coefficients vector to estimate and ε i is the error term. Proposition 2 states that both α 1 and α 2 should be positive 3 . The sign of β 3 is not stated by the model. A positive sign means that judicial efficiency could preserve forest stock despite the fact that environmental compliance is low whereas a negative sign means that judicial efficiency lessens forest stock in country with weak environmental compliance. Moreover, a negative effect suggests that there is a threshold effect because the coefficient (α 3 ) term and the additive term (α 2 ) have an opposite sign. The threshold effect is:

δF orest i δJudicial i = α3 + α2 * EnvironmentalCompliance i = 0 ⇒ EnvironmentalCompliance i = - α3 α2
Among control variables, the literature on factors of deforestation (here the forest stock is the inverse of deforestation) is substantial. First, the path of deforestation is often associated positively with the 3 The marginal effect of compliance on the forest growing stock is:

δgrowing δcompliance = α1 + α2 * P astJudicial.
initial forest area (Forest Lag) for three main reasons: (i) the scarcity effect implies that the remained forested lands are more preserved; (ii) logging or forest conversion activities are more expensive when forest areas are low; (iii) the non-forested lands (in proportion to total area) are more available to other land uses such as agriculture, cattle ranching, tree plantations or urbanization when forested lands are important.

Second, the Environmental Kuznets Curve (EKC) approach states that the level of environmental degradation, measured by environmental indicators as deforestation, is linked to economic development [START_REF] Bhattarai | Institutions and the environment kuznets curve for deforestation: A crosscountry analysis for latin america, africa and asia[END_REF][START_REF] Culas | Deforestation and the environmental kuznets curve: An institutional perspective[END_REF]. This relation implies a non linear effect of economic growth on deforestation (GDP per capita and GDP per capita squared ): the marginal income effect is positive for low income countries and become negative for high income economies.

Third, demographical effects and more particularly population pressures are associated with more deforestation. The common explanation advanced is that population growth encourages the conversion of forest land to other uses (and almost agricultural uses) by increasing the need for arable land. The growth of Population (Pop) and the extent of rural population (Rural ) are introduced to control for these pressures on forested land [START_REF] Cropper | The interaction of population growth and environmental quality[END_REF].

Fourth, the relative price of timber (Timber ) is introduced being an important determinant in the trade-off between the keeping forest option or the clearing one [START_REF] Arcand | Deforestation and the real exchange rate[END_REF].

Fifth, we introduce legal origins dummy to capture institutional differences due to different legal system (La [START_REF] Porta | The quality of government[END_REF]. A latitude variable as well as region dummies are used to control for non observed differences.

The Issue of Endogeneity

Our model states that corruption and environmental compliance are simultaneously determined implying a reverse causality bias. A naïve estimation of the parameters of the model may lead to biased estimates if the issue of endogeneity is not taken into account. To tackle this issue, a selection on observables in adding a large number of control variables or a selection on unobservables measuring all other time-invariant determinants could be implemented. However, the first approach does not allow to control for all the bias whereas the second could not be implemented in this paper using cross country data.

Thus, a third approach relies on the use of instrumental variables (IV) under three conditions.

First, IV should be correlated with the supposed endogenous variable. Second, the error term in the instrumentation equations has to be uncorrelated with the measurement error in the structural equations. Third, the IV should not be correlated with the dependent variable, except through the endogenous variables or through the effect on the other variables that have been already controlled for. Estimation are made with the 2SLS estimator.

In our model, corruption and compliance are assumed to be endogenous but we also assume that judicial efficiency could be endogenous. The choice of pertinent instruments for each one of the three endogenous variables relies on the literature. As in [START_REF] Damania | The persistence of corruption and regulatory compliance failures: Theory and evidence[END_REF], environmental compliance could be instrumented in the corruption equation by the level of civic liberties and the degree of environmental education. These two variables measure the extent of informal regulatory pressures in the society and positively influence environmental compliance. Moreover, concerning the forest stock equation, environmental compliance is instrumented by a variable measuring the ethic of firms in a given country and by the environmental education variable.

Concerning the instrumentation of corruption in the compliance equation, we use, as instruments, a political federation dummy and the effectiveness of legislature. [START_REF] Treisman | The causes of corruption: a cross-national study[END_REF] shows that federalism is associated with more corruption because "the competition of different autonomous levels of government to extract bribes from the same economic actors [...] lead(s) to "overgrazing"" (Treisman, 2000, P.433). Legislature effectiveness should decrease corruption by increasing the use of constitutional mechanisms to make politicians and officials more accountable to citizens and so to be viewed as an external control on corruption [START_REF] Serra | Empirical determinants of corruption: A sensitivity analysis[END_REF].

Last, as instruments of judicial efficiency in the corruption equation, we use a variable of constitutional changes whereas in the compliance equation we also use a variable of judicial independence4 .

Basically, we assume that judicial efficiency is negatively influenced by the frequency of changes in the legal system [START_REF] Damania | The persistence of corruption and regulatory compliance failures: Theory and evidence[END_REF] and positively by the degree of judicial independence [START_REF] Porta | Judicial checks and balances[END_REF].

Dataset

We begin by a description of main interested variables: environmental compliance, corruption, judicial efficiency and forest stock. Concerning data on petty corruption, we also found no information on this topic. Thereby, the index provided by Transparency International (averaged on 2000-2007) is used and focuses on corruption in the public sector seen by business people, risk analysts and the general public (from 0 (highly corrupt) to 10 (highly clean), see table 5, page 31 for rankings of 15 worst and best countries in term of corruption, a higher value of this index implies a low corruption).

As a measure of judicial efficiency, the Rule of Law index developed by [START_REF] Kaufmann | Governance matters viii: Aggregate and individual governance indicators 1996-2008[END_REF] "capturing perceptions of the extent to which agents have confidence in and abide by the rules of society, and in particular the quality of contract enforcement, property rights, the police, and the courts, as well as the likelihood of crime and violence" is introduced (from -2.5 (low) to 2.5 (high), averaged on [2005][2006][2007][2008]. This index could be reasonably expected to approach the degree to which laws are enforced.

To measure the forest stock, we use the Growing Forest Stock which is defined as the standing volume of the trees in a forest above a certain minimum size. Higher growing stock implies more standing biomass, which often translates to better forest conditions. The variable used measures the change between 2000 and 2005, in cubic meters per hectare and comes from Environmental Performance Index (EPI) provided by Yale University.

Econometric Results

Interrelationships between Corruption and Compliance

The first proposition of our model states that environmental compliance and petty corruption are positively correlated and conditioned to the level of judicial efficiency. Moreover, result 2 states that judicial efficiency lessens corruption as well as environmental non compliance. Also, in the theoretical model, these results are also controlled by the level of harvest quota. To take into account this effect, we introduce the forest stock variable.

In consequence, compliance and corruption are simultaneously determined and so endogenous. To deal with this issue, we use excluded instrumental variables.

Table 7 displays estimation results from OLS and IV regression of both corruption and compliance equation. Moreover, the use of compliance creates a potential generated regressor bias which could truncate the estimate of standard errors downward and make an inefficient estimation [START_REF] Pagan | Econometric issues in the analysis of regressions with generated regressors[END_REF].

To deal with this issue, standard errors of the compliance variable are bootstrapped (250 replications) in the corruption equation [START_REF] Wooldridge | Econometric Analysis of Cross Section and Panel Data[END_REF].

We find in all regressions that environmental non compliance and corruption are positively correlated as predicted in the model (proposition 1). However, this effect is conditioned by the quality of judicial system6 . In fact, in both OLS and 2SLS regression, the casual effect of compliance on corruption or corruption on compliance becomes non significant when judicial efficiency is introduced as control variable. Result 2 of the model is also confirmed by the econometrical results. A strong judicial framework increases environmental compliance (col.6 and col.8) as well as undermines corruption (col.2 and col.4). This supports our prediction that strengthening the legal framework reduces opportunities for non compliance as well as corruption and rent-seeking activities. Hence, this result highlights the importance of legal infrastructure to understand the interrelationships between non-compliance and corruption. Judicial efficiency is a condition to enhance the appropriation of sustainable reforms by population but also to impede the extent of corruption.

Turning to the control variable effects in the corruption equation, we find that an important forest stock is associated to low corruption. This result supports our prediction which states that less stringent harvest quota strengthens corruption (result 1). Consistent with the literature, the presence of democracy (Democracy Dummy) appears to significantly weaken corruption but only when judicial efficiency is not taken into account contrary to [START_REF] Damania | The persistence of corruption and regulatory compliance failures: Theory and evidence[END_REF]. Also, Log GDP has significant effects in all specification, whereas Openness, legal origins and latitude are insignificant at conventional levels.

Turning to the control variable effects in the compliance equation, we do not find support of our prediction concerning the positive effect of a more stringent harvest quota on compliance. Indeed, the effect of forest stock is negative and insignificant in all specifications. Consistent with the literature, an increase of environmental concerns in people education allow to strengthen the environmental compliance. Among the other control variables, Urban and Population Density have the negative expected effects but not robust in all specifications and civil liberties are significant only in specification with judicial efficiency as control variable. Also, Log GDP has only a significant effect in the last column but negative whereas legal origins and latitude are insignificant at conventional levels.

Finally, for completeness Table 8 reports the first stage regressions.

[Table 7 around here]

Forest Stock Equation

The proposition 2 of the model states that environmental compliance is a substitute for a low level of judicial efficiency or a complement for a high judicial efficiency in order to preserve forest stock.

The table 9 display results related to proposition 2. As validity check, we use excluded instrumental variables for environmental compliance and judicial efficiency.

We find that environmental compliance could help to increase the forest stock. In both specification, compliance has a positive effect which is only significant in the 2SLS specification. Moreover, this effect is increased by the quality of legal infrastructure. The interaction term (Compliance * JudicialEf f.)

is positive and significant (in the 2SLS specification) suggesting that more judicial efficiency improves the POSITIVE effects of positive environmental compliance on forest stock.

However, the additive coefficient of judicial efficiency is negative suggesting that a improvement of the legal system could reduce forest stock but only in a society with a low environmental compliance.

This result highlights that good governance reforms provided by politics has to be appropriated by demand side to become efficient. Moreover, there is a threshold effect because the coefficient term and the additive term of judicial efficiency have an opposite sign. From column 6, the threshold level of environmental compliance that ensures the marginal impact of judicial efficiency on forest stock stands at 4.847 . Also, 95 percent of the countries have levels consistent with an overall negative effect of judicial efficiency on forest stock. This result suggests that the low level of environmental compliance in developing countries could explain why good governance reforms as judicial efficiency may be become non efficient.

Among control variables, only socialist law and latitude have a positive and significant effect.

Finally, for completeness Table F.2 reports the first stage regressions.

[Table 9 around here]

Concluding Remarks

This paper has provided explanations on interrelationships between environmental compliance, corruption and the effectiveness of regulatory institutions in the specific case of forestry in developing countries.

Using a principal-agent model, we highlight two propositions: (i) firm's environmental non compliance and petty corruption are positively correlated (firm-inspector relation) and conditioned to the efficiency of the legal and regulatory framework which lessens both petty corruption and environmental non compliance; (ii) environmental compliance is a substitute of low judicial efficiency or a complement of high judicial efficiency to strengthen forest stock.

Empirical estimations, using cross section data for 59 developing countries, are supporting main theoretical predictions. First, concerning Proposition 1, we find that (i) environmental compliance and corruption are positively correlated but conditioned to judicial efficiency; (ii) judicial efficiency lessens both corruption and compliance. Second, Proposition 2 is empirically validated. Environmental compliance help to preserve the forest stock but this effect is strengthened by the legal system. In countries where legal system is efficient to monitor economic activities and challenge disputes, environmental compliance is a good complement to legal infrastructure to avoid environmental damages.

However, in countries where legal system is too weak to prevent environmental losses, environmental compliance could be a good substitute. Also, in country where environmental compliance is low, an improvement of the legal system could raise losses of the forest stock.

This paper brings a new explanation to understand the weak sustainability of good governance reforms in the environmental field and call for more consideration of the appropriation of institutional reforms (compliance) by main stakeholders to move towards sustainable change.

A Proof of propositions

H v + f I v H ee -λ(f H vv + f I vv ) < 0 (14)
2. Judicial efficiency (λ) decreases the effective bribe payments (B * ).

B * λ = 1/2[-R(v) -(f H (v) -f I (v))] < 0 (15)

A.1.3 Proof of Proposition 1

Proof. Given that a marginal increase of harvest quota lessens both non compliance and petty corruption and given that a marginal increase of judicial efficiency decreases also both non compliance and petty corruption, then the covariance of non compliance and petty corruption is positive. Proof.

Marginal Effect

e * λ = >0 f H v H ee + α β -αβ (W H H ee + W ee ) -λf H vv <0 < 0 (16)
The sign of the numerator f H v is positive and the sign of the denominator is negative (H ee < 0, W H > 0 and H ee < 0, W ee < 0, f H vv ). Thereby the sign of the marginal effect of λ on e * is unambiguously negative.

A.2.2 Result 4

Proof.

e * β = ? - α (1 -α)β 2 [W H H e + W e ] H ee + α β -αβ (W H H ee + W ee ) -λf H vv <0 ( 17
)
The sign of the denominator is negative because H ee < 0, W H > 0 and H ee < 0, W ee < 0, f H vv > 0.

Thereby, the sign of the marginal effect of β on e * depends on the sign of the numerator which depends If λ tends to zero so W H H e + W e < 0 and the sign of e * β is negative (the numerator is positive).

If λ tends to 1, the sign of W H H e + W e depends on the level of f H v . In the case where the firm is compliant, f H v will be nil and the sign of W H H e + W e will be negative as well as the sign of e * β .

A.2.3 Proposition 2

Proof. Given that from result 3, the effect of non compliance β on e * is conditioned to the level of judicial efficiency λ and that from result 4 the effect of judicial efficiency λ on e * is negative, thus we have the proposition 2.

B List of countries

F.2 Forest Stock Results

Table 1 :

 1 Strategies pay-off

	Strategy	Harvester	Inspector
	Safe	H

  Table 4, page 30 summarizes descriptive statistics and Table 2, page 28 provides definitions and sources of variables used.In the literature, we found no data on environmental compliance at country level. To challenge this issue, we build an index of environmental compliance from data of several reports provided by the World Economic Forum. Compliance is predicted values of the corporate ethic 5 of firms in a given country which has been regressed on (i) a variable measuring the burdensome for businesses to comply with governmental administrative requirements (averaged on the period 2007-2009) and on (ii) a variable related to the stringency of environmental regulation (averaged on the period 2007-2009) (see table3, page 31 for more information on these data and table 5, page 31 for rankings of 15 worst and best countries in term of compliance, a higher value of this index implies a high compliance).

.2 Proof of the marginal effect of judicial efficiency

  The harvest quota e decreases the effective bribe payments. (B * ).

	A.1 Proposition 1
	A.1.1 Proof of the marginal effect of harvest quota
	Proof.
	1. The harvest quota e increases the effective harvest effort (e * )
	e * e =	-λ(f H vv + f I vv ) H ee -λ(f H vv + f I vv )	> 0	(11)
	but decreases non compliance (v = e * -e) given that
		e * e =< 1		(12)
	2. B * e = 1/2[-H e + (1 -λ)R vv -λ(f H vv -f I vv )] < 0	(13)
	A.1Proof.
	1. Judicial efficiency (λ) decreases the effective harvest effort (e * ) and so non compliance (v = e * -e,
	for a given harvest quota, e).
	e * λ =	f

  on the sign of W H H e + W e given that the sign of β-αβ+α (β-αβ) 2 is positive. However, W H H e is positive and W e negative, the sign of W H H e + W e is ambiguous. H H e must be lower to -W e + λf H v or W H H e + W e < λf H v and so the sign of W H H e + W e depends on λf H v .

	From equation 7, we have 1 + α β-αβ > α β-αβ so that W

Interrelationships between Corruption and Environmental Compliance

	F Econometric results
	F.1
		List of Developing Countries
		Central and South America
	Argentina	Bolivia	Brazil	Chile	Colombia
	Costa Rica Dominican Republic Ecuador	Guatemala	Guyana
	Honduras	Mexico	Nicaragua	Panama	Paraguay
	Peru	Suriname	Uruguay	Venezuela
			Africa
	Algeria	Botswana	Burkina Faso	Cameroon	Ivory Coast
	Ethiopia	Ghana	Kenya	Madagascar	Malawi
	Mali	Morocco	Mozambique	Namibia	Nigeria
	Senegal	South Africa	Tanzania	Tunisia	Uganda
	Zambia	Zimbabwe
			Asia
	Azerbaijan Bangladesh	Cambodia	China	India
	Indonesia	Kazakhstan	Kyrgyz Republic Korea, Rep.	Malaysia
	Mongolia	Pakistan	Philippines	Saudi Arabia Sri Lanka
	Thailand	Turkey	Vietnam

Table 7 :

 7 Interrelationships between Corruption and Environmental ComplianceThe omitted continent is Africa and the omitted legal origins is common law.

	Dep. Variable:		Corruption			Compliance
		OLS Regression	IV Regression	OLS Regression	IV Regression
		(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
	Envir. Compliance	0.702 * * *	0.071	1.355 * * *	-.070
		(0.174)	(0.124)	(0.395)	(0.316)
	Corruption					0.386 * * *	0.027	0.405 *	-.674
						(0.088)	(0.134)	(0.21)	(0.503)
	Judicial Efficiency		1.395 * * *		1.321 * * *		0.901 * * *		2.793 * * *
			(0.23)		(0.4)		(0.3)		(0.898)
	Forest Stock	4.148 * * *	1.555	3.324 * *	2.111 *	-1.073	-1.332	-1.175	-2.165
		(1.561)	(1.337)	(1.591)	(1.249)	(1.066)	(0.943)	(1.533)	(1.484)
	Log Gdp per capita	0.484 * * *	0.208 *	0.242	0.255 *	0.046	-.103	0.038	-.438 * *
		(0.144)	(0.119)	(0.187)	(0.135)	(0.13)	(0.125)	(0.149)	(0.196)
	Trade (of GDP)	0.00009	-.0004	-.0007	0.0007
		(0.002)	(0.002)	(0.003)	(0.002)
	Democracy	0.147 * * *	0.006	0.11 *	0.023
		(0.043)	(0.035)	(0.059)	(0.038)
	Civic Liberties					0.083	0.199 * *	0.09	0.463 * * *
						(0.088)	(0.094)	(0.107)	(0.137)
	Urban population					-.011 * *	-.005	-.011 * * *	0.008
						(0.005)	(0.006)	(0.004)	(0.008)
	Population density					-.0003	-.0006 * *	-.0003	-.001 * *
						(0.0004)	(0.0002)	(0.0004) (0.0005)
	Environ. Edcuation					0.162 * *	0.149 * *	0.16 * *	0.115 *
						(0.074)	(0.06)	(0.068)	(0.069)
	French Civil law	-.022	-.081	0.15	-.193	-.038	-.152	-.033	-.377
		(0.196)	(0.148)	(0.25)	(0.135)	(0.161)	(0.137)	(0.154)	(0.234)
	Latitude of capital	0.948	0.729	1.431	0.584	-.505	-.221	-.504	0.378
		(0.998)	(0.785)	(1.063)	(0.751)	(0.677)	(0.668)	(0.597)	(0.812)
	Asia	-.297	-.450 * * *	-.230	-.457 * * *	0.041	-.064	0.042	-.280
		(0.211)	(0.173)	(0.241)	(0.162)	(0.23)	(0.199)	(0.2)	(0.227)
	America	-.648 * *	0.093	-.350	0.075	0.2	0.497 * *	0.214	1.159 * * *
		(0.256)	(0.239)	(0.323)	(0.265)	(0.227)	(0.209)	(0.23)	(0.346)
	Constant	-7.755 * * *	0.593	-7.740 * * *	0.149	2.867 * * *	5.094 * * *	2.944 * *	9.987 * * *
		(1.614)	(1.692)	(1.484)	(2.108)	(1.040)	(1.237)	(1.303)	(2.130)
	Obs.	59	59	58	58	58	58	58	57
	Adjusted R2	0.678	0.831	0.569	0.828	0.462	0.54	0.462	0.126
	F-stat	10.295	17.002	9.044	20.629	7.16	10.939	6.936	5.733
	Compliance instrum. equation F-stat			3.851	5.95
	Judicial Eff. instrum. equation F-stat				20.295				8.454
	Corruption instrum. equation F-stat							7.532	20.943
	Hansen P-Value			0.055	0.219			0.07	0.605
	Robust standard errors. *** p<0.01, ** p<0.05, * p<0.1.

Table 8 :

 8 Instrumentation equation for environmental compliance and judicial efficiency Robust standard errors. *** p<0.01, ** p<0.05, * p<0.1. The omitted continent is Africa and the omitted legal origins is common law.

		Corruption Equation		Compliance Equation
	Depend Variable	Compliance Compliance Judicial Eff.	Corruption Corruption Judicial Eff.
	Col. Table 7	col.3	col.4	col.4	col.7	col.8	col.8
		(1)	(2)	(3)	(4)	(5)	(6)
	Excluded Instruments
	Civic Liberties	-.228	-.231 *	-.462 * * *
		(0.141)	(0.139)	(0.078)
	Environ. Education	0.191 * *	0.193 * *	0.061
		(0.09)	(0.085)	(0.048)
	Constitutional change		-.731 * *	-.435 * *		0.332	-.235
			(0.297)	(0.179)		(0.408)	(0.216)
	Judicial Independence					0.311
						(0.063)	(0.033)
	Federalism				-.441	-.342	-.121
					(0.279)	(0.229)	(0.123)
	Legislature Effectiveness				0.352 *	0.169	0.026
					(0.203)	(0.179)	(0.098)
	Included Instruments
	Forest Stock	0.556	0.519	2.203 * * *	4.937 * * *	3.333 * * *	1.510 * *
		(1.046)	(1.053)	(0.645)	(1.815)	(1.222)	(0.641)
	Log Gdp per capita	0.148	0.104	0.226 * * *	0.518 * * *	0.063	0.114
		(0.125)	(0.134)	(0.067)	(0.193)	(0.216)	(0.092)
	Trade (of GDP)	0.002	0.002	0.001
		(0.002)	(0.002)	(0.001)
	Democracy	-.100	-.120	-.124 * * *
		(0.084)	(0.085)	(0.038)
	Civic Liberties				-.289 * * *	-.156 * *	-.160 * * *
					(0.1)	(0.077)	(0.042)
	Urban population				0.006	0.015 * *	-.001
					(0.008)	(0.007)	(0.003)
	Population Density				-.0008 * *	-.0008 *	-.0001
					(0.0004)	(0.0004)	(0.0002)
	Environ. Education				0.06	0.075	0.056
		(0.09)	(0.085)	(0.048)	(0.084)	(0.084)	(0.04)
	French Civil law	-.174	-.253 *	-.058	-.397 *	-.024	0.121
		(0.16)	(0.151)	(0.107)	(0.23)	(0.234)	(0.103)
	Latitude of capital	-.712	-.485	-.304	-.300	-.041	-.125
		(0.79)	(0.803)	(0.416)	(0.88)	(0.739)	(0.413)
	Asia	-.087	-.023	0.21 *	0.063	-.0002	0.184
		(0.193)	(0.205)	(0.114)	(0.302)	(0.325)	(0.144)
	America	-.216	-.132	-.559 * * *	-.786 * * *	-.159	-.237
		(0.235)	(0.247)	(0.122)	(0.263)	(0.32)	(0.152)
	Constant	3.020 * *	3.480 * *	-1.916 * * *	-4.705 * * *	-2.333 *	-3.020 * * *
		(1.492)	(1.473)	(0.718)	(1.486)	(1.212)	(0.684)
	Obs.	58	58	58	58	57	57
	Excluded instrument F-stat	4.32	4.54	17.19	3.11	7.25	8.88

Table 9 :

 9 Environmental Compliance, Judicial Efficiency and Forest Stock Robust standard errors. *** p<0.01, ** p<0.05, * p<0.1. Africa (omitted) common law (omitted). Robust standard errors. *** p<0.01, ** p<0.05, * p<0.1. The omitted continent is Africa and the omitted legal origins is common law.

	Dep. Variable: Growing Stock of Forest		OLS Regression	IV Regression
		(1)	(2)	(3)	(4)	(5)	(6)
	Envir. Compliance	0.02	0.006	0.02	0.048 *	0.154 * *	0.078 * *
		(0.017)	(0.021)	(0.021)	(0.028)	(0.071)	(0.036)
	Envir. Compliance*Judicial Eff.			0.047 * *			0.052 * *
				(0.023)			(0.023)
	Judicial Efficiency		0.025	-.152 *		-.123 *	-.252 * *
			(0.022)	(0.087)		(0.072)	(0.102)
	Log Lag Forest	-.0001	0.0006	-.0002	0.001	-.0006	-.002
		(0.008)	(0.008)	(0.008)	(0.007)	(0.01)	(0.008)
	Log Gdp per capita	-.013	-.020	0.125	-.096	-.101	0.046
		(0.197)	(0.189)	(0.204)	(0.174)	(0.27)	(0.211)
	Log Gdp per capita squared	0.003	0.003	-.007	0.008	0.01	-.0006
		(0.014)	(0.014)	(0.015)	(0.012)	(0.02)	(0.015)
	Rural	0.0005	0.0005	0.0006	-.00002	-.0003	0.0004
		(0.0008) (0.0008) (0.0007)	(0.0007)	(0.001)	(0.0007)
	Pop. Growth	-.015	-.013	-.013	-.002	-.005	-.004
		(0.02)	(0.021)	(0.02)	(0.019)	(0.021)	(0.018)
	Timber	-.007	-.014	-.003	-.018	0.016	0.008
		(0.037)	(0.037)	(0.035)	(0.035)	(0.055)	(0.037)
	French Civil law	0.016	0.015	0.01	0.03	0.039	0.02
		(0.041)	(0.041)	(0.041)	(0.032)	(0.042)	(0.035)
	Socialist/Communist Laws	0.118 * *	0.113 * *	0.114 * *	0.135 * * *	0.169 * *	0.138 * *
		(0.052)	(0.05)	(0.051)	(0.051)	(0.086)	(0.058)
	Latitude of capital	0.153	0.146	0.152	0.205 *	0.297 *	0.24 *
		(0.131)	(0.129)	(0.123)	(0.122)	(0.163)	(0.13)
	America	-.019	-.012	0.002	-.028	-.056	-.026
		(0.039)	(0.041)	(0.042)	(0.036)	(0.046)	(0.03)
	Asia	-.076 * *	-.076 * *	-.074 * *	-.065 * *	-.061 *	-.064 * *
		(0.037)	(0.037)	(0.036)	(0.029)	(0.034)	(0.03)
	Constant	0.808	0.917	0.343	1.017 *	0.501	0.284
		(0.676)	(0.668)	(0.726)	(0.592)	(0.951)	(0.7)
	Obs.	52	52	52	50	50	50
	Adjusted R2	0.182	0.176	0.221	0.18	-.363	0.148
	F-stat	3.525	3.097	3.219	3.317	1.212	2.694
	Compliance instrum. equation F-stat				4.852	7.096	19.551
	Compliance*Judicial Eff. instrum. equation F-stat						116.61
	Judicial Eff. instrum. equation F-stat					12.529	12.398
	Hansen P-Value				0.035	0.217	0.343

An audit agency takes place in the game but only to monitor inspector's reported harvest production. Hence, the audit agency does not take part into the equilibrium process.

In contrast, corruption occurring between the harvester and incumbent government is considered as grand corruption.

In the corruption equation, judicial independence could explain corruption through other channel that judicial efficiency i.e to be endogeneous.

Corporate ethic is the ethical behavior in interactions with public officials, politicians, and other enterprises of firms in a given country. Data are averaged on the period2007-2009.

Remind that a high value of the corruption variable implies a low level of corruption and a high value of the compliance variable represent a high level of compliance.

Environmental compliance ranges from 2.57 to 5.25 with a mean at 3.80.

C Data Sources

The right of the people to freely organize in political parties, to make politic. choices (0: worst; 16: best).

Freedom House Judicial independence

Judiciary is independent from political influences (0 (low) to 10 (high).

Fraser Institute

Table 3: Data used to create the index of compliance

Variables and Definition Sources Corporate Ethics GCR, WEF How would you compare the corporate ethics (ethical behavior in interactions with public officials, politicians, and other enterprises) of firms in your country with those of other countries in the world? (1 = among the worst in the world; 7 = among the best in the world) (2008)(2009) weighted average Burdensome to comply GCR,WEF How burdensome is it for businesses in your country to comply with governmental administrative requirements (e.g., permits, regulations, reporting)? (1 = extremely burdensome; 7 = not burdensome at all) (2008)(2009)

D Descriptive Statistics


Raoudha Chebil

Wided Lejouad Chaari

Stefano A Cerri

PERFORMANCE EVALUATION OF E-COLLABORATION

Keywords: E-collaboration, Performance Evaluation, Efficiency, Ergonomics, Effectiveness

The current global dimension of human exchanges in any domain (work, commerce, learning, entertainment…) is accompanied by technologies that enhance synchronous and asynchronous communication thus facilitating both collaboration and competition: the two driving forces for progress since ages. Collaboration can be made essentially in asynchronous mode by e-mails, files and information exchanges, or in synchronous mode by organizing meetings where collaborators communicate directly. Geographical and temporal distance may be overcome by several ICT (Information and Communication Technologies) solutions, usually under the label of e-collaboration. This concept is based on a high number of interactions that could be classified in three types: Computer to Computer Interaction (1), Collaborator to Computer Interaction (2) and Collaborator to Collaborator Interaction (3). Consequently, performance evaluation of ecollaboration has to be considered as consisting separately on the evaluation of each of the three types of interaction. This view leads to focus on three main aspects: the first is the system -efficiency-the second is the interface -ergonomics-the third is the collaborator's behavior during collaboration and its influence on the outcome of the joint effort -effectiveness. Three evaluation layers are so found. In this paper, we propose an appropriate evaluation method to each layer, so that future developments, applying the new evaluation method and exploiting results in actual settings, may improve separately efficiency, ergonomics and effectiveness of e-collaboration in a complementary way.

INTRODUCTION

Electronic collaboration (or e-collaboration) can be defined as "the collaboration among individuals engaged in a common task using electronic technologies" [START_REF] Kock | Expanding the boundaries of e-collaboration[END_REF]. Two centuries ago, collaboration was possible only between persons in the same place at the same time, then inventions followed and a primitive form of ecollaboration appeared by exploiting the telegraph then the telephone until, in the 1980ties, the mainframes. Despite these developments, e-collaboration was always quite difficult. With the advent of e-mail, ecollaboration has been remarkably favored. Subsequently, other technologies were developed such as Group Decision Support Systems. The Web, in particular its technologies facilitating users that communicate both by "reading and writing", accelerated tremendously the emergence of social networks of many kinds, where "easy" bidirectional communication by the "casual" user permits quite sophisticated forms of e-collaboration.

The concept of e-collaboration has revolutionized many domains like e-commerce and e-learning; so its improvement and dissemination are very interesting and may be beneficial for any application domain. But it was surprising that in the state of the art, works on e-collaboration performance evaluation and improvement present still several limits and are not yet based on widely accepted criteria. This fact will, in our opinion, affect negatively the evolution of the concept. As a solution to this problem, we propose here an ecollaboration performance evaluation method. This paper will be organized as follows. In section 2, we position the reader in the context by summarizing most of the existing work on e-collaboration. In section 3, we detail the proposed performance evaluation solution by explaining first the new interaction view that is behind the three proposed aspects to evaluate: efficiency, ergonomics and effectiveness and second, the evaluation method of each. In section 4, we discuss the validation procedure of the suggested method.

E-COLLABORATION STATE OF THE ART

The state of the art of e-collaboration is quite rich and the existing works can be classified into several categories according to the problem type. The first category consists of the conception and development of collaborative platforms providing services increasingly useful like Agora [START_REF] Dugénie | Agora UCS, Ubiquitous Collaborative Space[END_REF] and AGrIP [START_REF] Zhongzhi | Distributed System Integration in Agent Grid Collaborative Environment[END_REF]. The second category focuses on the most suitable technologies permitting to improve and refine services offered by collaborative platforms. Two particular technologies were studied by the majority of these research works and, at the same time, exploited in some concrete collaboration developments [START_REF] Jonquet | Agent-Grid Integration Language[END_REF]: they are Grid and Agent technologies.

The third category of works deals with performance evaluation of e-collaboration. This concept has no general definition; it is characterized by its strong dependence on the studied domain's constraints. In general, technical evaluations are based on aspects dealing with the performance of the software, like computing time, results and accuracy: these measures can't be applied straightforward in collaborative contexts, because they don't adopt a holistic view of the socio-technical system (the system and the humans) and can't predict its future evolution. To obtain a realistic and useful evaluation, many other factors should be considered, like the objective of e-collaboration, and the actual data and resources (what is traditionally called the pragmatic context) 1 . This strong dependence of e-collaboration from its context renders the evaluation of its performance rather difficult and the identification of general performance evaluation solutions not evident. In the literature [START_REF] Damianos | Evaluation for Collaborative Systems[END_REF], there are different types of evaluations: feasibility evaluation that is based on the cost, iterative evaluation that aims to improve collaborative platforms, comparative evaluation that compares systems and appropriateness evaluation that determines if a system is appropriate to a given organization's process. In e-collaboration performance evaluation works, there are no largely known standard evaluation methods. The most used performance evaluation approach is top-down; it consists on "identifying useful metrics from goals" [START_REF] Steves | A Framework for Evaluating Collaborative Systems in the Real World[END_REF]. There are many methods based on it, like Quality Function Deployment (QFD), Software Quality Metrics (SQM) and Goal/Question/Metric (GQM).

Also, many works on new collaborative platforms speak about performances but do not mention how they evaluate. In our opinion, it is due to the lack of standard and well-known e-collaboration performance evaluation methods. We consider them a key task in the development and maintenance of any software; they can affect negatively the evolution, the reliability and even the life cycle of the whole promising concept of e-collaboration. For these reasons, we propose our evaluation method.

A VIEW ON PERFORMANCE EVALUATION

Interaction view

In order to evaluate e-collaboration, let's begin by analyzing and describing its properties in time. In general, an e-collaboration environment is supported by a distributed system, composed by human collaborators and disposes of software and hardware resources. It is characterized by one or many objectives and involves, to reach them, a certain number of exchanges between collaborators. A successful ecollaboration, is supposed to provide the most adequate conditions to the achievement of all needed exchanges. In fact, to communicate with collaborator B; the collaborator A needs to interact with its 1 One of the reasons underlying the emergence of a " is exactly this: on the future Web, technologies (infrastructures and applications) will not be fruitfully conceived, deployed and exploited unless a very accurate empirical (scientific) study has been associated that analyses the use of those technologies by societies of humans. It becomes therefore evident the profound conceptual shift from the classical "application context" to the future "requirement elicitation, evaluation and exploitation scenario of use" (http://webscience.org/home.html). The same "paradigm shift" is claimed by most of the scientists currently engaged in Service Oriented Computing.

computer which needs to interact on his turn with the recipient's computer. of interactions can be identified during an e Computer Interaction, Collaborator to Computer Interaction, Collaborator to Collaborator Interaction.

As e-collaboration is based on the overlap of these different types of interactions, its evaluation can be considered with respect to the evaluation of each type of Computer Interaction judges the system's performance, i.e. e Computer to Collaborator Interaction judges the interface of the platform finally the evaluation of Collaborator to Colla collaboration and its influence on the global outcomes, i.e. e permit us to consider e-collaboration's evaluation as the analysis of the superposed layers will not consist in proposing a new evaluation method for each layer; but in investigating the most adequate method for each one in the combination needed for accounting the previously explained superposition with respect to studied contexts (scenarios of use).

Evaluation method

Efficiency evaluation

In the literature [START_REF] Jain | The Art of Computer Systems Performance Analysis[END_REF], the main performance evaluation techniques are analytical modeling, simulation and measuring. The first technique consists in analysis of this model permits to extract the system performance parameters implementation and gives precis some mathematical hypothesis and approximations The second technique consists in implementing a software model permitting to imitate in a simple manner the system's evolution. It is interesting when the studied system is under construction, inaccessible or too complex to be handled directly. But it does not always guarantee a faithful representation of the real system. The third technique consists in measuring certain characteristi results. These measures are taken by specific instruments or realized by the system itself. The advantage of this technique is the precision of results. However, the task of measuring could degrade the system's functioning.

To obtain a reliable evaluation faithful manner, namely, the measuring based on it and we have to identif guarantee rapidity of communication and integrity of transferred data. To evaluate these two criteria, we propose to carry out some statistics on communication time and rate of collaboration. As shown in Table 1, we distinguish synchronous and asynchronous modes.

computer which needs to interact on his turn with the recipient's computer. From this description, three types of interactions can be identified during an e-collaboration session as shown by figure 1 collaboration is based on the overlap of these different types of interactions, its evaluation can be considered with respect to the evaluation of each type of these interactions. The evaluation of Computer to uter Interaction judges the system's performance, i.e. e-collaboration's efficiency Computer to Collaborator Interaction judges the interface of the platform, i.e. the ergonomic finally the evaluation of Collaborator to Collaborator Interaction judges the user's behavior during collaboration and its influence on the global outcomes, i.e. e-collaboration effectiveness collaboration's evaluation as the analysis of the superposed layers will not consist in proposing a new evaluation method for each layer; but in investigating the most adequate method for each one in the combination needed for accounting the previously explained superposition with (scenarios of use).

], the main performance evaluation techniques are analytical modeling, simulation and measuring. The first technique consists in representing the system by an abstract mathematical to extract the system performance parameters. This technique precise results. But its application to complex systems requires some mathematical hypothesis and approximations that may affect the fidelity of the The second technique consists in implementing a software model permitting to imitate in a simple manner is interesting when the studied system is under construction, inaccessible or too complex to be handled directly. But it does not always guarantee a faithful representation of the real system. The third technique consists in measuring certain characteristics of the system and analyzing the obtained results. These measures are taken by specific instruments or realized by the system itself. The advantage of this technique is the precision of results. However, the task of measuring could degrade the system's a reliable evaluation, we have to choose the technique representing the reality measuring technique. Consequently, the presented efficiency identify the significant measures to capture. We estimate that this layer must guarantee rapidity of communication and integrity of transferred data. To evaluate these two criteria, we propose to carry out some statistics on communication time and rate of losses having occurred during the collaboration. As shown in Table 1, we distinguish synchronous and asynchronous modes. collaboration is based on the overlap of these different types of interactions, its evaluation can be interactions. The evaluation of Computer to efficiency. The evaluation of ergonomic aspects and user's behavior during effectiveness. This view will collaboration's evaluation as the analysis of the superposed layers. Our contribution will not consist in proposing a new evaluation method for each layer; but in investigating the most adequate method for each one in the combination needed for accounting the previously explained superposition with ], the main performance evaluation techniques are analytical modeling, simulation and mathematical model. The This technique allows rapid requires the assumption of the system representation. The second technique consists in implementing a software model permitting to imitate in a simple manner is interesting when the studied system is under construction, inaccessible or too complex to be handled directly. But it does not always guarantee a faithful representation of the real system. cs of the system and analyzing the obtained results. These measures are taken by specific instruments or realized by the system itself. The advantage of this technique is the precision of results. However, the task of measuring could degrade the system's the reality in the most the presented efficiency evaluation will be the significant measures to capture. We estimate that this layer must guarantee rapidity of communication and integrity of transferred data. To evaluate these two criteria, we losses having occurred during the collaboration. As shown in Table 1, we distinguish synchronous and asynchronous modes.

Losses

Percentage of unsatisfied synchronous requests (having no response): ൌ כ N ns is the number of unsatisfied synchronous requests and N 1 is the total number of synchronous requests (N ns = N 1 -N s ).

Percentage of asynchronous lost requests (not transferred): ൌ כ N p is the number of asynchronous lost requests and N 2 is the total number of asynchronous requests (N p = N 2 -N as ).

After the evaluation, obtained results have to be interpreted by comparing them to expected values. Since the reliability of evaluation depends heavily on the interpretation, these values have to be rigorously chosen. The analysis of several series of experimentations has to be realized to fix these particular values.

Ergonomic evaluation

To evaluate ergonomics, many methods exist in the literature [START_REF] Doubleday | A Comparison of Usability Techniques for Evaluating Design[END_REF]. They can be divided in two categories: analytical and empirical. Analytical methods consist in the simulation of task executions without involving the user while empirical methods observe users behavior during their interaction. Each of these two methods implements diverse techniques: GOMS (Goals, Operator, Methods and Selection Rules), cognitive exploration and heuristic evaluation for analytical methods; and interviews, questionnaires and measuring through required time to execute a task, accuracy of results and number of errors for empirical methods.

Since this layer concerns Computer to Collaborator Interaction, its evaluation should be oriented to the user behavior. So, we adopt the empirical techniques and we propose the following plan to the evaluator: Before the beginning of e-collaboration work: 1. Designate a collaboration member mastering all the session details (objectives, constraints, members profile…) to give precise and correct responses when asked in the following steps and also in effectiveness evaluation. This member will be named the collaboration leader. 2. Determine the global and intermediate objectives of collaboration by interacting with the collaboration leader. 3. According to recovered information, identify the important tasks having to be carried out to reach collaboration objectives. During the collaborative session: 4. Test the collaborators' capacities to execute the identified tasks in step 3. For this aim, we propose two measures estimated as the most significant in this context: time spent to launch a task, number of committed errors before launching a task. The obtained values are interpreted by comparing them to theoretical values fixed by evaluator. After achieving the collaborative work: 5. Retrieve positive and negative collaborators' remarks about the system interface. 6. Generate an evaluation report summarizing the detected failures of the evaluated interface as well as its positive aspects.

Effectiveness evaluation

In general, the success of an e-collaboration is related to the adequacy between the envisaged objectives and the ones actually attained. This adequacy depends on collaborators' behavior and their efficacy in accomplishing the work in question. The evaluation process is as follows: Before the beginning of the collaboration work:

1. Identify e-collaboration constraints by interacting with the collaboration leader. These constraints can consist, for example, in some dependencies between different collaboration steps or distinct collaborators. Their non-compliance could be the cause of unsatisfactory results.

2. Select the events having to be captured according to the stated constraints in the previous step. The evaluation system is intended to offer the possibility to capture different types of events as connection and disconnection of collaborators, the profile of each collaborator, the used software resources and the exchanges carried out during the collaboration session. After achieving the collaborative session: 3. Verify if the global and intermediate objectives were attained through a questionnaire sent to the collaboration leader.

DISCUSSION AND CONCLUSION

As explained in section 2, related works on e-collaboration present several missing conventions, standards, methods and even failures especially in performance evaluation of the socio-technical system consisting of machines and humans engaged in distant collaboration for performing jointly complex tasks. The conception of the presented evaluation method was motivated by the lack of clear guidelines in the literature and the conviction of the importance of validated criteria. Our contribution started by a new vision of the ecollaboration concept, then a new evaluation method was proposed, composed by three evaluation layers: efficiency, ergonomics and effectiveness. As many works have been done in efficiency and ergonomics evaluations, we were able, after some readings, to choose an evaluation method for each of the quoted aspects. The third aspect reflecting performance of collaborator's behavior is specific to e-collaboration: there is no work discussing its evaluation in the literature. So we proposed a new procedure to evaluate it. The overall method is so composed of the three proposed evaluation procedures. The described evaluation does not stop at judging performances but also detects and explains problem origins enabling a more targeted improvement of the evaluated e-collaboration environment. In order to be put in practice, this contribution has to be validated by a number of different collaboration scenarios, each significant for a class of applications. This validation is intended to ensure that the application of the proposed evaluation method reflects correctly the collaborators' satisfaction and permits to detect the eventual collaboration problems. The interpretation process can also be adjusted by many series of experimentations.

  : Computer to mputer Interaction, Collaborator to Computer Interaction, Collaborator to Collaborator Interaction.

Figure 1 .

 1 Figure 1. Interaction diagram

From

  this description, three types collaboration session as shown by figure 1: Computer to mputer Interaction, Collaborator to Computer Interaction, Collaborator to Collaborator Interaction.

Table 1 .

 1 Efficiency measures

	Criterion	Synchronous Mode		Asynchronous Mode
		Average response time to a synchronous request:	Average response time to an asynchronous request:
		ൌ	∑ ୀ	ൌ	∑ ୀ
	Communication
		TRk is the response time to the synchronous	TTk is the response time to the asynchronous
		request k and Ns is the number of satisfied	request k and Nas is the number of asynchronous
		synchronous requests.		transferred requests.


Pascal Auscher

Change of angles in tent spaces

We prove sharp bounds for the equivalence of norms in tent spaces with respect to changes of angles. Some applications are given.

Let B(x, t) denote an open ball centered at x ∈ R n with radius t > 0. Define for a locally square integrable function g(t, y), (t, y) ∈ R n+1 + , for α > 0 and x ∈ R n , A (α) g(x) := R n+1 +

, (0.1) and for 0 < p < ∞, say that g ∈ T p,2 α if

g T p,2 α := A (α) g p < ∞.
This space was introduced in [START_REF] Coifman | Some new function spaces and their applications to harmonic analysis[END_REF]. As sets the spaces for a given p are the same and the norms (or quasi-norms if p < 1) are equivalent: whenever α, β > 0, one has

A (α) g p ∼ A (β) g p . (0.2)
For p = ∞, the limiting space is defined with a Carleson measure condition. Let T α B be the tent with aperture α above the open ball B = B(x, r), i.e., the set of (t, y) such that 0 < t < r/α and y ∈ B(x, rαt). We define g T ∞,2 α as the infimum of C ≥ 0 such that for all ball B,

TαB |g(t, y)| 2 dydt t ≤ C 2 |B| α n . (0.3)
Again, the spaces T ∞,2 α are the same, the norms are equivalent and the isometry property holds. To expain the choice of the normalisation in (0.3), we remark that for p = ∞ included, g(t, y) → h(t, y) := α n/2 g(t/α, y) is an isometry between T p,2 1 and T p,2 α equipped with their respective (quasi-)norms.

It is shown in [START_REF] Coifman | Some new function spaces and their applications to harmonic analysis[END_REF] that the spaces T p,2 1 , 0 < p ≤ ∞, interpolate by the complex method and the real method. The same results hold for T p,2 α for fixed α, with constants (i.e., the constants in the equivalence of norms between T p,2 α and the interpolated space to which it is equal) independent of α by using the isometry property.

Motivated by an intensive usage of tent spaces in the development of new Hardy spaces associated to operators with Gaffney-Davies estimates first made in [START_REF] Auscher | Hardy spaces of differential forms and Riesz transforms on Riemannian manifolds[END_REF], [START_REF] Hofmann | Hardy and BMO spaces associated to divergence form elliptic operators[END_REF], and also by the study of maximal regularity on tent spaces towards applications for parabolic PDE's ( [START_REF] Auscher | The maximal regularity operator on tent spaces[END_REF], and some more work in progress), it became interesting to know the sharp dependence of the bounds in (0.2) with respect to α, β. The L 2 bound is immediate by Fubini's theorem:

g T 2,2 α = (α/β) n/2 g T 2,2 β . For p = 2,
the argument in [START_REF] Coifman | Some new function spaces and their applications to harmonic analysis[END_REF], originating from [START_REF] Fefferman | H p spaces of several variables[END_REF], does not give optimal dependence. The inequality

g T p,2 α ≤ C(1 + log α)α n/τ g T p,2 1 ,
for 1 < p < ∞ and α ≥ 1, where τ = min(p, 2) and C depends only on n and p, is proved in [START_REF] Hytönen | Conical square function estimates in UMD Banach spaces and applications to H ∞ -functional calculi[END_REF] as a special case of a Banach space valued result, and, moreover, the polynomial growth α n/τ is shown 1 to be optimal for such an inequality to hold. The restriction p > 1 occurs in this argument because the UMD property is required and a maximal inequality is used. Note that even the L 2 bounds is not immediate in a Banach (non Hilbert) space valued context. In discussion with T. Hytönen, we convinced ourselves that the logarithmic factor is not produced by this argument in the scalar case when p ≥ 2. Still, this argument is quite involved and elimination of the logarithm in the p < 2 situation was unclear.

Here we give the sharp lower and upper bounds for (0.2) in the scalar case by a very simple argument. Define h(p, α)

= min α -n/2 , α -n/p , h(p, α) = max α -n/2 , α -n/p . Note that h(p, α) = α -n/p if (α -1)(p -2) ≥ 0 and h(p, α) = α -n/2 if (α -1)(p -2) ≤ 0,

and inversely for h(p, α).

Theorem 0.1. Let 0 < p ≤ ∞ and α, β > 0. There exist constants C, C ′ > 0 depending on n, p only, such that for any locally square integrable function g,

Ch(p, α/β) g T p,2 α ≤ g T p,2 β ≤ C ′ h(p, α/β) g T p,2 α .
Moreover, the dependence in α/β is best possible in the sense that this growth is attained.

In particular, for α > 1, τ = min(2, p) and σ = max(2, p), one has

g T p,2 α ≤ Cα n/τ g T p,2 1 , (0.4) g T p,2 1 ≤ Cα -n/σ g T p,2 α . (0.5)
The second one improves the obvious bound g T p,2 1 ≤ g T p,2 α . By symmetry using the relation h(p, α) -1 = h(p, α -1 ) and scale invariance, all cases reduce to (0.4) and (0.5) with α > 1.

Corollary 0.2. Let 0 < p < ∞. There is a constant 0 < C < ∞ depending on n, p only such that for any locally square integrable g, if

V g(x) = ∞ 0 |g(t, x)| 2 dt t 1 2 , V g p ≤ C g T p,2 1 , if p ≤ 2, V g p ≥ C g T p,2 1 , if p ≥ 2.
The corollary was proved by a different method in [START_REF] Auscher | Vertical versus conical square functions[END_REF] when p < 2 and the p > 2 case dates back to [START_REF] Stein | Singular integrals and differentiability properties of functions[END_REF]. The opposite inequalities are false if p = 2. Starting from Theorem 0.1, the proof is a mere application of Lebesgue differentiation theorem when α → 0 for α -n/2 A (α) g(x) converges to V g(x) assuming g smooth with compact support. This assumption is easily removed.

Corollary 0.3. If 0 < p < ∞ and λ > max(2/p, 1), for any locally square integrable g,

R n+1 + t |x -y| + t nλ g(t, y) 2 dydt t n+1 1 2 p ≤ C(n, p, λ) A (1) g p .
The left hand side equals the grand square function of Stein when g(t, y) = t∇u(t, y), u being the harmonic extension of a suitable distribution u 0 on R n . Hence, for all 0 < p < ∞ and λ > max(2/p, 1), it is dominated in L p by A (1) g p which is the L p norm of the area functional of Lusin defined from u 0 . However, it is known from Stein-Weiss' theory that A (1) g ∈ L p (R n ) if and only if n-1 n < p < ∞ and u 0 belongs to the Hardy space H p (R n ) (See [START_REF] Stein | Singular integrals and differentiability properties of functions[END_REF]). This gives a simple proof of Theorem 2, Chap. IV in [START_REF] Stein | Singular integrals and differentiability properties of functions[END_REF]. The lower exponent n-1 n is only due to the choice of the extension. Using an extension by convolution with t -n ϕ(x/t) with ϕ ∈ C ∞ 0 (R n ) having all vanishing moments but the one of order 0, n-1 n becomes 0 by the results in [START_REF] Fefferman | H p spaces of several variables[END_REF]. At λ = 2/p and p < 2, a weak type inequality is plausible, the Lorentz norm L p,∞ replacing the Lebesgue norm L p in the left hand side. It would give a simple proof of the weak type (p, p) result of Fefferman [START_REF] Fefferman | Inequalities for strongly singular convolution operators[END_REF] for Stein's grand square function. We leave this open.

The proof of the corollary is easy by splitting the upper half space according to |x-y|/t compared to powers 2 k , k ≥ 0, and one obtains

R n+1 + t |x -y| + t nλ g(t, y) 2 dydt t n+1 1 2 ≤ C(n, λ) k≥0 2 -knλ/2 A (2 k+1 ) g(x) .
It remains to use A (α) g p ≤ Cα n/τ A (1) g p for α = 2 k+1 in appropriate arguments for p ≥ 1 or p ≤ 1.

The proof of Theorem 0.1 is an easy matter using in part atomic theory for tent spaces, again proved in [START_REF] Coifman | Some new function spaces and their applications to harmonic analysis[END_REF]. Recall that for 0 < p ≤ 1, the tent space T p,2 1 has an atomic decomposition: A T p,2 1 atom is a function a(t, x) supported in a tent T 1 B with the estimate

T1B |a(t, x)| 2 dxdt t ≤ |B| -( 2 p -1)
.

There is a constant C = C(n, p) > 0 such that a T p,2

1 ≤ C. Any T p,2
1 function g can be represented as a series g = λ j a j where a j is a T p,2 1 atom and

|λ j | p ∼ g p T p,2 1
. By the isometry property, a T p,2 α atom is a function A(u, x) supported a tent T α B with the estimate

TαB |A(u, x)| 2 dxdu u ≤ α -n |B| -( 2 p -1)
and the decomposition theorem holds in T p,2 α . Proof of Theorem 0.1. Recall that we may assume α > β = 1 and it is enough to prove (0.4) and (0.5). Fix p = ∞ first. Let g T ∞,2 1 = 1 and B be a ball. As

T α B ⊂ T 1 B , TαB |g(t, x)| 2 dxdt t ≤ T1B |g(t, x)| 2 dxdt t ≤ |B| = α n |B| α n . Hence, g T ∞,2 α ≤ α n/2 . This shows g T ∞,2 α ≤ α n/2 g T ∞,2
1 for all g. Let g T ∞,2 α = 1 and B be a ball. As T 1 B ⊂ T α (αB) where αB is the ball concentric with B dilated by α,

T1B |g(t, x)| 2 dxdt t ≤ Tα(αB) |g(t, x)| 2 dxdt t ≤ |αB| α n = |B| . Hence, g T ∞,2 1 ≤ 1 and g T ∞,2 1 ≤ g T ∞,2
α for all g.

Fix now p ≤ 1. Let B be a ball and a be a T p,2 1 atom supported in a tent T 1 B. As T 1 B ⊂ T α (αB), we have a is supported in T α (αB) and

Tα(αB) |a(t, x)| 2 dxdt t = T1B |a(t, x)| 2 dxdt t ≤ |B| -( 2 p -1) = α 2n/p α -n |αB| -( 2 p -1)
.

Thus α -n/p a is a T p,2 α atom. An atomic decomposition of any element of T p,2

1 is up to multiplication by α -n/p an atomic decomposition in T p,2 α , proving g T p,2 α ≤ C(n, p)α n/p g T p,2 1 . Next, let B be a ball and a be a T p,2 α atom supported in a tent

T α B. As T α B ⊂ T 1 B, we have a is supported in T 1 B and T1B |a(t, x)| 2 dxdt t = TαB |a(t, x)| 2 dxdt t ≤ α -n |B| -( 2 p -1) . Thus α n/2 a is a T p,2 1
atom. As above, we conclude that g T p,2 1 ≤ C(n, p)α -n/2 g T p,2 α . For 1 < p < 2 and 2 < p < ∞, we conclude by interpolation with the p = 2 equality g T 2,2 α = α n/2 g T 2,2 1 . We have shown (0.4) and (0.5). The sharpness of the bounds is seen by saturating these inequalities. Fix α > 1 large. Let B be the unit ball. Set a 1 (t, y) = 1 T1B (t, y)1 [1/2,1] (t). It is easy to see that a 1 T p,2 1 ∼ 1. Now, we have that A (α) a 1 has support equal to B(0, α), is bounded by a constant c(n) > 0 and equal to that constant on the ball B(0, α+1

2 ). Thus a 1 T p,2 α ∼ α n/p . This proves that (0.4) is optimal when p ≤ 2 and (0.5) is optimal when p ≥ 2. Next, let a 2 (t, y) = a 1 (αt, y). By scaling a 2 T p,2 α = α n/2 a 1 T p,2 1 ∼ α n/2 . Now, A (1) a 2 is supported in B, bounded by a constant c(n) > 0 and equal to that constant on B(0, α-1 2α ). Thus a 2 T p,2 1 ∼ 1. This proves that (0.4) is optimal when p ≥ 2 and (0.5) is optimal when p ≤ 2.