Matthieu Roux
email: matthieu.roux@centralesupelec.fr

Yi-Ping Fang
email: yiping.fang@centralesupelec.fr

Anne Barros
email: anne.barros@centralesupelec.fr

A hybrid approach to solve the maintenance problem of an offshore wind farm formulated as a large-scale POMDP

Keywords: complex industrial system, Partially Observable Markov Decision Process, maintenance optimization, imperfect monitoring, large-scale POMDP, offshore wind farm

Introduction

For a couple of decades, we have observed a growing interest in condition-based maintenance (CBM) strategies, a framework in which maintenance decisions are based on the current degradation level of the items [START_REF] Alaswad | A review on condition-based maintenance optimization models for stochastically deteriorating system[END_REF]. In this work, we seek to optimize the CBM policy of a distributed system where inspections and remote sensors can inform on the current degradation level. The system is composed of many units that function and degrade independently. They are monitored continuously by remote sensors and occasionally inspected. The sensors imperfectly estimate the item's state at a low cost, whereas inspections reveal perfectly the true state at a higher cost. We model the problem as a partially observable Markov decision process (POMDP). For that, time is discretized and each unit is characterized by a discrete degradation state s t ∈ S. Sensors provide imperfect observations o t ∈ O, where imperfection in the monitoring process is modeled by the conditional probabilities P(o t = o|s t = s). Eventually, at the beginning of each observation epoch (a group of T time steps), one observation o t is used to update a belief b t representing the probability that the item is in each state.

We study, in particular, the optimization of maintenance operations in the offshore wind turbine industry and propose an extension of [START_REF] Yildirim | Integrated predictive analytics and optimization for opportunistic maintenance and operations in wind farms[END_REF] to the case of mixed sources of condition monitoring information. However, although researchers recently made significant progress in POMDP solvers [START_REF] Papakonstantinou | Planning structural inspection and maintenance policies via dynamic programming and Markov processes[END_REF], the obtained POMDP remains way too large to be solved efficiently. Such complexity is due to the combinatorial explosion in the state and action spaces when having multiple units in the system. Our main contribution is to propose a novel and efficient hybrid heuristic, mixing dynamic programming (DP) and integer linear programming (ILP), to overcome the curse of dimensionality. We also analyze the impact of imperfect monitoring on optimal maintenance policies, extending a previous work [START_REF] Roux | Impact of imperfect monitoring on the optimal condition-based maintenance policy of a single-item system[END_REF].

Problem description

At the beginning of each observation epoch, imperfect observations o t from the remote sensors are collected and lead to update the belief b t using Bayes' formula. For each time step of the observation epoch and each unit of the system, we should select one maintenance action among NA (do nothing), PM (preventive maintenance), CM (corrective maintenance) and I (perfect inspection). Each action is associated with a cost and requires a certain amount of resources (e.g., number of technicians). An opportunity cost is also incurred each time a unit remains failed (e.g., electricity not produced). The objective is to minimize the total maintenance cost over a finite time horizon H (with H T ) while respecting a resource constraint. Since deploying maintenance crews is an expensive operation, there is a solid incentive to group interventions together (opportunistic maintenance). Such a system-level cost, combined with a resource limitation at each time step, explains why the problem cannot be easily decomposed and solved item per item. As a result, the maintenance policy should be optimized and coordinated at the scale of the system, which justifies the need for a scalable solving method capable of handling a system composed of 20 to 200 units.

Hybrid heuristic approach

The maintenance planning is optimized sequentially. At each observation epoch, we solve the following ILP [START_REF] Alaswad | A review on condition-based maintenance optimization models for stochastically deteriorating system[END_REF] to schedule the interventions that should be conducted within the epoch (i.e., for t ∈ {0, T -1}). We split the set of units I into I w (working units) and I f (failed units). Binary variables z a i,t indicate whether the maintenance action a should be performed on item i at time t; x t is a binary variable indicating whether the maintenance crew should be deployed for a least one intervention at time t.

To ensure this framework does not result in a repair-at-failure policy, where PM would never be conducted because of cost minimization, we carefully design the objective function to balance costs from immediate decisions with expected future costs (close to the concept of value function from DP). To do so, we introduce the functions C a (b, t). They estimate the expected future costs resulting from the schedule of intervention a ∈ {PM, CM, I} at time t for a unit that is, at t = 0, in a state described by the belief b. In a sense, it is a heuristic estimation of the added value that can be expected from any available action. In addition, the function C N A (b) estimates the future costs resulting from the choice not to schedule any intervention within the current epoch. This gives us the following objective function to minimize:

min x,z∈{0,1} T -1 t=0 cost deploy • x t + i∈Iw T -1 t=0 C P M (b i , t) • z P M i,t + C I (b i , t) • z I i,t + C N A (b i ) • z N A i + i∈I f T -1 t=0 C CM (t) • z CM i,t (1)
The critical element of our method consists in approximating those expected future costs C a (b, t) using the Q-function obtained when solving an appropriate and well-chosen single unit POMDP. We numerically validate this approach on a numerical use case, a wind farm containing 50 offshore turbines, and show that, although sub-optimal, our method performs significantly better than two alternative approximations. In addition, the fact that the proposed decomposition method can exploit the value of information coming from imperfect condition monitoring further confirms its relevance. Eventually, this is also encouraging as it computes quite efficiently the policy for a relatively large system, for which using a traditional POMDP solver would have been impossible.


Alexandre T J Maria

Clement Delmas

Cyrille Coustal

Pascale Palassin

François Roubille
email: francois.roubille@gmail.com

Alexandre T J Maria1

Immune checkpoint inhibitor-associated myocarditis and coronary artery disease: There may be more than meets the eye!

Keywords: Myocarditis, Heart failure, Immune checkpoint blocker, Immune-related adverse events, Myocardial biopsy, Coronary angiogram

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Immune checkpoint inhibitor-associated myocarditis and coronary artery disease:

There may be more than meets the eye!

Difficult ICI-myocarditis diagnosis

Patients with cancer are also at increased risk of coronary artery disease (CAD) with both chronic coronary syndromes (angina and/or elevated biomarkers) and acute events (mainly acute coronary syndromes). It is mainly explained by shared risk factors for cardiovascular diseases and cardiovascular toxicity, as they present a cancer-induced pro-inflammatory and prothrombotic state [START_REF] Drobni | Association between immune checkpoint inhibitors with cardiovascular events and atherosclerotic plaque[END_REF]. Consistently, in the recent ESC guidelines [START_REF] Lyon | ESC guidelines on cardiooncology developed in collaboration with the European hematology association (EHA), the European Society for therapeutic radiology and oncology (ESTRO) and the international cardiooncology Society (IC-OS)[END_REF], ICI are acknowledged to promote both accelerated atherosclerosis and plaque rupture, but also coronary thrombosis.

That is the reason why, when ICI-myocarditis is suspected, alternative diagnoses have to be ruled out first (acute or chronic artery disease leading to acute coronary syndromes, toxic cardiomyopathy, takotsubo cardiomyopathy, pericarditis, etc.) [START_REF] Lyon | ESC guidelines on cardiooncology developed in collaboration with the European hematology association (EHA), the European Society for therapeutic radiology and oncology (ESTRO) and the international cardiooncology Society (IC-OS)[END_REF]. A rigorous diagnostic workup is mandatory because of the potentially severe consequences of myocarditis under or overdiagnosis (respectively cardiovascular complications including cardiac death, or ICI discontinuation leading to compromised cancer's outcomes). However, the best strategy to manage suspected ICI-myocarditis remains a bone of contention, especially since clinical, biological, and imaging presentation are not specific (14-37% chest pain, 71e76% dyspnea/fatigue, 17-40% arrhythmia, 50-100% troponin elevation, 49-51% decrease in LVEF, and 23-48% cMRI late gadolinium enhancement) [START_REF] Lehmann | Clinical strategy for the diagnosis and treatment of immune checkpoint inhibitor-associated myocarditis: a narrative review[END_REF], leading to specific classification [START_REF] Bonaca | Myocarditis in the setting of cancer therapeutics: proposed case definitions for emerging clinical syndromes in cardio-oncology[END_REF] and new definitions [START_REF] Herrmann | Defining cardiovascular toxicities of cancer therapies: an International Cardio-Oncology Society (IC-OS) consensus statement[END_REF].

High prevalence of associated coronary artery disease

Through the large multicentric retrospective JOint use of database to identify risk factors of CARDIo-vascular Toxicity InducEd by Immune checkpoint Blocker (JOCARDITE) registry [START_REF] Nowatzke | Coronary artery disease and revascularization associated with immune checkpoint blocker myocarditis: report from an international registry[END_REF] (n =474 patients in 57 centers/11 countries), Nowatzke et al. showed that only half of the patients diagnosed with ICI-myocarditis underwent coronary angiography (n= 261/474, 55.1%) while a concomitant coronary artery disease (CAD defined as coronary artery stenosis >70%) was found in about a quarter of them (22.6%; n = 59/261), consistent with our recent pharmacovigilance study where CAD represented one-third of all [9] MACE 9. The absence of difference in clinical, electrocardiographic, and biological presentation between patients with or without CAD highlights the utmost importance of systematic coronarography, especially since a coronary revascularization was required for 32.3% of them (19/59).

Need for a definite diagnosis of ICI-myocarditis

In accordance with clinical practice, only three patients out of four in this report [START_REF] Nowatzke | Coronary artery disease and revascularization associated with immune checkpoint blocker myocarditis: report from an international registry[END_REF] have a confirmed ICI-myocarditis diagnosis by cMRI or histology suggesting possible under or overdiagnosis. As previously suggested, systematic cMRI with dedicated tissue characterization techniques (T1, T1 with gadolinium, T2, T1, and T2 mapping) should be practiced in each suspected case based on modified LakeeLouise criteria [START_REF] Ferreira | Cardiovascular magnetic resonance in nonischemic myocardial inflammation: expert recommendations[END_REF]. Nonetheless, the normality on transthoracic echocardiography and cMRI should not dismiss the diagnosis of myocarditis, and endomyocardial biopsy (EMB) should be considered, especially in patients with recent exposure to ICI for whom an alternative cardiac diagnosis has not been determined. This may concern patients who exhibit clinical symptoms or have elevated biomarkers, electrocardiographic changes, malignant arrhythmias, or a new reduced left ventricular ejection fraction. However, these patients are complex, with a need for cardiologic and pathologic expertise for EMB, and thus might be referred to dedicated cardio-oncology centers [START_REF] Lyon | ESC guidelines on cardiooncology developed in collaboration with the European hematology association (EHA), the European Society for therapeutic radiology and oncology (ESTRO) and the international cardiooncology Society (IC-OS)[END_REF]. In this paper, the picture is probably not fully representative of real-life settings, where ICIMACE may be largely under-reported [START_REF] Palassin | Under-reporting of major cardiac adverse events with immune checkpoint inhibitors in clinical trials: importance of post-marketing pharmacovigilance surveys[END_REF]. CAD, coronary artery disease; CCTA, coronary computed tomography angiography; ICB, immune checkpoint blockers; irAE, immune-related adverse events; NSAI, nonsteroidal anti-inflammatory drugs; TTE, transthoracic echocardiography.

Need to standardize evaluation of ICI-myocarditis suspected cases

The recent ESC guidelines underline that the diagnosis of ACS is based on the same principles as in patients without cancer, but this remains challenging, because of atypical presentation and symptoms masked by cancer or therapy-related side effects [START_REF] Lyon | ESC guidelines on cardiooncology developed in collaboration with the European hematology association (EHA), the European Society for therapeutic radiology and oncology (ESTRO) and the international cardiooncology Society (IC-OS)[END_REF]. Importantly, an invasive strategy is recommended in the case of NSTEMI (class I, level B) [START_REF] Collet | ESC Guidelines for the management of acute coronary syndromes in patients presenting without persistent ST segment elevation[END_REF]. In that perspective, most patients presented in this study [START_REF] Nowatzke | Coronary artery disease and revascularization associated with immune checkpoint blocker myocarditis: report from an international registry[END_REF] should have undergone coronary angiogram. That was not the case, mainly because myocarditis was first suspected. The risk is to consider only this possibility in clinical practice because there is no high level and pragmatical recommendation that could help clinicians to make a definite ICI-myocarditis diagnosis. Nevertheless, ICI-associated myocarditis diagnosis urges for early steroids and/or immunosuppressants administration and may definitively contraindicate ICI, both affecting the cancer prognosis of these patients [START_REF] Lehmann | Clinical strategy for the diagnosis and treatment of immune checkpoint inhibitor-associated myocarditis: a narrative review[END_REF]. In the other hand, the poorer prognosis found for ICI-myocarditis patients with CAD requiring revascularization highlights the importance to search and detect associated CAD, a situation where steroids may conversely be deleterious.

Older age, male sex, preexisting cardiovascular risk factors, and current cardiometabolic protective drugs seem associated with more coronary revascularization and should reinforce the need for coronarography evaluation. History and physical examination should also evaluate for other irAEs and should more specifically include a thorough musculoskeletal and neurologic examination and dedicated biomarkers (CK, anti-acetylcholine receptor antibodies) with regard to the risk of associated myositis and/or myasthenia gravis (3M syndrome) [START_REF] Nguyễn | Rheumatic disorders associated with immune checkpoint inhibitors: what about myositis? An analysis of the WHO's adverse drug reactions database[END_REF].

Conclusion

Evaluation of ICI-associated cardiac injury should aim to confirm the diagnosis of ICImyocarditis while looking for an associated CAD in order to adapt both the neoplastic and cardiological management of the patient (Fig. 1). Ideally, such patients should benefit from specific cardio-oncologic units of expertise. To adequately address the issues mentioned here, randomized clinical trial remain mandatory to assess first the value of a systematic diagnostic strategy in the face of clinicobiological and electrocardiogram signs of cardiac injury in the context of ICI treatment. Others will have to evaluate the interest of the concomitant management of CAD on the cardiovascular and general prognosis of these patients.

Fig. 1

 1 Fig. 1 Suggested algorithm for the diagnosis and management of suspected ICImyocarditis.

Fundings

None.

Conflict of interest statement

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.


Clément Bosquet

Hervé Boulhol

Gravity, log of gravity and the "distance puzzle" *

Keywords: JEL Codes: F10, F15, C13, C21, C23 distance puzzle, gravity equations, international trade, pseudo-maximum likelihood methods

, this elasticity is estimated to have been stable around 0.65-0.70 since the 1960s. Moreover, although FTAs tend to cover neighboring countries, this main result is robust to dierent treatments of FTA eects. The main estimated change refers to the impact of colonial linkages, which has been at least halved. This paper brings also several important methodological contributions to the analysis of gravity equations, including broad support for the Poisson PML estimator.

Introduction

Despite globalization, the role of distance in shaping world trade across trading partners does not seem to have diminished over time. Indeed, according to the meta-analysis carried out by [START_REF] Disdier | The Puzzling Persistence of the Distance Eect on Bilateral Trade[END_REF], trade decreases with distance by at least the same amount today than thirty years ago, with an increase in the (absolute value of) the trade elasticity to distance since the late eighties, a stylised fact framed as the "distance puzzle" by [START_REF] Buch | The Distance Puzzle: On the Interpretation of the Distance Coecient in Gravity Equations[END_REF] or the "missing globalization puzzle" by [START_REF] Coe | The Missing Globalization Puzzle: Evidence of the Declining Importance of Distance[END_REF]. The latter argue that taking into account zero trade ows using a nonlinear estimator of gravity equation in levels, rather than the common practice of using a linear estimator based on the logarithm of ows, enables to resolve the puzzle: they nd that the (absolute value of the) elasticity of trade to distance signicantly decreased from roughly 0.5 in 1975 to 0.3 in 2000.

In order to simplify the text, the current paper always discusses the evolution of this elasticity in absolute values since there is no ambiguity about its sign.

It is not clear in the rst place why a stable elasticity would represent a puzzle. The rather vague presumption seems to be that the expansion of world trade associated with a fall in distance-related trade costs means that distance is having a lesser impact on the structure of trade. Noting that the elasticity of trade to distance is the product of the elasticity of trade to trade costs and of the elasticity of trade costs to distance, there are several reasons to be sceptical about this presumption.

First, the idea that a non-decreasing elasticity represents a puzzle seems somehow related to the "world-is-getting-atter" hypothesis that [START_REF] Leamer | A Flat World, a Level Playing Field, a Small World After All, or None of the Above? Review of Thomas L. Friedman's The World is Flat[END_REF] questions, pointing out that trade remains mostly a neighbourhood phenomenon, as long-distance ows seem to have increased less than short-distance ones. Second, in a careful formalisation of gravity equation, [START_REF] Anderson | Gravity with Gravitas: A Solution to the Border Puzzle[END_REF] show that trade is actually a homogenous function of degree zero in trade costs due to the multilateral resistance terms. Therefore, even though a general decrease in taris spurs international relative to domestic trade, a uniform decrease in transport costs might not lead to increased trade. Third, an overall decrease in transport costs does not necessarily imply a lower distance elasticity of trade. For example, if trade costs, τ ijt , between countries i and j in year t is a function of the bilateral distance d ij such as a t d γt ij , distance can become irrelevant over time through either a decrease in a t or in γ t , but a uniform decrease in distance-related transport costs would be associated with a fall in a t with no implication for the elasticity γ t (Buch et al.). 1 Fourth, the elasticity of trade with respect to trade costs might have rather increased. Based on theory (e.g. Anderson and van Wincoop), this elasticity is positively related to the elasticity of substitution between varieties, and it is often believed that globalization is associated with an increase in the degree of substitutability between varieties, thereby inducing an increase in the elasticity of trade to distance.

However, beyond the semantical debate about whether we are facing a puzzle, the analysis of how the elasticity of trade to distance has evolved in past decades is interesting in its own right. In that respect, the most important contribution of Coe et al. consists in highlighting that a nonlinear estimation of gravity equation specied in levels could lead to a radically dierent conclusion from that obtained using a linear estimation of the same equation in log.

Nevertheless, there is scope for improving the analysis of the "distance puzzle". Santos [START_REF] Silva | The Log of Gravity[END_REF] show that heteroskedasticity in trade levels is such that it biases the main parameters of interests in the log specication of the gravity equation, including the distance elasticity. They propose a Poisson Pseudo-Maximum Likelihood (PPML) estimator and argue that it is likely to be much more ecient than the nonlinear least squares (NLS) estimator.

However, their study covers a single year (1990) only. With this in mind, the Coe et al.'s assessment could be revisited in several directions. First, the main result is established using NLS. A robustness check is performed using a Pseudo-Maximum Likelihood, but it is not totally clear which one is used. Second, the sample is restricted to 73 countries and start in 1975 only. Third, the sum of exports and imports is used as the dependent variable, but making a distinction between exports and imports, as one must according to [START_REF] Baldwin | Gravity for Dummies and Dummies for Gravity Equations[END_REF], might lead to dierent results. Fourth, the data used for Free Trade Agreements (FTAs) are not well dened. However, because FTAs have mainly promoted regional integration, they are de facto inversely related to distance. Therefore, not properly controlling for FTAs might be misleading. The current paper addresses methodological issues related to the estimation of gravity equations and analyses carefully the sensitivity of the estimates to the treatment of FTAs. The main results are the following.

Methodology. The assumption that the conditional variance of ows is proportional to the conditional expectancy (Poisson hypothesis) cannot be rejected in any (post-1952) year. Second, the most ecient estimator might, however, be in between NLS and PPML, i.e. consistent with the variance of trade ows being about proportional to the square root of the conditional mean.

Third, there remains a serious puzzle with respect to the whole methodology based on the class of PML estimators relying on the proportionality of the conditional variance to a power of the conditional mean. Indeed, the gamma PML estimates which should be consistent, albeit inecient, under the proportionality assumption is signicantly dierent from the Poisson PML ones, being actually closer to the biased OLS of the log specication. Fourth, there are some limitations to the type of estimators one can used. For example, the negative binomial PML estimator is not appropriate because it articially depends on the unit chosen to measure the value of trade ows. Fifth, weighted least squares (WLS) of the log specication that uses observed ows as weights leads to estimates that are similar to PPML on the level specication (the same is true of iterated WLS that uses estimated ows as weights). Sixth, given the high level of serial correlation of trade ows, a "rst-dierencing" type of data transformation seems to be preferable to a xed-eect estimator in a panel specication.

Empirics. Based on PPML and without controlling for FTAs, the distance elasticity of trade has been broadly stable within a 0.60-0.75 range since 1950, even though it has increased from the bottom to the top of that range since the late eighties. The gap between this PPML elasticity and that estimated based on the log specication has steadily increased over time, and this trend is shown to be related to the growing heterogeneity of trade ows. This result is consistent with the explanation proposed by Santos Silva and Tenreyro for the bias of the log specication. The most notable change refers to the eect of colonial linkages which is estimated to have basically vanished over time from a very high level in the fties.2 Taking into account the inuence of FTAs to analyse the "distance puzzle" raises some intricate issues, as

shown by [START_REF] Baier | Do Free Trade Agreements Actually Increase Members International Trade?[END_REF] who use a log specication. However, the inuence of FTAs appears somehow limited. In all carried out robustness checks, including panel estimates, the inclusion of FTAs does not alter the diagnosis of a broad stability of the elasticity, although within a tighter 0.60-0.70 range, still leading to a clear rejection of the rising elasticity obtained in usual log specication. Compared with Baier and Berstrand, all parameters related to the determinants of trade costs are allowed to vary over time using a panel specication. The eect of FTAs is then estimated at around 0.3 with few variations over time, which means that a trade agreement increases trade ows by about 35%.

The rest of the paper is organised as follows. Section 2 discusses the main methodological and empirical issues when estimating gravity equations to analyse the "distance puzzle". Section 3 presents the data and specications, while Section 4 is devoted to the cross section results obtained when FTAs are not included in the list of explanatory variables. Section 5 focuses on the impact of accounting for FTAs, in both cross section and panel estimates. Section 6 briey discusses the estimated trends in the other determinants of trade. Section 7 concludes.

2 The empirics of gravity equations

Microfoundations of gravity equations

There have been major advances in the formalisation of bilateral trade ows since the midnineties, as the traditional specications of gravity equations were largely a-theoretic. In an eort to lay out the microfoundations of gravity equations, [START_REF] Deardo | Determinants of Bilateral Trade: Does Gravity Work in a Neoclassical World?[END_REF] shows that not only the bilateral distance between two countries but also their geographical positions relative to all other countries matter for the level of bilateral trade ows. Consequently, [START_REF] Wei | Intra-national versus International Trade: How Stubborn are Nation States in Globalization?[END_REF] and many researchers since then have added a remoteness indicator to the list of explanatory variables, approximating remoteness by the weighted average of distances from all trading partners, with trading partners' GDP as the weights.

The decisive methodological contribution of [START_REF] Anderson | Gravity with Gravitas: A Solution to the Border Puzzle[END_REF] consists in deriving an operational gravity model in which "multilateral resistance" that depends on all bilateral trade costs is a determinant of bilateral trade ows. The absence of the multilateral resistance terms in traditional gravity estimations leads to biased estimates of some key parameters such as the eect of a common border, as these missing terms are correlated to traditional explanatory variables. In Anderson and van Wincoop, the nominal value of exports from i to j, x ij , depends on the total income, Y . , of each country, world income, Y W , the bilateral trade cost, τ ij , the elasticity of substitution between all goods, σ, and the multilateral resistance, P . , of each country, according to:

x ij = Y i Y j Y W τ ij P i P j 1-σ (1)
where the P . terms are related to each other as follows:

P 1-σ j = i P σ-1 i τ 1-σ ij Y i Y W ∀j (2)
From this specication, Anderson and van Wincoop draw two implications that are especially relevant for the current study. First, the remoteness variables as commonly approximated are disconnected from the theory. Second, given a specication of trade costs, replacing the multilateral resistance terms by country xed eect leads to consistent estimates of the gravity equation ( 1) in log form by ordinary least squares. Even though this xed-eect estimator is less ecient than the nonlinear least-squares estimator that uses information on the full structure of the model, i.e. ( 1) and ( 2), it has the huge advantage of simplicity.

Log of gravity: consistency, eciency and competing estimators

In turn, Santos [START_REF] Silva | The Log of Gravity[END_REF] highlight another typical bias of gravity equations that are estimated in log form, on top of the sample selection bias that results from the implicit exclusion of zero trade ows. Starting from a stochastic version of the gravity equation in levels such as (1), the log-linear specication generates biases as a consequence of Jensen's inequality (E(ln x) = ln E(x)), because the expected value of the logarithm of trade ows depends on higher moments, including the variance. Formally,

x ij = exp(Z ij β)u ij , E(u|Z) = 1 (3) V ar(u|Z) = 0 ⇒ E(ln u|Z) = 0 (4)
where the Z explanatory variables include importer and exporter xed eects, (log of) bilateral distances and other control variables inuencing the trade costs. Since the variance of the residuals is likely to depend on explanatory variables such as importer and exporter characteristics (that cover observed ones like GDP), estimators using the log specication would bias the parameters of interest.3 Thus, the magnitude of the bias depends on the structure of the variance of the residuals, and heteroskedasticity in the trade level equation could become a serious concern for inferences make from estimates based on the log-linear specication.

This problem can be overcome by estimating the level equation (3) using a nonlinear estimator. Santos [START_REF] Silva | The Log of Gravity[END_REF] propose the Poisson Pseudo-Maximum Likelihood estimator (PPML), assuming that the variance of x is proportional to its conditional expectancy, which is likely to make this estimator more ecient than the simple nonlinear least squares (NLS). Indeed, it is unrealistic to assume, as implicit with NLS, that the variance of estimated trade ows is the same for small/remote and large/central countries. Besides, whatever the specic choice of a nonlinear estimator, a level specication allows for the inclusion of zero trade ows, even though Santos Silva and Tenreyro show ex post, i.e. based on the empirical analysis, that including the zero ows does not make a material dierence.

A natural extension consists in assuming other distributions than Poisson. This would include gamma distribution according to which the variance is proportional to the square of the conditional mean, and more generally any power of it. Some authors have also used the negative binomial distribution (e.g. [START_REF] Head | How Remote is the Oshoring Threat?[END_REF], but this is inappropriate when applied to trade ows because such an estimator articially depends on the choice of the nominal unit of the dependent variable. Indeed, the assumption of the negative binomial distribution is:

V ar(x|Z) = E(x|Z) + η 2 E 2 (x|Z) (5)
where η is a scalar to be estimated. The problem arises because the ratio between the expectancy of x ij and its square can be made either innitely small or large depending on the unit choice. Formally, if the unit is changed such that the empirical analysis is conducted on X = κ x, assuming that X follows a negative binomial distribution implies that:

V ar(X|Z) = E(X|Z) + η 2 E 2 (X|Z) = κE(x|Z) + κ 2 η 2 E 2 (x|Z)
Hence, when κ → 0, V ar(X|Z) ≈ κE(x|Z) = E(X|Z), and the negative binomial PML estimator tends towards PPML. Conversely, when κ → ∞, V ar(X|Z)

≈ κ 2 η 2 E(x|Z) =
η 2 E 2 (X|Z), and the negative binomial PML estimator tends towards gamma PML.

In order to discriminate between the various a priori legitimate PML estimators, [START_REF] Manning | Estimating Log Models: To Transform or Not to Transform?[END_REF]

suggest that if V ar(x ij |Z) = λ 0 E(x ij |Z) λ 1
, the choice of the appropriate estimator can be based on an asymptotically valid estimate of λ 1 from:

(x ij -xij ) 2 = λ 0 xij λ 1 + ζ ij ( 6
)
where xij is the value of E(x ij |Z) estimated from an initially consistent estimator like PPML. 4

A nal comment refers back to the estimation of gravity equations in logarithm. A Taylor series that is limited to the second moment around the conditional mean gives:

Log x ij ≈ Log E(x ij |Z) + x ij -E(x ij |Z) E(x ij |Z) - 1 2 [x ij -E(x ij |Z)] 2 E 2 (x ij |Z)
And therefore 5 ,

E(Log x ij |Z) ≈ Log E(x ij |Z) - 1 2 V ar(x ij |Z) E 2 (x ij |Z) (7) V ar(Log x ij |Z) ≈ V ar(x ij |Z)/E 2 (x ij |Z) (8)
On top of the possible selection bias due to the elimination of zero trade ows, these equations summarize two issues with the log of gravity. Equation ( 7) highlights the bias that is stressed by Santos Silva and Tenreyro. Beyond that bias, equation ( 8) shows that assuming that 4 ntos ilv nd enreyro tully suggest testing the dequy of prtiulr vlue of λ 1 from ylor expnsion of @TAD whih they pply in the empiril prt of their pperF nfortuntelyD this proedure is sujet to the sme prolem s for the negtive inomil estimtorX it rti(illy depends on the unit hoie of trde )owsD nd ould therefore e misledingF 5 he omputtion of the vrine uses the ylor series t the (rst order @helt methodAF his is only n pproximtion of ourseD nd going to the seond degree sometimes improves the pproximtion of the vrine importntly @e.g. iwri nd ilstonD IWWWAF errors of the log specication are i.i.d., as implicit when estimating with OLS, is consistent with the conditional variance of the ow being proportional to the square of the conditional mean, i.e. with the gamma distribution. Therefore, if the true distribution were gamma, estimating the log level equation using OLS would only bias the intercept (ignoring the sample selection bias, see eq. 7), and not the other parameters of interest such as the distance coecient. In other words, the magnitude of the biases (except the constant) of the gravity equation that is estimated using the log-linear specication depends on how far the distribution of trade ows is from the gamma distribution. If, however, the true distribution is Poisson, ( 7) and ( 8) become, where α is a constant, respectively:

E(Log x ij |Z) ≈ Log E(x ij |Z) -α/E(x ij |Z) V ar(Log x ij |Z) ≈ 2α/E(x ij |Z)
In that case, the bias would be very severe for small ows. Moreover, OLS estimates of the log specication would ignore that the variance of the log is very large for small ows; in other words, it would give far too much weight to small ows. 6 Ignoring the bias, the "ecient" weighted least squares (WLS) is obtained in that case by weighting each observation by the inverse of the variance, i.e. in that case by the conditional mean. This WLS estimator of the log specication might be appealing because it reduces the bias mechanically, as low weights are given to observations that contribute the most to the bias.

Panel estimates and the "distance puzzle"

As argued by [START_REF] Baier | Do Free Trade Agreements Actually Increase Members International Trade?[END_REF], cross section estimates of gravity equation might be biased due to the endogeneity of free trade agreements (FTAs). In particular, properly controlling for the inuence of FTAs might be important for the estimate of the evolution of the elasticity of trade with respect to distance. Indeed, FTAs cover an increasing share of world trade and are often agreements between neighbouring countries, hence an obvious correlation between FTAs and distances. For example, [START_REF] Berthelon | On the Conservation of Distance in International Trade[END_REF] refer to regionalism as the most obvious explanation for the persistence of distance as a determinant of trade ows. However, nding an instrument for FTAs that does not inuence trade by any other channel is extremely dicult. In this context, Baier and Bergstrand argue that country pair idiosyncrasies should be accounted for via so-called "dyadic xed eects" to eliminate the bias due to the endogenity of FTAs; more generally panel specications of gravity equations make it possible to control for a battery of xed eects. Besides, multilateral resistance terms require the inclusion of origin and destination country dummies for each year in panel data.

Importantly, when introducing dyadic xed eects, the level of the distance elasticity is lost, and only the changes through time can be estimated. It is clear also that introducing the i * j, i * t, j * t xed eects in a nonlinear specication represents a numerical challenge that could be adressed e.g. by period-averaging.

3 Data and econometric specication The geographical variables, distance between countries, common border, common language and colonial linkage dummies, are taken from the CEPII database. 7 The FTA data is broadly the same as the one used in [START_REF] Baier | Do Free Trade Agreements Actually Increase Members International Trade?[END_REF]. Specically, the database used by 7 httpXGGwwwFepiiFfrGnglisgrphGddGdistnesFhtmD gentre d9itudes rospetives et d9snformtions snterntionlesF these authors has been corrected and improved by [START_REF] Fontagné | A Re-evaluation of the Impact of Regional Agreements on Trade Patterns[END_REF] in their reestimation of the impact of FTAs. 8 The proportion of the value of world trade covered by FTAs goes from 7% in 1958 to 31% in 2006.

Finally, it proved useful to work also with a balanced panel to account for the increasing number of trade ows as well as for the change in the sample over time. Hence, the largest possible balanced panel consits of the same 2550 pairs of countries between 1952 and 2006 covering 90 countries and 78% of world trade on average. In particular, the construction of the balanced panel drastically reduces the number of dyadic xed eects, that are necessary to estimate the FTA eect in panel.

Specication

Following the discussion in section 2, the gravity equation is estimated in levels including importer and exporter xed eects. Although the Poisson PML is used for the central estimates, NLS and gamma PML estimators are also computed. Moreover, the most ecient power of the conditional mean is estimated according to equation ( 6), which enables to test the Poisson assumption.

Formally in the cross section analysis, the following equation is estimated for each year:

x ij = exp(α 0 + γ ln d ij + α 1 B ij + α 2 L ij + α 3 C ij + α 4 F T A ij + F X i + F M j )u ij (9) with V ar(x ij |Z) = λ 0 E(x ij |Z) λ 1 .
x ij is the nominal US$ value of export from i to j, F X i and F M j are the xed eects for exporting and importing countries, respectively. B ij , L ij and C ij are the traditionnal control covariates: common border, common ocial language and colonial linkage dummies, respectively. u ij are the multiplicative error terms of the nonlinear estimates. The log version is also estimated using ordinary and weighted least squares estimators (sub-section 2.2).

In order to separate the various factors inuencing the analysis of the distance puzzle, the gravity equations are rst estimated without controlling for FTAs (F T A ij ). Because these rst results might be subject to the omitted variable biases, the analysis focuses, in a second step, on the eect of controlling for FTAs. Finally, following the discussion in sub-section 2.3, a panel specication including dyadic xed eect is estimated:

x ijt = exp(γ t ln d ij +α 1t B ij +α 2t L ij +α 3t C ij +α 4t F T A ijt +F X it +F M jt +Dyadic ij )u ijt (10)
4 Cross section results without controlling for FTAs

This section presents the cross section results obtained without controlling for free trade agreements. The focus is on the elasticity of trade with respect to bilateral distance, the other parameters of interest in the gravity equation are discussed in greater detail in Appendix A.

As a benchmark, estimates using the PPML are presented in sub-section 4.1 while sub-section 4.2 shows why this benchmark is actually the baseline.

PPML

The gravity equation as specied in equation ( 9) is estimated for each year by PPML. Table 1 presents the results for six specic years between 1955 and 2005. The elasticity of trade to distance is estimated to have been broadly stable over the period within a (0.60, 0.75) range.

This range is tight compared with those found in the literature based on log specications.

The estimated robust standard error has steadily declined from 0.040 to 0.025 indicating an improvement over time in the precision of the estimate.

Figure 2 presents the evolution of the trade elasticity to distance, estimated using either OLS in logs or PPML in levels, along with condence intervals. The PPML estimates are not sensitive to whether the zero trade ows are included or not (condence intervals are also similar), a result also found by Santos Silva and Tenreyro, and Coe et al. using NLS. Based on the log-linear specication, the elasticity would have steadily increased from 0.70 to 1.60, which characterizes the distance puzzle. As a result, the dierence between "PPML" and "log-linear" elasticities has dramaticaly increased over time.

This increasing dierence seems to be due to the growing heterogeneity of ows and induced heteroskedasticity, consistent with the idea introduced by Santos Silva and Tenreyro. The intuition behind such a link is illustrated in two ways. First, Figure 3 replicates Figure 2 and adds the elasticity estimated from the smaller albeit more homogenous balanced panel. While the PPML estimate is not sensitive to the choice of the sample, the reduced heterogeneity in the balanced panel leads to a lower estimated elasticity in the log-linear specication compared with that for the whole sample, the more so for the more recent years. Second, two measures of dispersion and one of heteroskedasticity were computed. The measures of dispersion are the interquartile ratio (ratio of 3rd to 1st quartile) of trade ows, and the coecient of variation (standard deviation divided by mean). They are computed on the sample on which the loglinear specication is based, i.e. without zeros (again, the inclusion of zero ows has minor eects on the PPML estimates). The measure of heteroskedasticity related to the bias of the log-linear estimator is the share of the variance of log û explained by (the log of) distance, where û is the PPML estimated multiplicative residual. Indeed, according to Jensen's inequality, the bias of log OLS is due to the dependence of log u on Z. 9

Figure 4 represents these three indicators in addition to the dierence in the distance elasticity between PPML and log-linear OLS. Over the period, the q3 / q1 ratio has increased by a factor of 12. This is due to the tremendous increase in small non-zero ows, as q1 decreased from $ 2 millions (US $ is deated by US GDP deator with 2000 as the base year) in the 1950s to $ 0.1 million since the mid-1990s. Within the same period, the average ow increased from $ 100 M to $ 400 M, and the standard deviation increased even faster as the coecient of variation rised from 4 to 10. Since the small non-zero ows carry a disproportionate weight in log, the increase in its share is likely to contribute heavily to the widening of the gap between the PPML and the log-linear elasticities. Visually, the variations of the dierence between log OLS and PPML elasticities are strikingly closely related to those of the contribution of distance to the variance of the residuals.

9 he log of the residul is diretly relted to the is s eqution Q nd U imply tht E(log u|Z) ≈ -1 2 V ar(u|Z)F

4.2 Which pseudo-maximum likelihood estimator?

This part investigates whether the assessment of the distance puzzle is sensitive to the choice of the nonlinear estimator among the class that veries V ar(x ij |Z) = λ 0 E(x ij |Z) λ 1 , all of them being consistent under (3). This includes the nonlinear least squares (NLS, λ 1 = 0), the PPML (λ 1 = 1) and the gamma PML (GPML, λ 1 = 2). 10

Figure 5 compares the NLS and PPML estimates of the distance elasticity. The level and evolution of the estimated elasticity is similar between the two estimators, even though the variations are greater with NLS (and the elasticity unrealistically low at the beginning of the period). On average, the NLS estimated standard error is twice as large as the PPML one, suggesting that PPML is more ecient. The main dierence in the point estimates is that the elasticity is estimated to have fallen since the mid-1980s with NLS, while it is broadly stable with PPML.

The signicant dierence between the elasticity estimated by PPML and GPML is striking, as illustrated by Figure 6. 11 Actually, the trend in the GPML elasticity looks very similar to the log-linear OLS one, which is problematic: even though both GPML and log-linear OLS give a high weight to small ows, which might be a source of poor eciency (and bias for log), the GPML should be consistent under (3). However, it is signicantly dierent from PPML, another consistent estimator under (3): this is the main remaining puzzle of the whole approach.

Figure 6 also adds the negative binomial estimator for dierent unit values of the trade ows in order to illustrate the theoretical result established in sub-section 2.2: this estimator is indeed sensitive to the unit choice, converging at the limits either to the PPML or the GPML, which makes it inadequate to estimate gravity equations.

As discussed in Section 2, estimating equation ( 6) should help to select the most ecient estimator. However, this test actually proves to be decient, as its conclusions depend on the choice of the estimator used to calculate xij . When PPML is used, the average estimate over the period is 1.03 with an average estimated standard error of 0.26 (Figure 7 and Table 2 for 10 por λ 1 = 0D xv or mximum likelihood leds to lmost identil estimtesF 11 he stndrd errors of oth estimtorsD not represented in the grphD re round HFHQD whih mkes them signi(ntly di'erentF specic years). PPML is never rejected as optimal, whereas NLS and GPML always are at 95% condence level (except for a few years for GPML). When NLS is used to calculate xij , λ 1 is estimated at 0.64 on average. So far, this seems to clearly discriminate in favour of PPML.

Unfortunately, when GPML is used for xij , λ 1 is estimated at 2.31 on average, indicating that GPML should be preferred over both PPML and NLS. The reason why this test is inadequate is not totally clear; our hypothesis is that GPML is not consistent to start with, and this is left for further research.

GPML is a questionable estimator according to three types of arguments. The rst is based on a judgement call that is illustrated by taking two trade ows of $ 10,000 and $ 1 Billion.

While NLS gives the same importance to making an estimated error of $ 10,000 on each of them, GPML gives the same importance to making an error of say 10% of each ow, i.e. of $ 1,000 and $ 100 Millions, respectively. PPML seems to be a good compromise between these two extremes. Second, Figure 8 presents the scatter plots of the observed ows (x-axis) and estimated ones (y-axis) using NLS, PPML and GPML. The t for GPML is strikingly very bad.

As a matter of fact, the sum of squares of the residual is equal to 4.3% of the total variance with NLS, 9.8% with PPML and 4200% with GPML. Although NLS does better by denition based on this indicator, the poor performance of GPML is extreme. Finally, and perhaps even more convincingly, for 2000 as an example, the total sample has been split in two using the median of trade ows as a cut-o. As shown in Table 3, NLS and PPML produce similar estimates on the whole and split samples. In contrast, with GPML (and log OLS), the elasticity is lower with both the below-and above-median samples compared with the whole sample, and closer to PPML. This suggests that GPML does not account for heterogeneity properly. We take all these as evidence against GPML.

Finally, as PPML seems to be the preferred estimator, one is tempted, following the discussion in sub-section 2.2, to compute the WLS estimator of the log specication, where the weights are either observed or iterated estimated (starting with OLS) trade ows. Both WLS linear estimates are amazingly close to the PPML ones, as shown in Figure 9. This highlights that using WLS to improve eciency is also powerful to reduce, or even eliminate, the bias of the OLS log specication.

5 Results with FTAs, and panel specication Sub-section 5.1 discusses whether the baseline obtained in section 4 without controlling for FTAs is sensitive to dierent values of the FTA parameter when it is constrained in cross sections. Sub-section 5.2 analyses the "distance puzzle" using panel data.

Sensitivity to the eect of FTAs in cross section

Accounting for FTAs has a small impact on the assesment of the "distance puzzle". The sensitivity of the distance elasticity of trade to the FTA parameter is shown in Figure 10, the parameter being equal to 0, 0.3 or 0.6 using PPML in cross sections. These values are based on the dierent estimates of the FTA eect in the panel approach (sub-section 5.2). Naturally, the rst case (parameter = 0) corresponds to the results presented in the previous section. As expected, because FTAs are negatively correlated with distance, taking into account the eect of FTAs reduces the estimated distance coecient, although the dierence is never greater than 0.12.

Whether the FTA parameter is contrained to 0, 0.3 or 0.6 does not make any dierence in the evolution of the elasticity of trade to distance until 1972. From 1973, the gap between the dierent estimates increases, as does the coverage of trade ows by FTAs (right scale). 12When the FTA parameter is constrained to 0.3, for example, the estimated distance coecient remains stable around 0.65 (average standard error around 0.03) and within a 0.60-0.70 range.

From the mid-eighties the evolution is hump-shaped with a recent increase from 0.60 to 0.70 between 1994 and 2006.

In sum, the main dierence between these three estimates lies in the end point value for the elasticitiy. It is 0.76, 0.71 and 0.66 in 2006 when the FTA parameter is constrained to 0, 0.3 and 0.6 respectively. The shape of the evolution is aected accordingly, but without changing the broad assessment of a stable elasticity over the whole period. In particular, these dierences are small compared with the magnitude of the bias indentied by Santos Silva and Tenreyro.

Panel analysis of the distance puzzle

Following section 2.3, the panel estimation of gravity equations requires both time-varying importer and exporter xed eects as well as "dyadic xed eects" in order to account for bilateral heterogeneity. All these xed eects generate computational diculties. As a result, the estimation of equation ( 10) has been carried out using 5-year averaging. 13 Also, working on the perfectly balanced panel dataset presented in section 3 (covering 90 countries) allows to drastically reduce the number of xed eects.

With dyadic xed eects, only the evolution through time can be estimated, the levels of the parameters that are xed through time such as geographic characteristics being wiped out.

However, unlike Baier and Bergstrand, elasticities are here allowed to vary. As shown in Figure 11, estimation of equation ( 10) using PPML leads to a similar evolution of the trade elasticity to distance to that obtained in the cross section analysis, even though the estimated elasticity has increased by about 0.10 since the mid-60s.

Depending on the autocorrelation level of the residuals, the xed-eect estimator might not be the most ecient (Woolridge, 2001, chapter 10). As robustness checks, two other panel estimators, that mirrors rst-dierencing, have been implemented to deal with the dyadic xed eects. The rst uses x ijt /x ijt-1 as the dependent variable. 14

x ijt x ijt-1 = exp(∆γ t ln d ij +∆α 1t B ij +∆α 2t L ij +∆α 3t C ij +∆(α 4t F T A ijt )+∆F X it +∆F M jt )v ijt (11)
where

v ijt = u ijt /u ijt-1 .
Due to heteroskedasticity, this specication is estimated eciently by weighted NLS where the weights are the inverse of the variance of x ijt /x ijt-1 . Appendix B shows that under the

Poisson assumption V ar(x ijt /x ijt-1 |Z) is proportional to the inverse of E(x ijt-1 |Z). Hence, the

13 o e onsistent with the grvity spei(tion in levels suh s @WA or @IHAD the geometri men of trde )ows is used s the dependnt vrileF fy omprisonD fier nd fergstrnd use spei(tion in logs with elstiities with respet to distneD orderD olonil linkD etF tht re onstnt through timeD nd redue the numer of (xed e'ets y keeping only one out of (ve yersF 14 he lned pnel does not inlude zero )ows whih re eliminted y this trnsformtionF he nlysis in setion R hs shown tht zero )ows do not mtter nywyF ratio x ijt /x ijt-1 is weighted by x ijt-1 . 15 The second alternative estimator, following the results established at the end of section 4, consists in a linear WLS of equation ( 11) specicied in logs

Log( x ijt x ijt-1 ) = ∆γ t ln d ij +∆α 1t B ij +∆α 2t L ij +∆α 3t C ij +∆(α 4t F T A ijt )+∆F X it +∆F M jt + ijt (12)
Appendix B shows that the ecient estimator also uses x ijt-1 as weights.

As shown in Figure 11, the broad picture is not aected by the choice of estimators, supporting the view of an overall stability of the trade elasticity to distance through time.

However, although the choice of the parameter has basically no impact on the assesment of the distance puzzle, some other parameters are aected, as shown in Section 6. Testing serial correlation of the residuals (Wooldridge,equation 10.71) enables to discriminate between the xed-eect and the "rst-dierence" estimator, depending on whether the auto-correlation parameter of log v ijt is close to 0 and 1. Based on this test, the "rst-dierence" estimators (eq. 11 and 12) should clearly be prefered over the level estimator (eq. 10). 16 6 Other trade determinants 6.1 FTA parameter Although Baier and Bergrstrand constrain the elasticities to be constant over time, the panel approach allows for time-varying elasticities, as required for the analysis of the "distance puzzle". However, for comparison purposes, estimates of equations ( 10) and ( 11) are also reported holding the FTA parameter α 4t to be constant over time, and Figure 12 presents the evolution of the FTA parameter across the dierent estimators. By contrast to the elasticity of distance, the eect of FTAs is sensitive to the choice of the panel estimator. Holding the FTA parameter constant leads to an estimate of 0.52 and 0.27 using equations ( 10) and (11), while

Baier and Bergstrand obtain 0.49 and 0.36, respectively, using a specication of trade ows in 15 sdelly one would like to use n iterted weighted xvD ut only the rtios re estimtedD not the level of )owsF portuntelyD results in setion R indite tht v nd iterted v estimtes re very lose to eh otherF 16 his utoEorreltion prmeter is estimted to e very lose to H in oth weighted xv nd logEliner v @eqF II nd IPD respetivelyAF logarithm. While the "rst-dierence" transformation (eq. 11) generates only small variations of the FTA parameter through time, the estimated coecient using the level specication (eq. 10) varies from 0.27 to 0.74 between 1952 and 1975, and steadily decreases to 0.50. As discussed above, the tests for the serial correlation of residuals discriminate in favour of the "rst-dierence" transformation. A point estimate of 0.27 means that FTA increase trade by 35%.17

6.2 Contiguity, common language and colonial linkages dummies

Because the dummies for colonial linkages, contiguity and common ocial language do not vary through time, only the changes of the corresponding coecients can be estimated in panel specications. Figures 13(a-c) present these evolutions using the three panel estimates, as well as those obtained using PPML in cross sections. The latter is particulary useful as it provides estimates of the parameters in levels. For the rst period (1952)(1953)(1954)(1955)(1956), the cross section point estimates for colonial linkages, common border and common ocial language dummies are 1.11, 0.48 and 0.14, respectively, with estimated robust standard errors of 0.15, 0.14 and 0.13.

All estimators point to a notable decrease in the eect of colonial linkages over the years, especially pronounced through the mid-eighties, even though the amplitude varies importantly across estimators (Figure 13a). Based on cross sections, the eect sharply decreases from 1.1 to about 0 over the whole period, while the decrease is of "only" 0.5 with PPML in panel and of 0.9 with the nonlinear "rst-dierence" panel estimator. Figure 13b shows that the eect of contiguity is broadly stable in cross sections, around an average value of 0.47. This elasticity decreases by 0.20 on average across panel estimators over the whole period. Finally, the eect of a common ocial language is broadly stable for all estimators, except for the nonlinear "rst-dierence" panel one leading to an estimated increase of 0.2 throughout the whole period (Figure 13c).

Conclusion

Evolution through time of the main determinants of trade ows has been mostly studied through "log of gravity" specications, generally pointing to an increasing role of distance in shaping world trade. This paper focuses on this "distance puzzle" starting with the Poisson Pseudo-Maximum Likelihood (PPML) estimator recently proposed by Santos Silva and Tenreyro, which they apply to one single year. The main result is that this elasticity has been broadly stable Estimation of the panel specication (10) with pseudo-maximum likelihood might be inecient depending on the structure of the residuals. An appealing transformation that gets rid of the dyadic xed eects and is consistent with the level specication is the ratio x t /x t-1 as given by (11).

x

ijt x ijt-1 = exp(∆γ t ln d ij +∆α 1t B ij +∆α 2t L ij +∆α 3t C ij +∆(α 4t F T A ijt )+∆F X it +∆F M jt )v ijt (13)
Assuming that the conditional variance of trade ows is proportional to the conditional mean (Poisson assumption), equation ( 13) can be estimated eciently by weighted (nonlinear) least-squares where the weights are the inverse of the conditional variance of x t /x t-1 . The latter can be computed from a Taylor-series of the ratio around the means. Indeed, for any two

variables X and Y , Y X -E Y X ≈ - EY E 2 X (X -EX) + 1 EX (Y -EY ) (14)
It follows that, noting ρ the linear correlation coecient between X and Y:

V ar Y X = E 2 Y E 4 X V ar(X) + 1 E 2 X V ar(Y ) -2ρ EY E 3 X V ar(X)V ar(Y ) (15)
where κ is a constant. Equation ( 15) is used with X = x t-1 |Z and Y = x t |Z, assuming that the conditional variance is proportional to the conditional mean and that the conditional mean of x t is proportional to the conditional mean of x t-1 :

V ar x ijt x ijt-1 |Z = κ E(x ijt-1 |Z)
Hence, based on these assumptions, the ecient estimator of (11) uses E(x ijt-1 |Z) as weights. 18A similar exercise is replicated to compute the weights for the log specication in eq. ( 12):

Log Y X -E Log Y X ≈ 1 EY (Y -EY ) - 1 EX (X -EX)
from which one derives:

V ar Log x ijt x ijt-1 |Z = κ E(x ijt-1 |Z)
where κ is a constant. xotesX e grvity eqution is estimted for eh yer with di'erent estimtorsF sn levelsD using oisson seudoEwximum vikelihoodD gmm wv nd negtive inomil wv ndD in log using yvF he negtive inomil estimtor is omputed using three di'erent 6 units to mesure trde )owsF hen )ows re mesured in thousnds of 6D the negtive inomil nd the gmm estimtors oinide visullyF xotesX ixept for the oisson seudoEwximum vikelihood estimtes in ross setion where grvity eqution is estimted for eh yerD the grvity eqution is estimted in pnel over the whole period with di'erent estimtorsF he weights of the eighted vest qures re the trde )ows of previous periodF he wv ross setion estimtes is the one with the pe prmeter onstrined to HFQF

3. 1

 1 DataTrade ow data come from the IMF Direction Of Trade Statistics (DOTS) database. This database provides trade ows for a long period, starting in 1948, which is important to study properly the distance puzzle, and for 205 trade partners. Moreover, DOTS includes zeros and dierentiates them from missing values, avoiding some necessary but doubtful assumptions when otherwise. Figure1plots the number of zero and non-zero trade ows through time, thereby illustrating the risk of selection bias using log-linear OLS. Indeed, despite the decreasing share of zero trade ows from 80% in 1948 to 29% in 2006, it still represents an important proportion. The sample of striclty positive trade ows, used for comparison of the dierent estimators, has about 3,700 ows in 1948 and 22,000 in 2006.

  since the 1960s at around 0.65-0.70. Despite the increasing coverage of free trade agreements, taking FTAs into account has a small eect on the distance elasticity. Another interesting nding is that the eect of colonial linkages has been vanishing.The paper brings additional methodological contributions by comparing various estimators to PPML; OLS when the trade equation is specied in logs, nonlinear least-squares (NLS), negative binomial and gamma PML when specied in levels, as well as panel estimates based on levels and "rst-dierence" specications. First, the bias identied by Santos Silva and Tenreyro between log OLS and PPML is shown to have increased over time in relation with the growing heterogeneity of trade ows. Weighting the logs by the (estimated) level of trade ows is sucient to eliminate this dierence. Second, although the PPML estimator is the most satisfactory of those tested, the most ecient one might be in between NLS and PPML, corresponding to the proportionality of the variance of trade ows to the square root of the conditional expectancy. PML based on negative binomial is not an option as it articially depends on the unit chosen to measure trade ows. Third, there remains a methodological puzzle. The gamma PML estimator is not only inecient, giving too much weight on small ows, it also leads to signicantly dierent estimates than PPML, contrary to what one should expect. Finally, auto-correlation tests of residuals discriminate the panel estimates in favour of the "rst-dierence" estimator relative to the xed eects one.

Figure A. 1 :

 1 Figure A.1: Impact of trade determinants other than distance

Figures

  Figures

Figure 1 :Figure 3 :Figure 4 :

 134 Figure 1: Number of total trade ows and strictly positive ones in the DOTS database

Figure 5 :

 5 Figure 5: Evolution of trade elasticity to geographic distance : PPML vs NLS estimates, cross sections

Figure 6 :

 6 Figure 6: Which PML estimator?

Figure 7 :Figure 8 :

 78 Figure 7: Estimated λ 1

Figure 9 :

 9 Figure 9: Log-linear WLS and PPML

Figure 10 :

 10 Figure 10: Trade elasticity to distance based on dierent values of the FTA parameter, cross sections

Figure 11 :

 11 Figure 11: Evolution of the trade elasticity to distance(rst period, 1952-1956, = 0)

Figure 12 :

 12 Figure 12: Trade eect of FTAs, panel estimates

Figure 13 :

 13 Figure 13: Evolution of other trade determinants(rst period, 1952-1956, = 0)

  1919 κ is proportionl to (1 + g -2ρ/g)F

	Tables
	Table 1: Gravity equations estimated with PPML, cross sections
	year	1955	1965	1975	1985	1995	2005
	Log distance -0.53*** -0.62*** -0.70*** -0.72*** -0.66*** -0.75***
		(0.06)	(0.04)	(0.03)	(0.03)	(0.03)	(0.03)
	Contiguity	0.57*** 0.32*** 0.35*** 0.33*** 0.65***	0.43***
		(0.19)	(0.11)	(0.11)	(0.09)	(0.10)	(0.09)
	Language	0.31**	0.40*** 0.29*** 0.32***	0.18**	0.20**
		(0.12)	(0.09)	(0.08)	(0.07)	(0.08)	(0.08)
	Colony	1.05*** 0.85*** 0.53***	0.14	0.11	0.16
		(0.15)	(0.12)	(0.12)	(0.11)	(0.10)	(0.12)
	Country FE	yes	yes	yes	yes	yes	yes
	Observations	4558	7449	11649	13063	19973	22201
	xotesX e grvity eqution is estimted for eh yerD where the dependnt vrile is the level of ilterl trde )owsF tndrd errors re in prenthesesY BBBD BB nd B re signi(ne levels t the I7D S7 nd IH7 thresholdsD respetivelyF

Table 2 :

 2 λ 1 is estimated from equation (6) using the dierent estimators as starting points for

	xij

Table 3 :

 3 Sample analysis of the dierent estimators, above and below the median of trade ows. eqution is estimted for the yer PHHH with di'erent estimtorsF mll nd ig )ows refer to the trde )ows whih re ove nd elow the medinD respetivelyF tndrd errors re in prenthesesF

	Trade elasticity to distance, 2000
		PPML NLS GPML OLS log
	Whole sample -0.69	-0.53	-1.26	-1.54
		(0.03) (0.05) (0.02)	(0.02)
	Big ows	-0.69	-0.53	-1.00	-1.03
		(0.03) (0.05) (0.02)	(0.02)
	Small ows	-0.57	-0.57	-0.69	-1.00
		(0.02) (0.02) (0.03)	(0.04)
	xotesX e grvity

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APPENDIX A Trade determinants in cross sections

In this Appendix, equation ( 9) is estimated for each year in cross section constraining the FTA parameter to 0.3. PPML and log OLS lead to similar estimates of the impact of a common border on international trade (Figure A1a). The parameter is estimated at about 0.3 between 1948 and 1985. Then the coecient increases for the two specications to about 0.7 in the early nineties.

The eect of a common ocial language is broadly stable around 0.2 when estimated by PPML (Figure A1b). In contrast, log OLS leads to a steady increase, somehow unrealistically, of the estimated impact up to 0.95 in 2006.

The evolution of the estimated eect of having colonial linkages is illustrated in Figure A1c.

While the two methods highlight the declining importance of colonial links, PPML seems to produce here also more realistic results. According to PPML, the impact of colonial linkages has been stable at about 0.2 since the mid-eighties, whereas it is still around 1.0 based on log OLS.


Chloé Le Bescond

Vincent Bertrin

Sébastien Boutry

Nathalie Reynaud

Héctor Rodríguez-Pérez

Thierry Tormos

INTERCALIBRATION OF REVISED CLASSIFICATION METHOD FOR LAKE MACROPHYTES IN FRANCE

Keywords: BQE, macrophytes Water category, lake Common intercalibration types, L-AL3 and L-AL4 1

Introduction

As part of the Water Framework Directive, France developed its own method to assess ecological status of lakes regarding macrophyte communities. This method was intercalibrated in 2011 together with four other Member States (Austria, Germany, Italy and Slovenia) from the Alpine Geographical Intercalibration Group (GIG). Since the intercalibration exercise was carried out, the French assessment method has been further developed. This document addresses the intercalibration of the revised "new" French classification method for macrophytes in alpine lakes, following the procedure described in the CIS Guidance Document No. 30 (European-Commission, 2015). The results show that the revised "new" assessment method fits the intercalibrated "old" method for common types L-AL3 and L-AL4 within the Alpine GIG.

Description of national assessment methods

The French assessment method for macrophytes in lakes is called "Macrophyte Index for Lakes" (IBML). It estimates all the pressures linked or associated with the degradation of the trophic level (eutrophication, HYMO, general degradation, etc.) of lakes with a water level fluctuation of less than two meters [START_REF] Boutry | Indice biologique macrophytique lac (IBML). Notice de calcul. Irstea, EABX[END_REF]. Both intercalibrated "old" method and revised "new" method have the same assessment concept.

Method and required BQE parameters

The French intercalibrated "old" assessment method includes one metric based on abundance of indicator taxa and composition (trophic level indicating species and stenoecy coefficient).

The revised "new" method uses the same metric as the intercalibrated "old" method.

Sampling and data processing

Full sampling strategy and method of calculation are detailed in Annex A.2 in [START_REF] Pall | 2010 établissant le programme de surveillance de l'état des eaux en application de l'article R. 212-22 du code de l'environnement[END_REF] Macrophyte communities are surveyed according to the French standard for macrophytes in lake (AFNOR, 2022) on several observation units, each consisting of one section of shore and three profiles perpendicular to the shore (see figure A.1 in [START_REF] Pall | 2010 établissant le programme de surveillance de l'état des eaux en application de l'article R. 212-22 du code de l'environnement[END_REF]. These observation units are located by applying the Jensen's method (geometric positioning, see [START_REF] Jensen | Objective method for sampling macrophytes vegetation in lakes[END_REF] and selected so that the main types of riparian zone around the lake are represented. Four types of riparian zone are available, based on the description of the vegetation structures and/or anthropic alterations of the shore: three types of shore correspond to natural habitats or habitats not significantly modified by human pressure, a fourth type indicates extensive human modification of the lake (see table A.15 in Pall et al., 2014). Macrophytes are sampled using a rake or a grapnel on three observation units at least. The surveyed compartment stretches from the entire littoral of each transect down to the vegetation limit.

On each observation unit, four trophic scores (one for the shore and three for the profiles) are calculated based on the relative abundance of about 300 indicator taxa with their own specific value and stenoecy coefficient. Specific values and stenoecy coefficients of indicator species are specified in table A.20 of the intercalibration technical report [START_REF] Pall | 2010 établissant le programme de surveillance de l'état des eaux en application de l'article R. 212-22 du code de l'environnement[END_REF]. A mean score is then calculated for shore samplings on one hand and profile samplings on the other hand, weighted by the proportion of a given riparian zone type around the lake. The final trophic score at the lake scale is given by the mean of the two weighted scores.

Both intercalibrated "old" and revised "new" methods use the same sampling and data processing. Nevertheless, during the intercalibration exercise, the surveys on the sections of shore (littoral zone surveys) and the weighting of scores by the riparian zone types (description of the vegetation structures and/or anthropic alteration of the shore) were not taken into account in the intercalibrated "old" method. The results were given at a transect scale (a combination of perpendicular profiles, data grouped by depth zones). Final ecological quality ratios (EQRs) were not bounded (likely > 1) in the intercalibrated "old" method.

The revised "new" method uses macrophytes data collected in the littoral zone surveys and perpendicular profiles, weighted by the proportion of the four riparian zone types [START_REF] Boutry | Indice biologique macrophytique lac (IBML). Notice de calcul. Irstea, EABX[END_REF].

The revised "new" method uses normalised EQR (bounded from 0 to 1).

National reference conditions

Reference lakes are those listed in a national circular on least disturbed condition sites (Ministère de l'Écologie et du Développement Durable, 2004), mostly based on the land use data of the catchment area and the chemical/physicochemical data of the lake. Regarding the macrophyte communities, only the presence of invasive aquatic species is taken into account.

National boundary setting

In both intercalibrated "old" and revised "new" methods, the reference value is given by the median of French macrophytes indices of reference lakes identified according to the pressure criteria. The high-good class boundary is defined as the 75 th percentile from the distribution of the reference lakes.

The boundaries of the four remaining classes (good, moderate, poor, bad) are given by the equidistant division of the continuum.

In the intercalibrated "old" method the reference value was calculated from samples collected between late July and early August 2008 on 12 observations units (transects) from three reference lakes (lac de Barterand -FRDL45 -, lac du Grand Maclu -FRDL30 -and grand lac d'Etival -FRDL19). The high-good intercalibrated "old" boundary was 0.92, expressed as EQR (see Table 1). During the intercalibration exercise, the comparison of Member Sate's assessment methods showed that the good-moderate boundary for France had to be more precautionary and was then adjusted from 0.69 to 0.72, expressed as EQRs.

In the revised "new" method, the high-good boundary is 0.80 and the good-moderate boundary is 0.60, also expressed as EQRs.

WFD compliance checking

The revised "new" assessment method fulfils all the WFD compliance criteria listed in the CIS Guidance Document No. 14, page 92 (European-Commission, 2011) as shown in Table 2.

Compliance criteria Compliance checking conclusion

Ecological status is classified by one of five classes (high, good, moderate, poor and bad). Yes, see Table 1 for class boundaries.

High, good and moderate ecological status are set in line with the WFD's normative definitions (Boundary setting procedure).

Yes.

All relevant parameters indicative of the biological quality element are covered (see Table 1 in the IC Guidance). A combination rule to combine parameter assessment into BQE assessment has to be defined. If parameters are missing, Member States need to demonstrate that the method is sufficiently indicative of the status of the QE as a whole.

Yes, French assessment method considers taxonomic composition and abundance of macrophytes and has defined a combination rule for these two parameters.

Assessment is adapted to intercalibration common types that are defined in line with the typological requirements of the WFD and approved by WG ECOSTAT.

Yes, IBML is appropriate for L-AL3 and L-AL4 lake types.

The water body is assessed against typespecific near-natural reference conditions.

Yes, reference lakes are selected following a national circular on least disturbed condition sites. Reference sites correspond to whole lakes.

Assessment results are expressed as EQRs.

Yes.

Sampling procedure allows for representative information about water body quality/ecological status in space and time.

Yes.

All data relevant for assessing the biological parameters specified in the WFD's normative definitions are covered by the sampling procedure.

Yes, sampling includes species composition and abundance parameters.

Selected taxonomic level achieves adequate confidence and precision in classification.

Yes, work at the species level.

Intercalibration feasibility checking

Typology

The intercalibrated "old" method was relevant for both L-AL3 and L-AL4 Alpine lake types, whose characteristics are described in Table 3. The revised "new" method is appropriate for the same Alpine lake types L-AL3 and L-AL4 and intercalibration is thus feasible regarding the common intercalibration types.

Pressures addressed

The revised "new" method addresses the same pressures than those in the Alpine GIG intercalibration exercise: eutrophication and general degradation (Table 4).

The relationships between the three pressure indicators identified in the intercalibration exercise (Secchi depth, total phosphorus and chlorophyll a concentrations) and the EQRs of the revised "new" method are significant (table 1). Chlorophyll a (in log) R²= 0.12 / p-value = 0.004

The Organization for Economic Cooperation and Development (OECD) has defined four trophic categories (OCDE, 1982), from oligotrophic to hypereutrophic, based on Secchi depth, total phosphorus and chlorophyll a concentrations. According to this trophic status assessment, oligotrophic lakes are associated with high EQR values whereas hypereutrophic lakes are associated with lower EQR values (Figure 1).

Assessment concept

The revised "new" method follows the same assessment concept as the intercalibrated "old" method: same sampling strategy and same data processing (species composition and abundance index). The main improvements of the revised "new" method are:

-littoral zone surveys are included; -trophic scores are weighted by the proportion of four riparian zone types (description of the vegetation structures and/or anthropic alterations of the shore); -normalised EQRs (bounded from 0 to 1) are used.

Conclusion on the intercalibration feasibility

The fitting of the updated classification method to the results of the completed Alpine GIG intercalibration exercise is feasible regarding typology, pressure addressed and assessment concepts.

5.

Compliance with the completed intercalibration exercise

Dataset collected

The fitting procedure of the revised "new" French classification method for macrophytes is carried out using a dataset from eight French lakes (Table 5) where macrophyte communities are considered a relevant biological quality element to assess ecological status (as defined in a national decree, Ministère de la Transition Ecologique, 2022). All the lakes are located in the Alps within the French hydro ecological area n°5. The use of ecoregions defined by the WFD is not feasible since only one lake is located in the WDF ecoregion n°4. The dataset consists of 84 observation units (transects) based on 18 field campaigns that took place between 2008 and 2016, and is considered a qualified national dataset since:

-it sufficiently covers the geographical area in which the common types L-AL3 and L-AL4 are located in France (see Figure 2); -it encompasses the complete ecological quality gradient ranging from high to poor ecological status, as shown in Figure 3 by the dashed lines representing the high-good and the goodmoderate class boundaries; -it is accompanied with non-biological and biological data to conduct pressure-impact analyses:

Secchi depth, total phosphorus and chlorophyll a (see Table 6).

Lake type Number of lake-transects Biological data

Physico-chemical data Pressure data L-AL3 120 5 lakes 5 lakes L-AL4 60 3 lakes 3 lakes

Relationship between intercalibrated "old" and revised "new" methods

The EQRs of the intercalibrated "old" method are strongly correlated with the EQRs of the revised "new" method (R²=0.81, see Figure 3).

Figure 3: Correlation between the EQRs of the intercalibrated "old" method (x-axis) and the revised "new" method (y-axis) for macrophytes in lakes using the French dataset. The dashed lines represent the intercalibrated highgood and good-moderate class boundaries (respectively 0.92 and 0.72 for the intercalibrated "old" method and 0.80 and 0.60 for the revised "new" method, expressed as EQRs).

Comparison of two methods' boundaries

The high-good and good-moderate boundaries of the intercalibrated "old" method were translated into EQR-values of the revised "new" method using the following ordinary least squares equation (see Figure 3):

New method EQR = 1.34 * Old method boundary EQR -0.44 (R²=0.81, p-value < 0.001)

The old and new methods' boundaries are summarised in Table 7. The intercalibrated "old" high-good boundary at EQR scale of the revised "new" method (0.79) is lower than the respective translated boundary of the revised "new" method (0.80). The intercalibrated "old" good-moderate boundary at EQR scale of the revised "new" method (0.52) is lower than the respective boundary of the revised "new" method (0.60). This implies that the boundaries of the revised "new" method are more precautionary than the translated boundaries of the intercalibrated "old" method and can therefore be kept as is.

Thus, the revised "new" French assessment method for macrophytes in lakes within the Alpine GIG is in accordance with the completed intercalibration exercise.

6.

Description of boundary setting procedure and biological communities

The ecological status in lake is based on lakes whose "taxonomic composition corresponds totally or nearly totally to undisturbed conditions" (European Parliament and Council, 2000). French reference lakes are listed in a national circular (Ministère de l'Écologie et du Développement Durable, 2004). The reference value corresponds to the median IBML score of those reference lakes and the high-good class boundary is as the 75 th percentile from the distribution of the scores. The other class boundaries (good-moderate and moderate-poor) are given by the equidistant division of the continuum.

The normative definition for each ecological status in lakes, as defined in the WFD Annex V table 1.2.2, is given in Table 8 along with its interpretation in the French assessment method for macrophytes in lakes. ≤ 0.20

The taxonomic composition of IBML includes: -Phanerogams (hydrophytes, amphiphytes and helophytes), also including aquatic forms of land species; -Macroalgae (charophytes); -Macroscopic colony of algae (benthic, epiphytic, floating); -Pteridophytes (submerged, helophytic or floating); -Bryophytes (mosses and liverworts).

Phanerogams, bryophytes, pteridophytes and charophytes are determined at species level. Unicellular organisms (algae excepted charophytes) are determined at genius level. A full list of indicator species taken into account in both intercalibrated "old" and revised "new" methods is available in intercalibration technical report for Alpine Lake Macrophyte (Pall et al., 2014, Table A.20).

7.

Figure 1 :

 1 Figure 1: Distribution of the EQRs of the revised "new" method in the four trophic status defined by the OECD

Figure 2 :

 2 Figure 2: Geographical areas of lake type L-AL3 (represented by circles) and L-AL4 (represented by triangles) in France. Alpine lakes that are relevant for macrophyte communities are shown as black symbols and other alpine lakes are shown as white symbols.

Table 1 :

 1 National class boundaries of intercalibrated "old" and revised "new" classification methods for alpine lake macrophytes in France

		Class boundaries of the	Class boundaries of the revised
	Class	intercalibrated "old" method	"new" method
		(in EQR)	(in EQR)
	High	0.92 -1	0.80 -1
	Good	0.72 -0.92	0.60 -0.80
	Moderate	0.46 -0.72	0.40 -0.60
	Poor	0.23 -0.46	0.20 -0.40
	Bad	0 -0.23	0 -0.20

Table 2 :

 2 List of the WFD compliance criteria and the WFD compliance checking process and results.

Table 3 :

 3 Characteristics of Alpine lake types

Table 4 :

 4 Correlation between the pressure variables and the EQR values of the revised "new" method in macrophytes-relevant lakes using the complete French dataset

	Pressure	Pressure indicators	Strength of relationship with revised "new" method
	Eutrophication and general degradation	Secchi depth Total phosphorus (in log) R²= 0.24 / p-value = 3.04e-05 R²= 0.30 / p-value = 8.10e-07

Table 5 :

 5 Lakes used in the fitting procedure of the revised "new" method

	Lake name	Lake code	Lake national code
	Aiguebelette	FRDL61	AIG73
	Lac d'Annecy	FRDL66	ANN74
	Lac de Barterand	FRDL45	BAR01
	Bourget	FRDL60	BOU73
	Lac de Chalain	FRDL22	CHA39
	L'Entonnoir-bouverans	FRDL8	ENT25
	Grand lac Etival	FRDL19	ETI39
	Paladru	FRDL81	PAL38

Table 6 :

 6 Number of non-biological and biological data for each lake type

Table 7 :

 7 Position of old and new methods' boundaries on the EQR scale of the revised "new"

method Boundary Intercalibrated "old" method (in EQR) Translated boundary (in EQR) Revised "new" method (in EQR)

	High-good	0.92	0.79	0.80
	Good-moderate	0.72	0.52	0.60

Table 8 :

 8 Comparison of the French assessment method for macrophyte with the WFD (Annex V) normative definitions

	Ecological status	Normative definition (WFD)	Interpretation	EQR
		"The taxonomic composition	Vegetation density. IBML
		corresponds totally or nearly totally	score and species
	High	to undisturbed conditions. There are	composition correspond	> 0.80
		no detectable changes in the average	totally or nearly totally to
		macrophytic [...] abundance. [...]"	undisturbed conditions.
	Good	"There are slight changes in the composition and abundance of the type-specific communities. [...] macrophytic [...] taxa compared to	Vegetation density. IBML score and species conditions. from undisturbed composition differ slightly	0.60 -0.80
		"The composition of macrophytic [...]
	Moderate	taxa differ moderately from the type-specific communities and are significantly more distorted than macrophytic [...] abundance are Moderate changes in the average those observed at good quality.	Vegetation density. IBML score and species undisturbed conditions. moderately from composition deviate	0.40 -0.60
		evident. [...]"
		Macrophyte "communities deviate	Vegetation density. IBML
		substantially from those normally	score and species
	Poor	associated with the surface water	composition deviate	0.20 -0.40
		body type under undisturbed	substantially from
		conditions".	undisturbed conditions.
	Bad	"Large portions of the relevant biological communities normally associated with the surface water body type under undisturbed conditions are absent".	Very low macrophytes abundances or lack of macrophytes without natural reasons.


Mélina Douchy

Mélina Douchy-Oudot

teaching and research institutions in France or abroad, or from public or private research centers.

Synthèse de la journée du colloque organisée par la Conférence des Présidents des Cours d'appel de l'Union européenne, Dijon, 13-15 octobre 2011, Les Technologies de l'Information et de la Communication (TIC) au service de la justice du XXIème siècle

par Mélina Douchy-Oudot, Professeur à l'Université du Sud Toulon-VAR, Doyen honoraire de la Faculté de droit de Faut-il véritablement se réjouir de cet accès à l'information offert au justiciable de façon illimitée alors qu'il n'a pas reçu la boîte à outils nécessaire à sa compréhension ? Faut-il se réjouir de l'accès rapide prévu par des points de visio-publics sortes de bornes interactives si j'ai bien compris et est-ce là le meilleur accès pour le justiciable à sa demande de justice, même si l'on comprend que c'est aussi une façon de répondre à l'égalité entre tous les justiciables comme le rappelait Madame le professeur Fricéro. La solution reste discutable et à tout le moins il faudrait ainsi que le suggérait Monsieur le président Lacabarats des services de proximité pour les accompagner. Evidemment la réponse est différente pour les juristes qui eux ne peuvent qu'apprécier par exemple l'iberius de informacion y documentacion judicial présenté par Monsieur le professeur Silguero.

Toujours dans une mise en perspective des TIC, doit-on rendre grâce aux TIC de pouvoir travailler de n'importe quel endroit, à n'importe quelle heure, sans relâche, sans temps mort, rappelant la semaine post-révolutionnaire de dix jours, où le travail finit par s'immiscer au plus intime des alcôves. Qui ici peut dire qu'il n'a pas travaillé jusqu'à point d'heure sur son lit avec son précieux ordinateur connecté en réseau ?

Après cette belle journée de travail, devons-nous avoir peu alors qu'il apparaît de façon indéniable qu'en matière de management l'efficacité est au rendez-vous ? Les demandes sont facilitées et l'on peut former déclaration d'appel en chaussons de son salon, les déplacements dispendieux sont évités en communiquant par « son et image », la procédure peut ou pourra être suivie pas à pas, comme nos envois chronopost ou pour ce qui me concerne mes commandes de livres anciens par abebooks, juste par un clic de souris.

Chacun est heureux de ces dossiers rationnalisés surtout pour le contentieux de masse, de ces jugements modélisés par la technologie, de ce contradictoire renforcé par une communication accélérée, même si l'atelier sur l'indépendance et l'impartialité a montré que la discussion demeure ouverte s'agissant de la modélisation. Il a également été exposé par Monsieur le président Lacabarats pour la Cour de cassation comme conséquence des TIC une amélioration du travail intellectuel des juges par la communication entre magistrats que les TIC permettent, a fortiori à l'international, sous réserve de se méfier des listes de discussion chronophage dénoncées par Monsieur le premier président Ferrière. Je ne peux toutefois ne pas songer au déficit de résultat qui pourrait résulter du travail sur du « tout numérique » dénoncé par les sociologues ainsi que le soulignait en début de journée Madame le professeur Amrani-Mekki.

J'ai exclu délibérément les dangers propres à la technique qui ont pourtant été dénoncés par Monsieur le professeur Hoeren. Il ne faut pas omettre les multiples pannes susceptibles d'enrayer la machine.

Comme le disait fort justement Monsieur le professeur Cadiet cité par sa disciple, la norme technologique n'a pas à dicter sa loi à la norme procédurale. Fort de cette évidence, on peut concevoir que la rationalité procédurale favorise les bonnes pratiques que peuvent lui apporter les nouvelles technologies poursuivait-il. Cela suppose que tous les acteurs soient associés aux travaux comme l'a parfaitement souligné Monsieur le président Lacabarats, y compris les utilisateurs finaux ajoutait Monsieur le professeur Hoeren.

  Je remercie vivement Monsieur le premier président Gaschard, et tout l'équipe qui s'est occupée de ces belles journées, je songe aux Conseillers Trapet et Bonhert, sans oublier mon amie Cécile Caseau-Roche et les étudiants du Master de droit processuel de la Faculté de droit de Dijon. Il y a de nombreux amis dans la salle, Maître Gerbay, Monsieur le président Munier et bien d'autres, et c'est Pourquoi s'inquiéter de ce déversement continu des informations juridiques, de ces banques de données orientant le champ de la réflexion par des champs bloqués, par le recours à des mots-clés limitant la recherche ? Le flux est tel que la priorisation des informations est devenu impossible à l'esprit humain et oblige soit à déléguer à d'autres, soit à utiliser des logiciels, pour assurer cette tâche de tri dont chacun sait pourtant qu'elle préjugera de notre choix intellectuel. L'atelier dont rapport a été fait par Monsieur le premier président Bangratz a réfléchi sur ce danger de la substitution d'un syllogisme technique au syllogisme proprement judiciaire. D'ailleurs, nul n'a semblé plus surpris que cela tout à l'heure de cette situation décrite par Madame le professeur Amrani-Mekki où l'écrit n'est plus que l'expression de ce qui a été spontanément et immédiatement pensé, sans réflexion, nos courriels trop tôt envoyés par exemple, et où l'oral où l'on pensait avoir une certaine liberté de ton se fige et se grave par la technique des visio enregistrées. Et l'on ne peut s'empêcher de se demander dans ces TIC où est la densité, si l'écrit qui devait porter la réflexion ne la porte plus et si l'oral où par nature elle l'est moins se substitue à l'écrit par sa fixation ? Monsieur le premier président Hincu en Roumanie notamment ; une surveillance aussi de l'activité de nos juges, de leur rendement qui pourrait altérer leur indépendance ainsi qu'il a été discuté dans l'atelier sur ce thème rapporté par Madame le professeur Amrani-Mekki, avec des indicateurs de performance. Le premier président Grange nous a rappelé qu'il est évidemment nécessaire de vérifier que le juge travaille et qu'il le fasse de façon « normale ». Il a ensuite précisé que pour l'instant nous n'avions pas de normes de travail communiquées selon le type d'activités, mais qu'une commission travaille sur cette question sous la responsabilité de Monsieur le premier président Degrandi. notifications et la discussion qui s'est engagée avec Maître Soulard représentant la chambre départementale des Huissiers de justice.

	Dijon,
	Membre du CDPC UMR 62-01
	un public réduit -quelques
	milliers de magistrats tout de même ! -mais nous avons tous compris avec Monsieur le président
	Lacabarats quelle était l'importance de la protection des données personnelles et Monsieur le
	professeur Silguero a montré la mise en oeuvre de cette protection dans le système judiciaire
	espagnol. Le risque du piratage demeure ainsi que le soulignait Monsieur le professeur Hoeren et
	l'on a vu l'étendue parfois des informations sur les dossiers ou sur les détenus grâce à l'exposé des
	plateformes existant en Roumanie par Monsieur le premier président Hincu.

une joie d'être là avec vous. Ceci étant la synthèse d'une journée est toujours un exercice périlleux car on risque d'une part de dire moins bien ce que d'autres ont mieux dit, et d'autre part car nous aurons plaisir à entendre demain le rapport de synthèse du colloque qui sera effectué par Madame le professeur Natalie Fricéro. Mon apport ce soir sera donc modeste et tout ramassé dans cette question posée en ouverture par Madame le professeur Soraya Amrani-Mekki : « Faut-il avoir peur des TIC ? ». Il nous a été répondu en ouverture que non.

Et en effet pourquoi devrions nous avoir peur de ces technologies qui permettent à de nombreuses informations nominatives d'être accessibles en ligne sur la toile via des mots de passe savants et sécurisés ? Parfois il est vrai que ces données ne sont accessibles qu'à Cette absence de formalisation s'accompagne de la disparition des formes au sens du rituel qui s'estompe derrière l'ordinateur, jusqu'à « l'ordinarité » a-t-on pu dire, caractère banal, ordinaire du recours à une justice facilitée. Ce faisant l'administration de la justice serait-elle équipollente à l'administration des postes ? Le risque dénoncé par le vice-président Van Dijk est la perte de confiance des justiciables en leur justice. Or, il faut penser à montrer que c'est la justice qui a été rendue. « On doit voir que la justice a été rendue » a bien souligné notre collègue Soraya Amrani-Mekki.

La forme au demeurant ne disparaît que pour renaître mais ce n'est plus la même, il s'agit des procédures formulaires si bien développées au sein de l'Union européenne ainsi que l'a exposé Monsieur le recteur Nourissat. Il nous a également été dit que la construction de la coopération judiciaire a intégré les TIC, « tous ces textes prévoient le recours aux TIC », car ils sont une réponse à la distance et à la frontière. Cette dématérialisation, ce développement des procédures formulaires risque a soutenu l'intervenant de réduire l'autonomie procédurale des Etats. La question sera peutêtre débattue demain avec Madame le professeur Fricéro.

Un autre danger ne saurait être occulté, celui de la surveillance ; une surveillance bien sûr par les systèmes de vidéo-surveillance, d'enregistrement dans nos juridictions mis en lumière par A plus long terme, le RPVA, le RPVJ et le RPSH (réseau privé sécurisé des Huissiers en cours de construction) rendent poreuse la délimitation des fonctions entre gens de justice. A un moment où la profession d'avoué disparaît, et je fais partie de ceux qui le regrettent, c'est la question des périmètres du droit qui se pose ainsi qu'il a été abordé par Madame le premier président Lottin à propos des

Faut-il avoir peur lorsque l'on voit l'économie des moyens supplanter le rapport humain et éviter par exemple l'extraction du détenu par le recours à la visio-conférence et qu'une circulaire du 5 février 2009 incite les juges à développer cette pratique ? Au coeur du succès du recours aux TIC demeure la question de l'humanité de la justice comme l'a dit hier Monsieur le Garde des sceaux Michel Mercier. Il y a bien sûr une crainte légitime envers cette « dépossession technique » réalisée par l'audience électronique selon les mots de Madame le professeur Fricéro. Ne faut-il pas s'inquiéter par exemple de ce champ de vision limité du juge qui procède aux auditions par visio, laissant le « hors champ » en dehors de son appréciation ? Il n'est pas surprenant d'avoir entendu l'idée tout au long de cette journée de la nécessité d'un principe de présence -principio de inmediacion en Espagne -repris par Madame le professeur Laure Milano. Cette nécessité du contact physique, tout simplement de ce rapport humain qu'est le face à face présentiel, Monsieur le premier président Ferrière nous l'a rappelé d'après l'expérience qu'il en fait à l'île de la Réunion lors de certains délibérés. Tous les dossiers ne s'y prêtent manifestement pas.