Fabio Menten

Benoît Chèze

Laure Patouillard

Frédérique Bouvart

The use of Meta-Regression Analysis to harmonize LCA literature: an application to GHG emissions of 2 nd and 3 rd generation biofuels

Keywords: Biofuels, GHG, LCA, Meta-analysis Study

This article presents the results of a literature review performs with a meta-regression analysis (MRA) that focuses on the estimates of advanced biofuel Greenhouse Gas (GHG) emissions assessed with a Life Cycle Assessment (LCA) approach. The mean GHG emissions of both second (G2) and third generation (G3) biofuels and the effects of factors influencing these estimates are identified and quantified by means of specific statistical methods. 47 LCA studies are included in the database, providing 593 estimates. Each study estimate of the database is characterized by i) technical data/characteristics, ii) author's methodological choices and iii) typology of the study under consideration. The database is composed of both the vector of these estimates -expressed in grams of CO 2 equivalent per MJ of biofuel (g CO 2 eq/MJ) -and a matrix containing vectors of predictor variables which can be continuous or dummy variables. The former is the dependent variable while the latter corresponds to the explanatory variables of the meta-regression model. Parameters are estimated by mean of econometrics methods. Our results clearly highlight a hierarchy between G3 and G2 biofuels: life cycle GHG emissions of G3 biofuels are statistically higher than those of Ethanol which, in turn, are superior to those of BtL. Moreover, this article finds empirical support for many of the hypotheses formulated in narrative literature surveys concerning potential factors which may explain estimates variations. Finally, the MRA results are used to adress the harmonization issue in the field of advanced biofuels GHG emissions thanks to the technique of benefits transfer using meta-regression models. The range of values hence obtained appears to be lower than the fossil fuel reference (about 83.8 in g CO 2 eq/ MJ). However, only Ethanol and BtL do comply with the GHG emission reduction thresholds for biofuels defined in both the American and European directives.

Introduction

This article addresses the environmental evaluation issues of advanced biofuels. It focuses on a specific environmental evaluation method -Life Cycle Assessment (LCA) -and its estimates of second (G2) and third generation (G3) biofuels greenhouse gas (GHG) emissions. The mean Global Warming impact indicator, expressed in grams of CO 2 equivalent per MJ of biofuel (g CO 2 eq/MJ), and the effects of factors influencing these estimates are characterized and quantified using a meta-regression analysis (MRA): a quantitative research method to review and synthesize empirical literature. This research is of primary importance as this measure may be interpreted as an estimate of the contribution to climate change of advanced biofuels.

First generation (G1) biofuels have been developed to provide a substitute for fossil fuels in order to enhance energy independence and mitigate climate change. They mainly correspond to Ethanol and biodiesel produced from conventional crops such as sugar cane, sugar beet, wheat, corn, rapeseed, sunflower, etc. Nevertheless, G1 biofuels have come up against sustainability issues. Indeed, the use of agricultural commodities for the production of biofuels induces an additional demand for these crops and, consequently, an increased use of arable land. Furthermore, it has been suggested that it may induce a rise of food prices [START_REF] Eide | The Right to Food and the Impact of Liquid Biofuels[END_REF]. Additionally, many life-cycle based studies point out that G1 biofuels do not reduce GHG emissions as significantly as expected [START_REF] Benoist | Origins of the debate on the life-cycle greenhouse gas emissions and energy consumption of first-generation biofuels -A sensitivity analysis approach[END_REF]. As a consequence, G2 and G3 biofuels (referred to in this paper as advanced biofuels) from biomass residues, non-alimentary crops and wastes have been developed in the recent years. These biofuels seem to be more efficient than G1 biofuels in terms of land use, food security, GHG emission reductions and other environmental aspects [START_REF] Williams | Environmental and Sustainability Factors Associated With Next-Generation Biofuels in the U.S.: What Do We Really Know?[END_REF].

G2 Ethanol is obtained from the biochemical conversion of lignocellulosic biomass 1 and synthetic diesel from biomass, also known as BtL (Biomass to Liquids) or biomass FT-diesel, is produced by the thermochemical conversion of lignocellulosic biomass. G3 biofuels are produced from microalgae using algal oil for biodiesel production from conventional transesterification (a.k.a Fatty Acid Methyl Ester, FAME) or hydrotreated vegetable oil (HVO) (See Appendix A for further details). Advanced biofuels are currently either in research and development or demonstration phase and still need further improvements to be commercially viable. Some states have set ambitious production targets for biofuels, supported by subsidies and legislative incentives. In the European Union (EU), the Renewable Energy Directive (RED, [4]) requires the use of 10% of renewable energies in the transport sector by 2020 (in 2009, the share was 3.6%). To achieve this goal, the contribution of biofuels produced from lignocellulosic materials, wastes and residues is considered to be twice that made by other biofuels. This can be viewed as an incentive to develop advanced biofuels. In the United States (US), the Renewable Fuel Standard (RFS2, [START_REF]Renewable Fuel Standard Program (RFS2) Regulatory Impact Analysis[END_REF]), under the US Energy Independence and Security Act of 2007, requires the use of 136 billion litters of biofuels by 2022 (in 2009, 41.9 billion litters were mandated). It specifies that 79,3 billion litters must be of "advanced biofuels" and "cellulosic biofuels" (the definition of "advanced biofuels" in the RFS2 is different from the one adopted in this paper and will be clarified later on). In addition, other countries (Australia, China, Japan, New Zealand, Brazil and others) have already been actively developing next generation biofuels and feedstock although there is little policy support in these regions [START_REF]Special Report -Next Generation Biofuels: Policy Review and Outlook[END_REF].

Furthermore, the EU and the US set a list of sustainability requirements for biofuel production. In both regions, the only mandatory quantitative criterion is related to life cycle GHG emissions calculated using the LCA method. The RED sets minimum life cycle GHG emission savings for all biofuels compared to a fossil fuel reference. These savings are of 35% since 2009, and will be of 50% in 2017 and 60% from 2018 for new biofuel plants. The RFS2 also sets minimum life cycle GHG emission savings that biofuels have to comply with in order to be eligible for appropriate subsidies. Those savings are set to 20% for first generation biofuels, 50% to be considered as "advanced biofuel" (as defined in the RFS2, different from our definition) and 60% to be considered as "cellulosic biofuel".

Those GHG emission requirements as well as biofuel incorporation targets are clearly in favour of G2 and G3 biofuels. This shows the will of policy makers to support their future development compared to G1 biofuel. That is one of the reasons why we choose to focus on advanced biofuels in this study.

We choose to conduct our literature analysis by reviewing only LCA studies assessing Global Warming impact indicators, i.e. GHG emissions, for the following two reasons. First, one of the main objectives for developing biofuels is to reduce global GHG emissions in order to mitigate climate change. As an illustration, recall that the only quantitative mandatory requirement for biofuel sustainability is related to life cycle GHG emission savings in the EU and in the US. Thus, it appears important to check advanced biofuel compliance with this requirement by comparing their life cycle GHG emissions with those of a fossil fuel reference. Second, a significant literature already exists that assesses GHG emissions of advanced biofuels using the LCA approach. Hence a sufficient number of studies is available to investigate this issue. Note that because GHG emissions have an environmental impact at a global scale (GHG emission effects do not depend on the place where they have been emitted), this literature review includes worldwide studies.

The first applications of LCA to biofuels to measure a Global Warming impact indicator were carried out on G1 biofuels in the 90's (such as Kaltschmitt et al. [START_REF] Kaltschmitt | Life cycle analysis of biofuels under different environmental aspects[END_REF]). Since, numerous LCA studies were conducted to analyze G2 and G3 biofuel pathways. Despite this substantial literature, the extent to which advanced biofuels may have lower GHG emissions than the fossil reference remains a subject of debate. While the majority of these studies shows GHG benefits for advanced biofuels compared to a fossil fuel reference, some authors come to the opposite conclusion. For instance, LCA GHG emission results selected for this study (47 studies providing 593 GHG emission results, see next section for more details) range from -142 (G2) to 1378 (G3) g CO 2 eq/MJ of biofuel (see Figure 1); the greatest variability of GHG emission results being for G3 biofuels. When looking at Figure 1, one can wonder i) if there is a consensus about GHG emission benefits from advanced biofuels and ii) why there is so much variation among results of these studies even though they are all investigating the same phenomenon.

Actually, even if the LCA approach is consistent throughout, each study -by nature -concerns different pathways and uses specific data and methodological assumptions. Previous narrative surveys of biofuel LCA studies mention that LCA results are inconclusive regarding GHG emission performances of advanced biofuels [START_REF] Menichetti | Energy balance and greenhouse gas emissions of biofuels from a life-cycle perspective[END_REF][START_REF] Gnansounou | Life cycle assessment of biofuels: energy and greenhouse gas balances[END_REF][START_REF] Cherubini | Energy-and greenhouse gas-based LCA of biofuel and bioenergy systems: Key issues, ranges and recommendations[END_REF][START_REF] Sunde | Environmental Impacts and Costs of Hydrotreated Vegetable Oils, Transesterified Lipids andWoody BTL-A Review[END_REF][START_REF] Borrion | Environmental life cycle assessment of lignocellulosic conversion to ethanol: A review[END_REF][START_REF] Wiloso | LCA of second generation bioethanol: A review and some issues to be resolved for good LCA practice[END_REF]. According to these literature reviews, LCA GHG emission results for advanced biofuels vary significantly depending on various factors such as: the assumptions made to describe the biomass production step (model used to estimate N 2 O emissions and inclusion of direct and indirect land use change), the data used to describe the biomass conversion into biofuel and the general LCA methodological choices (system boundaries, the method used to account for coproducts impacts, etc.). While these indicative results from literature reviews are really useful, primary study results remain difficult to compare because of differences in technical data or methodological choices.

As a consequence, it is quite difficult to attempt any summary and to form an accurate opinion on this topic using classical literature reviews methods. In particular, it seems hard to provide one GHG emission estimate appropriate for advanced biofuels.

Since most studies are inconclusive, their results may not be relevant for decision support [START_REF] Brandão | What Can Meta-Analyses Tell Us About the Reliability of Life Cycle Assessment for Decision Support[END_REF]. There is a strong need for harmonization of LCA results, especially for policy makers or investors, as suggested by Heath and Mann [START_REF] Heath | Background and Reflections on the Life Cycle Assessment Harmonization Project[END_REF] with the "LCA harmonization project". The purpose of harmonization, as defined by

Heath and Mann, is to identify and quantify key factors that influence the environmental impacts for a technology or product in order to be more conclusive concerning its real environmental performances. At present, few studies have tried to harmonize GHG emission results from various LCA studies for advanced biofuels. For instance, Handler et al. and Liu et al. [START_REF] Handler | Evaluation of environmental impacts from microalgae cultivation in open-air raceway ponds: Analysis of the prior literature and investigation of wide variance in predicted impacts[END_REF][START_REF] Liu | Algae biodiesel has potential despite inconclusive results to date[END_REF] propose to harmonize GHG emission results for G3 biofuels by normalizing their LCA models using same methodological assumptions and same generic pathways.

Although it is not possible to calculate one GHG emission estimate appropriate for all advanced biofuels, we believe it remains possible to determine central tendencies based on the distribution of previous study results. To do so, this article proposes an alternative summary to previous literature reviews, using the metaanalysis (MA) methodology to describe and synthesize existing estimates of the LCA GHG emissions of advanced biofuels.

MA is a quantitative research method developed to compare and/or combine outcomes of different individual quantitative studies, named primary studies, with more or less similar characteristics that can be controlled for [START_REF] Abreu | A meta-analysis of ȕ-convergence: The legendary twopercent[END_REF]. By nature, each result from a primary study (called an estimate) may be quoted to illustrate the uncertainty of estimates. Estimates of previous studies are grouped together in a database, called metadatabase, according to one or more differentiating characteristics. These estimates become then the observations, also named effect-size (e-s) (see below), of the meta-database whereas the differentiating characteristics become their potential explicative variables. In a MA framework, the e-s is assumed to be a function of these explicative variables; function which can be specified and assessed. When this metafunction is estimated by the means of multi-regression techniques, i.e. specific econometrics estimators, the MA is called a meta-regression analysis (MRA) 2 . This multivariate setup allowed by the meta-regression framework is very usefull in the field of literature reviews as it enables us to statistically identify and quantify -ceteris paribus -the effect of the most influent characteristics on the e-s. Thus, compared to narrative literature reviews, the MRA methodology -thanks to its multivariate setup -gives the opportunity to test the influence of specific characteristics, after having controlled for the effect of other ones. Besides, a "meta-regression" framework allows to produce an estimation of the mean e-s weighted by the systematic influence of its main drivers. Indeed, once statistically estimated, the meta-function can be used to deduce original values of the e-s by specifying new values for the main drivers identified corresponding to relevant case studies. This technique of benefits transfer using meta-regression models, as it is named in the MA literature, may be a particularly well adapted methodology to deal with the so-called harmonization issue specific to the LCA literature.

The literature of LCA studies estimating advanced biofuels GHG emissions is now large enough to support a statistical assessment of this measure of the mean Global Warming impact indicator. The primary purpose of this MRA is to identify and quantify by statistical estimates which factors among i) technical data/characteristics, ii) author's methodological choices and iii) typology of the study under consideration have an impact on variations of the GHG emission estimates. The second purpose of this MRA is to generate a distribution of the potential GHG emissions of advanced biofuels and to characterize the mean Global Warming impact indicator and its standard deviation across G2 and G3 biofuels. We investigate -through an application -the potential for MRA to synthesize LCA literature by highlighting the main determinants of result variability in order to perform harmonization.

This paper is organized as follows. Section 2 is a brief summary of both LCA approach applied to biofuels and MRA methodology. Section 3 is a description of the meta-database in which the e-s and explanatory variables are described. Meta-regression models and the associated results are presented and analyzed in Section 4. Main conclusions and methodological discussion are presented in Section 5.

Methods

First, this section briefly presents the LCA approach and then summarizes how it has been used in the literature to estimate Global warming impact indicators of advanced biofuels. Second, the meta-regression methodology is briefly presented. Both sections enable a better understanding of the e-s and explanatory variables of the MA.

General presentation of LCA method

Life Cycle Assessment (LCA) is a method based on ISO standards 14040/14044 [START_REF]:2006 Environmental managementlife cycle assessment-principles and framework[END_REF][START_REF]:2006 Environmental management -Life cycle assessment -Requirements and guidelines[END_REF] aimed at assessing several potential environmental impacts of a product or a service during all of its life cycle. This approach takes into account all steps of a product's life cycle: from the extraction of natural resources necessary for its production (oil, coal, gas, etc) to its end of life or destruction ("Cradle to Grave" analysis). The LCA approach enables the characterization of potential environmental performances of a production system in order to identify potential improvements and is a relevant tool for decision makers.

The methodological framework for LCA set by international ISO standards is divided into 4 steps: 1. Goals and Scope of the study: This step deals with the definition of questions that we want to answer in the study and the final users of the results. Hence all methodological assumptions, i.e. the scope of the study (system boundaries, functional unit, method to account for coproducts, environmental impact indicators, type of data, etc) are described according to the goals of the study. 2. Life cycle inventory: Input and output flows of matter and energy as well as emissions to the environment (air, water, soil emissions and solid wastes) included in the system are listed. 3. Life cycle impact assessment: Inventory flows are converted into potential environmental impact categories using a characterization method. Each flow can contribute to several environmental impact categories. Impact categories and associated characterization method are chosen in accordance with the goals and scope of the study. 4. Interpretation of results: Results are analyzed regarding the defined goal and scope of the study. This methodological framework is also clarified in the ILCD Handbook [START_REF]International Reference Life Cycle Data System (ILCD) Handbook -General guide for Life Cycle Assessment -Detailed guidance[END_REF] that provides further guidance to assure consistency and quality of LCA studies.

There are two main approaches adopted in LCA studies depending on the type of questions the authors want to answer: Attributional LCA (A-LCA) and Consequential LCA (C-LCA). In an A-LCA, all the flows physically linked to the product's life cycle are included in the system's boundaries [START_REF] Earles | Consequential life cycle assessment: a review[END_REF]. C-LCA has emerged as a modeling approach that captures impacts occurring beyond direct physical relationships assessed in A-LCA [START_REF] Earles | Consequential life cycle assessment: a review[END_REF]. It extends the system's boundaries compared to A-LCA in order to consider market information in the life cycle inventory to assess the effects of a decision on the system [START_REF] Weidema | Marginal production technologies for life cycle inventories[END_REF].

LCA results could also vary from one study to another because of different sources of uncertainties. The nature of these uncertainties could be stochastic uncertainties (i.e. uncertainties linked to values of process data or characterization factors for example) or choice uncertainties (i.e. choice of methodological assumptions, impact assessment method, system boundaries, localization of data, etc) or lack of knowledge of studied system [START_REF]International Reference Life Cycle Data System (ILCD) Handbook -General guide for Life Cycle Assessment -Detailed guidance[END_REF]. Uncertainties should be addressed in LCA studies by applying for instance Monte Carlo method to assess stochastic uncertainties or by conducting a sensitivity analysis to assess choice uncertainties.

Specificities of LCA applied to biofuel pathways

The first applications of LCA for the environmental evaluation of biofuels were carried out in the 90's and since then; many methodological issues concerning this product category have been emphasized. The main specific methodological assumptions on biofuel LCA studies are:

o system boundaries: usually, a distinction is made between "Well To Tank" (WTT) boundaries that include all steps from the production of biomass feedstock to the transport and distribution of fuel and "Well To Wheel" (WTW) boundaries that include the WTT steps and the fuel use (end-of-life). Infrastructures may or may not be included within the system boundaries. o functional unit: it is a measure of the function of the studied system. All LCA results from the same study should be expressed in the same functional unit to enable comparison. A usual functional unit in LCA of transportation systems is a "kilometer driven by a reference vehicle on a standard driving cycle (and assuming that generally the different fuels have a similar performance in terms of acceleration, max speed, etc.)". Another classical functional unit for assessing fuels is "the consumption of one MJ of fuel in a motor" expressed in MJ. o reference system: results of the studied system have to be compared with results of a reference system (usually a fossil fuel). This reference system has to be defined in accordance with study purposes and methodological choices; in particular it must have similar boundaries, the same functional unit and similar geographical and temporal context. o the method to account for coproduct: Another classical methodological issue in LCA concerns the fact that more than one product can be produced in the studied system (called coproducts).

Distributing environmental burdens among products and coproducts of a process is a controversial issue in LCA. Two types of methodology are generally applied for the multiproduct cases: the substitution method and allocation method. This last method consists in sharing proportionally the environmental impacts between products and coproducts based on physical (e.g. mass, energy) or economical characteristics of the products. With the substitution method, allocation is avoided and the burdens associated to alternative ways of producing the coproduct are subtracted from the final result. The LCA ISO standards recommend the system expansion method (also called substitution method) [START_REF] Tillman | Choice of system boundaries in life cycle assessment[END_REF][START_REF] Vigon | Life-cycle Assessment: Inventory Guidelines and Principles[END_REF] but the choice of the method to account for coproducts strongly depends on the purpose of the study and on the nature of the studied system.

Biofuels use biomass as raw materials. Hence, LCA applied to biofuel pathways has to deal with some classical issues linked with the biomass production: o Land Use Change (LUC): It refers to all changes induced by land conversion or land management changes. Direct LUC is mainly treated as the above and below ground carbon release from the conversion of forests or grasslands into agricultural land. Indirect LUC refers to all changes that occur when the increased demand for agricultural products induces land conversion in other parts of the world. It is important to note that these changes not only affect GHG emissions but other environmental aspects such as biodiversity, soil fertility, etc. Indirect LUC is the main subject of debate nowadays concerning biofuel environmental assessment, especially regarding GHG emissions [START_REF] Searchinger | Use of U.S. croplands for biofuels increases greenhouse gases through emissions from land-use change[END_REF] but there is no consensus on the way how to account for it in LCA methodology. o Nitrogen cycle: Nitrous oxide (N 2 O) field emissions are known to be the subject of controversy in the biofuel LCA world since Crutzen et al. [START_REF] Crutzen | N2O release from agro-biofuel production negates global warming reduction by replacing fossil fuels[END_REF] published "N 2 O release from agro-biofuel production negates global warming reduction by replacing fossil fuels". There is a huge uncertainty about these emissions because they depend on local factors and this gas has a high GWP (around 300 times as much as CO 2 ). In a G1 biofuel LCA study conducted for the French government, the uncertainty on these emissions is estimated to be 50% [START_REF]Analyses de Cycle de Vie appliquées aux biocarburants de première génération consommés en France -Rapport Final[END_REF]. To estimate these emissions, some studies use the IPCC Tier 1 methodology [START_REF] Houghton | Revised 1996 IPCC guidelines for National Greenhouse Gas Inventories: Workbook -Module 24 Agriculture[END_REF] based on the amount of nitrogen fertilizer applied in the culture. However, N 2 O emissions depend on other factors such as soil characteristics and climate. Other assessment methods including these factors should provide a more accurate estimation. o Carbon cycle: Considering the short-term carbon cycle, many biofuel LCA studies suppose that the amount of carbon captured by the biomass during the photosynthesis is equal to the amount of carbon released in the atmosphere during the biofuel combustion. So those studies do not take into account either the carbon stored by the biomass or the carbon releases during biofuel use, this is called the carbon-neutrality hypothesis.

General presentation of meta-analysis method

"Meta-analysis refers to the statistical analysis of a large collection of results from individual studies for the purpose of integrating the findings. It connotes a rigorous alternative to the casual, narrative discussions of research studies which typify our attempts to make sense of the rapidly expanding research literature" [START_REF] Glass | Primary, secondary, and meta-analysis of research[END_REF].

The Glass' pioneering articles [START_REF] Glass | Primary, secondary, and meta-analysis of research[END_REF][START_REF] Glass | Integrating findings: the meta-analysis of research[END_REF][START_REF] Glass | Meta-analysis in social research[END_REF] in educational research are usually cited in the literature as being the first ones to propose and develop this method. Over the past three decades, MA has first been extensively applied to clinical studies in psychological and educational research and then to health sciences. It is now increasingly employed in other research fields. Since the early 1990s, this method has been gradually more and more accepted in social sciences, such as marketing and economics3 .

To our best knowledge, two articles can be identified as the precursors of the application of this methodology to synthesize LCA estimates for biofuels [START_REF] Farrell | Ethanol can contribute to energy and environmental goals[END_REF][START_REF] Bureau | A quantitative assessment of the determinants of the net energy value of biofuels[END_REF]. Farrell et al. [START_REF] Farrell | Ethanol can contribute to energy and environmental goals[END_REF] aim at estimating reliable values for the net energy and life-cycle GHG emissions of corn Ethanol in the US. They carry out a harmonization exercise on 6 studies, adjusting their methods and data to what the authors argue to be best practices. Bureau et al. [START_REF] Bureau | A quantitative assessment of the determinants of the net energy value of biofuels[END_REF], on the other hand, focuses only on the energy balance since they consider there is too much controversy involving life-cycle GHG estimations (due to uncertainties in the quantification of N 2 O emissions from agricultural production and indirect land use change). Rather than trying to determine best estimates, they aim at identifying the main determinants of the net energy value for G1 biofuels.

MA is nothing else than a particular methodology of literature reviewing. This method has not been proposed to synthesize any kind of research literature, but only studies with quantitative results: "Metaanalysis is the analysis of empirical analyses" [START_REF] Stanley | Meta-regression analysis: A quantitative method of literature surveys[END_REF], not theoretical ones. Applied to environmental evaluation methods, this methodology is thus relevant to review previously reported LCA studies outcomes.

Research synthesis aims at summarizing findings in such a way that clear and uncontroversial conclusions may be drawn from previous accumulated knowledge. Yet, estimates obtained by LCA approach are characterized by large differences among study results. Even if different studies deal with a same issue, each one departs from previous literature by using different data sets, different methodological choices, etc.

Research synthesis may thus appear as an especially difficult task when reviewing LCA literature. Compared to qualitative literature reviews, the original idea behind MA is to consider study results in the same way as any scientific phenomenon. Each reported result is viewed as an "observation" of a complex dataset, "no more comprehensible without statistical analysis than would hundreds of data points in one [LCA] study" [START_REF] Glass | Meta-analysis in social research[END_REF]. MA may then be understood as a set of statistical techniques, such as econometrics, which allows to systematically summarize quantitative studies. It is a complementary method to narrative literature surveys that generally provide a more qualitative than quantitative analysis of estimate results. Using econometrics methods, MRA allows to review and analyze previous results through a ceteris paribus reasoning [START_REF] Capelle-Blancard | How do shareholders respond to downsizingௗ? A meta-analysis[END_REF]. By doing so, outcomes from many studies can be integrated and combined in such a way that comparison between their results become easier.

MA provides a quantitative summary of estimates results, such as mean estimates and confidence intervals of the quantitative results among studies. Compared to narrative literature surveys, the major contribution of MA consists in modelling estimate result variations as a function of different factors. The use of specific econometrics method allows then to statistically estimate and quantify their influence on study outcomes.

More formally, let the generic form of the linear regression model be the "original model" of the MRA equation:

(

) Y f X X ε β ε = + = + (1)
where Y is the (I ×1) dependent variable vector composed of the I reported estimates of the phenomenon of interest in the MA. For reasons that will be developed in Section 3.1.3, the reported estimates of a MA are named "e-s" estimates. These I estimates are drawn from J studies. Note it is generally stated I J ≥ . If only one estimate per study is retained, then J = I. As usual, the term ε is a (I×1) vector of a random disturbance.

It is assumed that the sampling error is normally distributed with mean zero and variance ( )

2 2 , , : 0, , 1, ,
i i i N i I ε ε σ ε σ ∼ ∀ = … .
X is the (I×K) matrix composed of the K-1 independent variables of this meta-model. The independent variables represent study characteristics which are supposed to have an influence on the systematic excess variation of Y. β is the (K ×1) vector of the coefficients of this meta- model. Once estimated, it gives a measure of the particular effects of each characteristic.

The following notational convention will apply in the remaining of this paper: let the first column of the (I×K) data matrix, ( )

, I K
X , be a column of 1s and the others column vectors be the I observations of the K-1 independent variables:

( ) ( ) ( ) ( ) ( ) 1 -1 , , 1 ,1 ,1 ,1
, , , , ,

l K I K I I I I X C X X X § • = … … ¨© ¹ (2) where ( ) ,1 1 1 1
I C § • ¨= ¨© ¹ and ( ) ,1 , ,1
,

l l i l I l I x x X x § • ¨= ¨© ¹ .
Let us specify the (I×1) vector of the coefficients, ( ) ,1 I β , as follow:

( ) 1 ,1 -1 K l K α β β β β § • ¨= ¨© ¹ .
According to this notational convention, , l i

x is the i-th observation of the l-th independent variable ( )

1, , and 1, , -

1 i I l K = … = … . l
β is the coefficient of the vector of the I observations of the l-th independent variable, l X , and α is the constant term in the model, also known as the intercept.

It may be convenient to refer to a single observation in eq. ( 1). Then, eq. ( 1) may be rewritten as follows:

( ) ( ) 1 1, 2 2, , -1 -1, -1 , ' ,1 1, , 1, , , 1, , , 1, ,
i i i l l i K K i i K l l i i l i i K K y x x x x i I x i I X i I α β β β β ε α β ε β ε = + + +…+ +…+ + ∀ = … = + + ∀ = … = + ∀ = … ¦ (3) where: ( ) ( ) ( ) ( ) ( ) ' 1 1, ' 2 1, ' , 1, ' 1,
K K I K i K I K X X X X X § • ¨= ¨© ¹ and ( ) ( ) ' 1, , 1, 1, 1, , , , , , 1, ,
i i l i K i K X x x x i I - = ∀ = …
In MRA dealing with LCA studies, X could be stated as being composed of three kinds of variables.

( )

( , ) ( , ) ( , ) ,1 ( , )
( , , , )

I K I t I m I I s X C T M S =
where T, M and S are assumed to be (I×t), (I×m) and (I×s) vectors, respectively. T is composed of t variables related to technical characteristics of pathways assessed in the primary studies. In this MRA, it corresponds to biofuel characteristics such as the type of biomass feedstock, the type of technologies and associated yields, etc. The m variables of M refers to methodological assumptions reflecting researcher choices: for instance the type of LCA approach (A-LCA or C-LCA), the system boundaries, etc. Finally, the s variables of S correspond to the typology of the study under consideration such as the type of this study (peer review or working paper for instance), the publication year or the geographical location of authors. Of course, the definitive specification of eq. ( 1) depends on both the particular issue investigated (here, Global Warming impact indicator of advanced biofuels) and studies reviewed in the MRA.

Treatment of heteroskedasticity in meta-regression analysis

Heteroskedasticity is a well-known problem in MRA literature. Recall that the basic linear regression model assumes ( )

2 ' E I ε εε σ = .
This assumption implies that the variance-covariance matrix of the vector of parameters estimates, ( )

,1 K β , is equal to ( ) 2 1
' X X ε σ -. More particularly, it is thus assumed:

2 2 , , 1, , i i I ε
ε σ σ = ∀ = … .
When applied to the MRA framework, the homoskedasticity assumption of the disturbances may not be held.

By nature, primary studies results are not estimated with the same precision. In econometric terms, it means that each estimate has a different standard error, that is: , , ,

i j i j ε ε σ σ ≠ ∀ ≠ .
As a consequence, the variance of ε in eq. ( 1) varies across its observations and e-s estimates, i y , may not be considered as having homogeneous variances. Indeed, "e-s" estimates are drawn from different primary studies. These studies use different i) technical data/characteristics, ii) author's methodological choices and iii) do not have the same typology. These reasons, among others, may explain why each e-s estimates are estimated with varying degrees of precision.

In presence of heteroskedasticity, the Ordinary Least Square (OLS) estimates, ( ) ,1 K β , remain unbiased and consistent. Nevertheless, heteroskedasticity often leads to wider parameter estimate confidence intervals which may cause insignificant relationships between independent and dependent variables if not accounted for 4 . Therefore, heteroskedasticity is potentially a serious problem and has to be explicitly treated in MRA. Various solutions have been used in the MRA literature to correct for heteroskedasticity 5 . Two majors approaches have been employed in the literature.

Methods of estimation using Heteroskedastic Consistent Covariance Matrix

One of the most common approaches is to use heteroskedastic consistent estimators such as White's or Huber-White's Heteroskedastic Consistent Covariance Matrix (HCCM). The Newey-West estimator has also been used in some MA. The latest has been designed for stationary time-series data and, as a consequence, Nelson & Kennedy [START_REF] Nelson | The use (and abuse) of meta-analysis in environmental and natural resource economics: An assessment[END_REF] do not recommend to employ this estimator in a MRA framework. The use of White and/or Huber-White standard errors theoretically corrects for heteroskedasticity.

Nevertheless, non homogeneous variances may remain in practice, more particularly when MRA are applied to small sample sizes. The white and Huber-White estimators are generally used because the source of heteroskedasticity is not exactly known. It is not the case in the context of MRA in which the source of heteroskedasticity is clearly identified. Indeed, it has already been explained that MRA are subject to heteroskedasticity because e-s estimates are obtained with varying degrees of precision. That is to say, their respective standard errors are not the same. In economic sciences, e-s estimates correspond to partial regression coefficients drawn from primary studies. When estimating these coefficients, primary studies also estimate their standard errors. These estimates provide a measure of the MRA heteroskedasticity. This information may be used to adequately correct for heteroskedasticity. The Weighted Least-Squares (WLS) method of estimation takes such information explicitly into account in its estimation procedure.

The weighted least-squares method of estimation

A second alternative consists in estimating the parameters by using the WLS regression. Indeed, if i y 's variances are known, the most straightforward method of the correction of heteroskedasticity is by means of WLS 6 . 4 A wider confidence interval of a coefficient, say i β , means that its variance, 2 i β σ , is greater than expected. Thus, it conducts to a decrease of the t-value of i β ,

2 i i i t β β β σ =
, which increases the probability of falsely accepting the null hypothesis of tests of significance. 5 See for instance Nelson & Kennedy [START_REF] Nelson | The use (and abuse) of meta-analysis in environmental and natural resource economics: An assessment[END_REF] for a review of heteroskedasticity treatments used in meta-analysis studies dealing with environmental economics issues. 6 As explained in Gujarati [START_REF] Gujarati | Basic Econometrics. Fourth[END_REF], once the original model has been transformed, the variance of "new" disturbance terms,

* i ε , is: ( ) ( ) ( ) ( ) ( ) 2 * *2 , 2 , 2 , 2 2 , , 2 ,
1 since is known 1 since

1 i i i i i i i i Var E E E E ε ε ε ε ε ε ε ε ε σ ε σ σ σ ε σ σ § • § • ¨= = ¨¸© ¹ © ¹ = = = = which is a constant. That
K l i i i l l i i i i x y i I ε ε ε ε ε α β σ σ σ σ = ⋅ + + ∀ = … ¦ (4) 1 , , , , , 1 , 1, ,
Second, the Ordinary Least-Squares (OLS) method of estimation is applied to the transformed variables, i.e. to eq. (4). The more ,i ε σ is important, the less is the precision of i y . Thus, by dividing each i y by its standard error estimate, ,i ε σ , the WLS allocates to each e-s estimate a weight which is inversely proportional to its degree of precision. Intuitively, less precise e-s estimates, i y with wider ,i ε σ , obtain relatively smaller weight than more precise ones in minimizing the (weighted) sum of residual squares. Indeed, recall that the OLS method consists of minimizing the sum of residual squares:

( ) ( ) 2 1, , 1 1 '
I i I I i Min e Min e e = § • = ¨© ¹ ¦ where ( )
,1 I e is the column vector of residuals defined as follows:

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ,1 , ,1 ,1 ,1 , ,1 ,1
I I K I K I I K I K Y X e e Y X β β = + ⇔ = - where ( )
,1 K β is the column vector of parameters estimated by the OLS method.

Thus, applying the OLS method to eq. ( 4), WLS parameters estimates are obtained by minimizing:

2 1 2 2 1 , 2 1 , 1 (5) (6)
= = = ⇔ ⋅ ⇔ § • ¦ ¨© ¹ ¦ ¦
According to eq. ( 5) and ( 6), the WLS estimators are obtained by minimizing a weighted sum of residual squares with the i y 's unconditional variances acting as the weights 8 :

( )

1 i i w Var y = (7)
Weights defined in eq. ( 23) are known as being those that minimize the variance of the WLS estimators. These weights will then provide estimators that are BLUE (Best Linear Unbiased Estimators). In a particular framework of MA (the Fixed Effects Size model), these particular weights are obtained from the estimated standard error of each e-s estimates, i y , drawn directly from primary studies [START_REF] Hedges | Statistical Methods for Meta-Analysis[END_REF][START_REF] Hedges | Fixed effects models[END_REF]. 7 Again, like e-s estimates, estimated standard errors are drawn from primary studies. 8 The comparison of eq. ( 4) and eq. ( 6) may explain some confusion encountered in the literature. As highlighted by Nelson & Kennedy, some studies refer to weights based on variances and others refer to weights based on standard errors. As shown in eq. ( 4), standard errors weights, ,i ε σ , are used to transform the variables, but as a consequence (see eq. ( 5)), it is variances weights, 2 ,i ε σ , which are required to minimize the weighted sum of residual squares.

3 Database of LCA results of GHG emissions for advanced biofuels

Construction and composition of the database

As mentioned before, the goal of this study is to explain the variations of LCA results for GHG emissions of advanced biofuels. Consequently, the variable of interest (so-called effect-size (e-s) or dependent variable) is the result for GHG emissions per MJ of biofuel calculated with a LCA approach. These estimates have been drawn from the study sample of this MA. One value for GHG emissions (i.e. the estimate) corresponds to one observation in our MA sample. As one study can contain several estimates, our database (i.e. our MA sample) can be composed of more than one observation per study ( I J ≥ , recall eq.( 1)).

The inclusion of all estimates from a single study is a source of disagreement in the MA literature. Some authors believe that only one estimate should be included per study based either on the mean of the available estimates, or selected on the basis of expert judgment, while other authors advocate including all estimates as a method of boosting sample size (see Stanley [START_REF] Stanley | Wheat from chaff: Meta-analysis as quantitative literature review[END_REF] for a discussion on this issue). We choose to include all estimates from a single study for the following two reasons. First, the choice of a particular estimate is subjective, and when facing the same estimates, different researchers may undoubtedly make different choices. To maintain a position as neutral as possible, we considered all available explicit results in the study or which are easily inferred. Second, the core of MA is to summarize quantitative literature in a systematic way regardless of its quality. Hence, it would not be relevant to select studies ex-ante regarding their quality since this choice would be arbitrary. The MRA literature proposes various ex-ante tests (such as statistical ones) that can lead to exclude some studies ex-post, or at least some of their estimates, from the database/MA sample.

Selection and description of studies

Before proceeding to a MA analysis, the database of the MA has to be constituted. To do so, some common procedures exist in MA. Stanley [START_REF] Stanley | Wheat from chaff: Meta-analysis as quantitative literature review[END_REF] describes three steps to conduct a MA. First, primary studies having estimated a common quantitative effect are identified among published and unpublished literature. This set of studies is the material of the MA. Second, each article results and features are coded in a database. By doing so, studies are characterized in a way that allows them to be compared. Their findings, i.e. their estimates, become the observed values of the dependent and independent meta-variables. The e-s and potential factors which are supposed to have any influence on its variations are identified and summarized in a coded form: the explanatory variables of the matrix X. Third, the MRA can be conducted to estimate the magnitude of the quantitative effect under consideration and better understand variations in the reported estimates.

This section details the selection process of studies included in this MA. To obtain and analyze estimates for the GHG emissions of advanced biofuels, a large bibliographical research has been carried out to collect studies using an LCA approach. We have taken a census of both published articles and "grey literature", such as unpublished papers, conference papers, official reports. The existence of published articles which present detailed literature reviews dealing with close issues than ours has already been mentioned: [START_REF] Menichetti | Energy balance and greenhouse gas emissions of biofuels from a life-cycle perspective[END_REF][START_REF] Gnansounou | Life cycle assessment of biofuels: energy and greenhouse gas balances[END_REF][START_REF] Cherubini | Energy-and greenhouse gas-based LCA of biofuel and bioenergy systems: Key issues, ranges and recommendations[END_REF][START_REF] Sunde | Environmental Impacts and Costs of Hydrotreated Vegetable Oils, Transesterified Lipids andWoody BTL-A Review[END_REF][START_REF] Borrion | Environmental life cycle assessment of lignocellulosic conversion to ethanol: A review[END_REF][START_REF] Wiloso | LCA of second generation bioethanol: A review and some issues to be resolved for good LCA practice[END_REF]. These literature reviews were the starting point of the bibliographic research. Entries of their bibliographic references have been systematically reviewed. Then, to complete this first paper selection, a web-based keyword search -e.g. "LCA", "biofuel", "second generation biofuel", "third generation biofuel", "advanced biofuel", "cellulosic ethanol", "lignocellulosic ethanol", "synthetic diesel", "syndiesel", "BTL", "microalgae", "microalgae biodiesel", etc. -has been done on relevant literature databases (Science Direct, Web of Science, SciVerse, Springer Link, etc ), web sites of major publishers of academic journals (Blackwell, Elsevier, Kluwer, Sage, Springer, Taylor Francis, and Wiley). The "grey literature" has been more particularly collected through Google and Google Scholar, Dissertation Abstracts, web sites of key academic institutions and authors and web sites of major environmental evaluation conferences.

To better insure the homogeneity of the sample, studies have to meet three selection criteria to be included in the sample of this MA: i) only studies with primary results were included to avoid double counting (no literature reviews) 9 , ii) only studies using an LCA approach were included10 , iii) only LCA studies on the following liquid transportation fuels were included: lignocellulosic ethanol, FT diesel, microalgae HVO and FAME 11 , iv) only studies assessing Global warming impact indicator (i.e. GHG emissions) with "Well To Tank" (WTT) or "Well To Wheel" (WTW) boundaries 12 . The proxy used to measure the GHG emissions has to be the expressed (or easily convertible) in term of grams of CO 2 equivalent per MJ of biofuel.

Moreover, no a priori filter was used concerning the type of publication (published or unpublished papers) but the date and the English language. This MA focuses on studies conducted since 2002 (until mid 2011) since, to our knowledge, no advanced biofuels LCA studies were conducted before this date.

At the end of this selection process, the database contains 47 LCA studies [4,[START_REF]Renewable Fuel Standard Program (RFS2) Regulatory Impact Analysis[END_REF] providing 593 estimates of life-cycle GHG emissions of advanced biofuels. Details of number of estimates by studies included in the sample are provided in Table 2 (see Table B.1 in Appendix B for details about selected studies).

Choice and description of the meta-variables

The object of this MA is twofold. First, this MA proposes a statistical summary of the role of different determinants for estimates of the e-s, i.e. the Global warming impact indicator for advanced biofuels in grams of CO 2 eq per MJ. By identifying and measuring the influence of these determinants, one may obtain a more in-depth explanation of how advanced biofuel LCA GHG emission estimates change as these factors vary. Second, an important aspect of this article is to provide average estimates of the Global warming impact indicator for advanced biofuels.

The dependent (e-s) and independent variables (potential factors) of this MA are now detailed.

The Effect-Size: the dependent variable

As mentioned before, the variable of interest, so-called effect-size (e-s) or dependent variable, is the result for GHG emissions per MJ of biofuel calculated with an LCA approach. Those estimates drawn from studies, i.e. the observations of our MA sample, are expressed in different units of measure. These values need to be converted in a way that allows them to be combined to constitute the meta-dependent variable.

The transformation of the dependent variable observations into a unique metric measure is a common procedure of MA studies. This step is called the e-s calculation and is central to MA literature. Indeed, it is this conversion of the dependent variable in a standard measure, the e-s, that allows to compare previous results and to investigate their determinants. In our sample, most of the studies present the GHG emissions, in grams of CO 2 equivalent, as a midpoint impact category using IPCC's characterization factors. Some other studies present only inventory data on GHG emissions so these results had to be converted into grams of CO 2 equivalent. We used the latest IPCC characterization factors [START_REF] Parry | Climate change 2007: impacts, adaptation and vulnerability. Contribution of Working Group II to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change[END_REF] for these conversion steps. It was not possible to harmonize all of the observations by using the IPCC's 2007 characterization factors because the decomposition in individual GHG emissions were not always presented. However it has been shown that the calculation method for global warming impact has an insignificant influence in LCA results [START_REF] Dolan | Life Cycle Greenhouse Gas Emissions of Utility-Scale Wind Power[END_REF][START_REF] Whitaker | Life Cycle Greenhouse Gas Emissions of Coal-Fired Electricity Generation[END_REF].

However, there is still another step in the calculation of the e-s since the LCA results are not always presented for the same functional unit. Typical functional units in biofuel LCA studies are a unit of fuel produced (liter, kg, MJ, etc.) or the service rendered by the biofuel (dislocation of a vehicle for a certain distance expressed in km, miles, etc.). Some other studies present their results using other less conventional functional units such as the surface of arable land used. All of these choices depend on the initial goals of the study. We choose to convert the GHG emission values in our database into a common functional unit, a MJ of fuel produced since this is the unit used in the RED (the RFS also presents results for biofuel energy content, in Btu). For a given study, we apply conversion factors using the provided information in the study for lower heating values (LHV), densities, engine fuel consumption, etc. Whenever these values did not appear in a study, information from a well-documented study was used [START_REF]Well-to-Wheels Analysis of Future Automotive Fuels and Powertrains in the European Context (Version 3)[END_REF]. Some studies had to be discarded because results were presented for a functional unit that could not be converted into a MJ (e.g. Melamu et al. [START_REF] Melamu | 2nd Generation biofuels a sure bet? A life cycle assessment of how things could go wrong[END_REF]. is a C-LCA study where the results are presented for a multi-functional unit, involving fuel and electricity production).

Lastly, a standard error is associated to every observation in order to be able the treatment of our sample for heteroskedasticity. As mentioned before, there are mainly two ways to treat uncertainty in LCA (and consequently estimate standard errors): Monte-Carlo analysis and sensitivity analysis. The standard error could be directly inserted in the database only for the observations from studies performing Monte-Carlo analysis. We calculated a standard error from the e-s variance of each sensitivity analysis performed (one study can present the sensitivity of LCA results for variations of more than one parameter, each performed separately). For the studies that did not assess the uncertainty of their results, we calculated the standard error based on all the available observations for a same type of fuel.

The potential factors: the independent variables

There are no guidelines concerning exactly which variables, potentially influencing LCA results, have to be included in a MA independent variable set. Like any other scientific investigation, this choice is determined by the available data [START_REF] Nelson | The use (and abuse) of meta-analysis in environmental and natural resource economics: An assessment[END_REF], LCA practitioner knowledge (see section 2.1) and the specificities of each technology (see Appendix A). Some non-intuitive variables are also included in the database. In addition, some study characteristics (country, year of publication, etc.) were included to account for potential publication biases.

Primary studies highlight different determinants of advanced biofuel GHG emission estimates whereas surveys offer a more in-depth discussion on their likely influences. According to the introduction of this section, three categories of potential determinants of GHG emission estimates are kept: technical data, methodological choices of authors and typology of the study under consideration. The latter variables are more particularly based on typical variables employed in previous MA.

The three categories of explanatory variables are broken down further as follows. Each category could be divided into subcategories (see Table 1). Those subcategories could gather from 2 to 18 variables. All variables are encoded either as binary -a.k.a. dummy or qualitative -variables or as quantitative variables. At present, more than 80 variables are available in the database. In the "type of biomass feedstock" category, due to the variety of feedstock used for biofuel production in our sample, we created groups for biomass having similar characteristics (e.g. poplar and eucalyptus are coded as farmed wood, corn stover and wheat straw are coded as agricultural residues, etc.). An additional variable was created in order to test the difference of using cultivated resources (energy crops and farmed wood) and waste / residues as feedstock (biomass from agricultural or forestry residues) on LCA results.

In the "type of technologies and associated yields" category, all different types of processes for biomass pretreatment and for conversion into fuel that we found in the literature were set as variables for BtL and Ethanol technologies. The "Mass yield provided" variable indicates if a value for a mass yield of the biofuel process unit is available in the study (this can be seen as a quality indicator for a given study) and the "Value of mass yield" indicates this value only for G2 biofuels. For G3 biofuels, we choose the daily productivity and the oil content of microalgae as quantitative variables since they have been often identified in the literature as the most influencing factors for life cycle GHG emissions of G3 biofuels. In addition, the fact to grow microalgae in open ponds or photobioreactors is set as a variable.

Methodological choices.

All classical methodological choices for LCA are set as variables. We differentiate LCA studies with an attributional approach from LCA studies with a consequential approach (see section 2.1) Some hypothesis relative to system boundaries are set as variables: we distinguish WTT from WTW studies and the inclusion, or not, of infrastructures within the system boundaries is also taken into account. As highlighted in Section 2.1, the methods used to account for coproducts can have a great influence in biofuel LCAs. Therefore they were also set as independent variables. We classify the observations as either using an allocation method (based on energetic, mass content, market value, etc.) or system expansion method. Some studies mix both methods, which we call hybrid method. The carbon-neutrality hypothesis is very common in G1 and G2 biofuel studies. However, this hypothesis is not straightforward for studies involving microalgae since they do not always capture CO 2 directly from the atmosphere. CO 2 , from flue gas for example, is generally fed into the system. Therefore, the carbonneutrality hypothesis is set as an independent variable for G3 biofuels.

To study the influence of the choice of a characterization method for impact assessment, we make a distinction between studies that take into account 3 GHGs (CO 2 , CH 4 , N 2 O) and studies that take into account more than 3 GHGs. As also mentioned in Section 2.1, N 2 O emissions from the field play an important role in the GHG emissions of biofuel lifecycles. The use of IPCC's method [START_REF] Houghton | Revised 1996 IPCC guidelines for National Greenhouse Gas Inventories: Workbook -Module 24 Agriculture[END_REF] or other more complex methods for estimating these emissions are set as independent variables. Studies that take into account direct or indirect or both Land Use Change for GHG emission calculation are also identified. The method for taking into account uncertainties is identified in each study: uncertainty analysis could be conducted by a Monte Carlo analysis or by a sensitivity analysis on specific factors (ceteris paribus) or no uncertainty analysis (recall section 2.1). We also try to identify if the fact that a study assess other environmental impacts than GHG emissions could influence the GHG emission results. So the number and type of environmental impact indicators assessed in the study is controlled.

Study typology.

Other aspects than technical data or methodological choices are included in the database. The type of study is identified: it could be peer review literature or official report or legislative text (Directive or Standard) or working paper. The year of publication as well as the geographical location of the authors is also included in the database.

Description of the database

This MA covers a large portion of studies that explicitly used LCA to evaluate environmental impacts of advanced biofuels. Finally, 47 LCA studies have been selected representing 593 observations of GHG emission results representing an average of 13 observations per study (see Table 2). Table B.1 displays a list of the studies selected for the MA as well as a description of some of their characteristics. As displayed in Table 2, the database contains 87% of studies assessing G2 biofuels (38% of studies assessing BtL and 70% Ethanol) and 17% of studies assessing G3 biofuels. Thus, among 593 observations included in the database, observations for G3 biofuels represent 13%. Other observations correspond to G2 biofuels of which 30% are BtL and 70% are Ethanol. Most of studies are based on attributional LCA approach; only 3% of observations are calculated with a consequential LCA approach. Half of the studies do not perform an uncertainty analysis on their results. Among studies that include an uncertainty analysis, 44% are performing a Monte Carlo analysis. Only 28% of studies included in the database take into account LUC (and only 4% are addressing Indirect LUC issues), representing 51% of the observations. Observations extracted from peer review literature represent 61% of observations (65% of studies), from the official reports 9% (12% of studies), from regulatory texts 3% (4% of studies), and from working paper 25% (19% of studies).

Furthermore, the number of studies assessing GHG emissions of advanced biofuels started to strongly grow since 2007 (see Figure 2). This phenomenon could be linked with the publication of legislative texts in the EU and the US regarding mandatory GHG emission savings threshold for biofuels (respectively RED in 2009 and RFS2 in 2010).

Observations per type of biofuels

As depicted in Figure 3 (see also Table 3), GHG emission mean for G3 biofuels is quite similar to GHG emissions for fossil fuel reference as defined in EU and US regulations (respectively 83.8 g CO 2 eq/MJ (same reference for gasoline and diesel) and 92.5 g CO 2 eq/MJ (mean of US gasoline and diesel references)). GHG emission mean value indicates that G2 biofuels could induce a GHG emission reduction compared to fossil fuel reference from 69% to 72% (depending on the fossil fuel reference chosen). So, from a statistical point of view, G3 biofuels seem to emit more GHG emissions during their life cycle than G2 biofuels. In the same way, GHG emission mean for BtL is lower than for Ethanol (GHG emission savings compared to fossil fuel reference from 77% to 79% for BtL and from 65% to 68% for Ethanol).

The range of GHG emission results for G3 biofuels is very wide compared to the one for G2 biofuel as illustrated by their standard deviations (see Table 3). Hence G3 biofuel could emit 20 times more GHG emissions than fossil fuel reference whereas G2 biofuel could emit from 4 to 9 times more by considering the maximum variation of the results. Conversely, all minimum results are negative and quite similar for G2 and G3 biofuels.

Even if LCA results are inconclusive regarding GHG emission performances of advanced biofuels because of a wide range of variation, some trends can be indentified: on average, GHG emissions for G3 biofuels are higher than for G2 biofuels and GHG emissions for Ethanol are higher than for BtL. Thus, the type of biofuel seems to be a variable that could explain the differences of GHG emission results for advanced biofuels.

-

Observations per regions

We make the distinction between the geographical location of the authors (affiliation of the first author) and the geographical location of the cases studies (i.e. geographical location of inventory data).

Regarding the geographical location of the authors, 45% of studies are from North American (NA) authors (including US and Canada) and 53% are from European authors (including EU countries and Switzerland), representing 32% and 67% of the observations respectively (see Table B.3 in Appendix B). The other study is from Australian authors [START_REF] Campbell | Life cycle assessment of biodiesel production from microalgae in ponds[END_REF]. For G3 biofuels, 42% of observations are from NA authors, 51% from European authors and 7% from Australian authors. For BtL, 23% of observations are from NA authors and 77% from European authors. For Ethanol, 34% of observations are from NA authors and 66% from European authors. In most of the studies, the geographical location of the authors fits with the geographical location of the assessed pathways. Only 3% of the observations do not match ( [START_REF] Luo | Allocation issues in LCA methodology: a case study of corn stover-based fuel ethanol[END_REF] and some observations of [START_REF] Hoefnagels | Greenhouse gas footprints of different biofuel production systems[END_REF]). Therefore, we focus only on the geographical location of the authors as a measure of the potential influence of geographical location on GHG emissions.

On average for all types of biofuel, GHG emission results from NA authors seem to be lower than from European authors with a gap that could be significant as illustrated in Table 3 (e.g. from 0.22 g CO 2 eq/MJ for NA to 150.63 g CO 2 eq/MJ for Europe for G3 biofuels). Hence, it seems that the geographical location of the authors can have an influence on the GHG emission variability observed for advanced biofuels. As already mentioned, the RED and RFS2 set minimum GHG emission savings for biofuels. Their more restrictive savings are set to 60% compared to their corresponding fossil fuel reference (fossil fuel reference are slightly different). According to Figure 3, 82% of GHG emission results from NA are compliant with their more restrictive GHG emission minimum threshold whereas only 59% from Europe are compliant with their corresponding threshold. At this stage of the analysis, we do not have objective reasons explaining this systematic difference between NA and EU estimates. It may come from the use of a different set of technical variables, for instance, but it may also reveal the existence of a potential publication bias in the literature.

In conclusion, this section based on descriptive statistics allows the formulation of some intuitions about factors that could influence GHG emission results for advanced biofuels. The type of biofuels (G2 vs G3 biofuel, BtL vs Ethanol) and the geographical location (North America vs. Europe) seem to have an influence on the variability of GHG emission results for advanced biofuels. However it is not possible to be more conclusive and accurate with the descriptive statistics presented in this Section. Descriptive statistics and inspection of graphics are very useful and often revelant but remain always vulnerable to subjective interpretation. Thus, more objective statistical tests are needed, as those that could be done with MRA. By using specific econometrics methods, we believe that a MRA should allow the i) confirmation of our intuitions previously identified and ii) to go further in the explanation of the variability by identifying and quantifying the main variation factors.

Let us now develop the MRA based on these LCA studies.

Results

Compared to narrative literature reviews, the MRA methodology allows us i) to statistically identify main drivers of the e-s variability and ii) to estimate both the direction and the magnitude of their respective effects across primary studies under consideration. The logic of MRA is illustrated here by applying this methodology to LCA literature evaluating GHG emissions of advanced biofuels. We first present the MRA model and its results for various G2 and G3 biofuel sub-samples. Second, we use the technique of benefits transfer using meta-regression models to propose a first attempt of harmonization of these LCA results.

The meta-regression model

Simply stated, to review a specific environmental evaluation literature, one must summarize its previous results already published on the issue under consideration.

We consider I advanced biofuels GHG emission estimates, the e-s, indexed by (1,..., ) i I = and assume that the "true" e-s value for a given estimate is given by13 :

( ) ( ) ' ,1 1, , 1, ,
i i i K K y X i I α β µ = + + ∀ = … (8)
where i y is the true e-s, α is a common factor, ' i X is a vector that measures characteristics of the biofuel case study and of the study under consideration, β is a vector of parameters to be estimated, and i µ is normally distributed with mean zero and variance

( ) 2 2 , , : 0,
i i i N µ µ τ µ τ ∼
The "true" e-s value, i y , is not observed. Instead, each study provides an estimated e-s, i y , so that:

( ) ( ) ' , 1 1, , 1, ,
i i i i i i K K y y X i I ε α β µ ε = + = + + + ∀ = … (9)
where i ε is an error term that is normally distributed with mean zero and variance ( )

2 2 , , : 0, , 1, ,
i i i N i I ε ε σ ε σ ∼ ∀ = …
Thus we allow the "true" e-s and the precision of the estimated e-s, 2 ,i ε σ to vary across estimates. The term 2 ,i ε σ is known as the within-variance and varies from study to study. As already mentioned, it is usually taken as given and derived from the original estimate. Any remaining heterogeneity between estimates is either explainable by the observable differences modeled through the moderator variables contained in ' i X or is random and normally distributed with mean zero and variance 2

,i µ τ , the between-variance.

If 2 , 0 i µ τ = , the model is referred to the fixed-effects model, and it is assumed that all heterogeneity in the "true" e-s can be explained by differences in study characteristics. If the between-variance is not equal to zero, the model is a REM, which is usually referred to a "mixed-effects" model because it contains observable "fixed" characteristics in ' i X as well as a random unobservable component with mean zero and variance 2

,i µ τ . The unknown variance can be estimated by an iterative (restricted) maximum likelihood process or, alternatively, using the empirical Bayes method, or a non-iterative moment estimator. Note that the meaning of the adjectives "fixed" and "random" in the MA literature is different from the usual interpretation for panel data models in standard econometrics, because they refer to assumptions about the underlying population e-s [START_REF] Hedges | Statistical Methods for Meta-Analysis[END_REF]. In standard econometric terms, the fixed-effects meta-estimator is equivalent to the weighted least squares (WLS) estimator using the estimated variances (derived in the primary studies) as weights and re-scaling the standard errors of the meta-regression by means of the square root of the residual variance. The random effects estimator is akin to a random coefficient model in which the withinand between-study variances are used as weights [90] 14 .

Meta-regression analysis results

Since the studies in the primary literature may use different data sets and different ways of modeling, we have good reasons to suspect the heteroskedasticity.

A common approach is to use White's Heteroskedastic-Consistent Covariance Matrix (HCCM). This estimator simultaneously corrects for heteroskedasticity and cluster autocorrelation, and hence accounts for the multiple data setup by allowing different variances and non-zero covariances for clusters of measurements from the same study. However, the White estimator is arguably rather restrictive assuming that all differences across observations and studies are observable and can entirely explain the empirical heterogeneity. In addition, the White estimator does not fully exploit all available information because it estimates the variance rather than taking it as given or recoverable from the primary studies. The latter can be remedied by using the fixed-effects meta-estimator that we already presented. As explained above, 2

,i ε σ is a sample estimate of the standard deviation of the meta-regression errors. When this kind of measure of the heteroskedasticity is available, then Weighted Least Squares (WLS) becomes the obvious method to obtain efficient estimates of eq. ( 9).

We start out by presenting the results obtained for the "whole" sample, which includes all the G2 and G3 biofuel studies included in the meta-database. Recall that our meta-database includes variables representing i) technical data/characteristics, ii) author's methodological choices and iii) typology of the study under consideration. As technical data are specific to each type of biofuel, it is not possible to include this set of variables in the "whole" sample in order to test and quantify their respective influence. In order to capture characteristics of each biofuel generation and the type of fuel analyzed, one needs to break the "whole" sample into these respective sub-samples. The subsequent sections present then results for smaller samples named as follows: "G3", "G2" samples and then "G2-BtL" and "G2-Ethanol" sub-samples. Hence, the "whole" sample corresponds to the merge of our "G3" and "G2" samples. Note that the "G3" and "G2" samples have been cut to 90% in order to exclude outliers which may have spurious influence on econometric estimates, as it is usually done in applied econometrics. So-defined, the "G2" sample contains 464 observations (321 for Ethanol and 143 for BtL) and the "G3" sample contains 69 observations. (See Figure 4 and Figure 5 for a visual representation of "G2" and "G3" samples outliers). "G2-BtL" and "G2-Ethanol" sub-samples are a subset of the "G2" sample.

Results of eq. ( 9) are presented in Table 4 for the "whole" and "G2" samples, and Table 5, Table 6 and Table 7 provide results for the "G2-Ethanol", "G2-BtL" and "G3" sub-samples respectively. For each model, results are systematically reported for two different corrections for heteroskedasticity: the first estimator uses the White's Heteroskedastic-Consistent Covariance Matrix (HCCM) (as denoted by the number 1 in columns) and the second one uses Weighted Least Squares (WLS) using inverse standard error weights (as denoted by the number 2 in columns).

Unless it is indicated, all regression results are presented in reduced form. These models were chosen by the general to specific approach to econometrics modeling. As usual, "***", "**" and "*" respectively indicate 1%, 5% and 10% significance levels and standard errors of the coefficient estimates are reported into brackets. In each column, "-" means that the variable under consideration has been first included but finally removed from the reduced form because its coefficient estimate was not statistically significant at the 10% significance levels. Regarding model information, N and Mean dep. Var indicate respectively the number of observations used to perform each regression and the corresponding mean of the dependent variable, i.e. the mean e-s expressed in g CO 2 eq/MJ of biofuel. In all tables, the quality of regressions is checked through the following diagnostic tests. Given that the simple R-squared statistic is sensitive to the number of variables included, only the adjusted R-squared is reported (Adj. R-squ.). The overall fit of the regression model is assessed by the logarithm of the Likelihood (Log-Likelihood) and the standard Fisher test which test for joint significance. The statistic of the latter test (F-stat.) and the corresponding measure of its statistical probability (P.value) are systematically reported.

The null hypothesis of this test is all coefficients but the constant one is equal to zero. Two additional diagnostic tests for the quality of the regressions (and their P. values) are also reported: the Skewness's asymmetric test (Skewness) and the Kurtosis's normality test (Kurtosis) of residuals. They respectively correspond to a test of skewness and nonnormal kurtosis compared with the null hypothesis of symmetry (the skewness coefficient is zero for symmetrically distributed data) and kurtosis coefficient of 3. The normality tests examine the normality of the residuals. Nonnormal residuals invalidate hypothesis tests on individual variables as these tests assume their normality, and is therefore an important consideration. All Tables also report the following two information criteria: the Akaike's Information Criterion (AIC) and the Schwarz's Bayesian Information Criterion (BIC). These two standard measures are used to allow (nonnested) model comparisons. Smaller AIC and BIC are preferred, because higher Log-Likelihood is preferred. Finally, in order to test and hence statistically confirm the importance of including technical data/characteristics in our models, it has been chosen to perform a likelihood-ratio test. The statistic of this test (LR test) and its corresponding P. value are reported in Table 5, Table 6 and Table 7. The line Nested model indicates against which model the investigated model is tested. In econometric terms, the nested model is the restricted model and corresponds to the reduced model without any technical data/characteristics.

We turn now to the comments of the results obtained for each samples and sub-samples. We only focus on the signs and significance of the estimated coefficients since the absolute magnitudes of those coefficients are not important.

Results for the whole sample

Estimates results for the "whole" sample are presented in Table 4, columns (1aAll) and (2aAll). Eq. ( 9) is estimated using both the White's HCCM (column (1aAll), Table 4) and the WLS (column (2aAll), Table 4) estimators. Contrary to economic primary studies, variances are usually not reported for each estimate in LCA primary studies and have to be retrieved (recall Section 3.1.3). For each observation of the MRA, variances have been directly inserted in the database or calculated depending whether the observations were coming from primary studies performing Monte-Carlo analysis or sensitivity analysis, respectively. As a consequence, the database does not provide a single measure of the variance for each observation. For this reason we prefer to comment coefficient estimates obtained by OLS estimator with a White procedure -OLS (White's HCCM), as indicated in last line, Table 4, -rather than WLS. However, we let WLS estimates for robustness check since they yield to similar results. The same choice is applied to the remainder of the paper to simplify the exposition.

Thus, we only comment results presented in column (1aAll), Table 4. 533 observations are included in this regression. As already explained in the previous Section, this regression only aims at testing the influence of i) the type of biofuels (gen_3, etha and btl variables) and ii) the geographical location (zlab_us, zlab_eu and zlab_other) on the e-s in order to confirm or deny what have been highlighted with the visual inspections presented in Sections 3.2.1 and 3.2.2. This may explain the rather low level of the adjusted R-squared (about 16%). As judged by the F-stat. P. value, the joint significance of results is accepted at the 1% significance level.

As a first comment, the econometric results displayed in Table 4 tend to confirm intuitions presented in Section 3.2, which were based on a simple visual inspection. etha and btl variables are indeed statistically significant at the 1% level and their coefficients are negative. According to these parameter estimates, GHG emissions are statistically lower for Ethanol and BtL (G2 biofuels) than for G3 biofuels (gen_3) by respectively about 41 and 52 g CO 2 eq/MJ. These results also confirm that life cycle GHG emission performance is better for BtL than for Ethanol. One can effectively not merge the etha and btl variables, as indicated by the Wald Test: we effectively reject the null hypothesis of this test, 0 H , because . 0.01 P Value < and conclude that the coefficient of etha is statistically different from the one of btl. Hence the biofuel generation is a key variable to explain the variability of advanced biofuels LCA results.

Regarding the geographical location, zlab_us and zlab_other variables have a negative impact on GHG emissions -their coefficients are significant at the 1% level. According to these results, GHG emissions are statistically lower when studies are from NA or from other countries (excluding NA and Europe) compared to those from Europe. Hence, the geographical location appears to have an influence on GHG emission results for advanced biofuels. There is no intuitive reason to explain the geographical influence highlighted by our results. At this step of the analysis, this result could be explained by either a model misspecification or the existence of a publication bias. The former could correspond to missing variables in our database, hence the geographical location could be a shadow variable hiding a real determinant. For instance, the geographical location variable could hide a set of technical data specific to one location. Unfortunately, it is not possible to include such variables in the "whole" sample model. To test this hypothesis, the "whole" sample is thus divided into G3 biofuel sample and G2 biofuel sample in order to assess specific characteristics (including technical data) of each biofuel generation.

Results for the G2 sample

Estimates results for the "G2" sample are presented in Table 4, columns (1aG2) to (2bG2). Our comments are based on results presented in column (1aG2). The adjusted R-squared is now equal to about 37%.

Technical variables etha variable is statistically significant at the 1% level and impacts positively GHG emissions for G2 biofuels. Thus GHG emissions are higher by about 6 g CO 2 eq/MJ for Ethanol than for BtL. The type of fuel conversion technology can thus explain the variability of GHG emission results for G2 biofuels. G2 sample is then split into "G2-Ethanol" sample and "G2-BtL" samples in order to take into account specificities of each fuel (see Sections 4.2.3 and 4.2.4, respectively).

Regarding the influence of mat_cult, this variable was tested first and had a negative effect on GHG emissions for G2 (results reported in columns (1bG2) and (2bG2), Table 4). Most LCA studies do not account for upstream burdens related to residue production and cultivated feedstock needs more inputs (especially fertilizers and pesticides) to be produced [START_REF] Williams | Environmental and Sustainability Factors Associated With Next-Generation Biofuels in the U.S.: What Do We Really Know?[END_REF] so this result was unexpected. However, it is also well known that perennial energy crops can stock carbon underground [START_REF] Mclaughlin | Evaluating environmental consequences of producing herbaceous crops for bioenergy[END_REF]. Therefore, our counter-intuitive result can be explained by this fact, but only if direct LUC is accounted for (accounting for above ground and underground carbon sequestration). However we noticed that luc_dir variable is not statistically significant. Hence, we decided to combine mat_cult variable with luc_dir variable (aggregated in mat_cultxdluc) in order to confirm this effect (results reported in columns (1aG2) and (2aG2), Table 4). Our meta-model shows that mat_cultxdluc variable is statistically significant at the 1% level and impacts negatively GHG emissions for G2 biofuels. It means that GHG emissions for G2 biofuels produced from cultivated feedstock that take into account dLUC are lower than GHG emissions for G2 biofuels from cultivated feedstock that do not take into account dLUC or from waste feedstock. Thus, the type of feedstock combined with the fact to take into account dLUC influence GHG emissions for G2 biofuels.

Methodological variables lca_cons variable is statistically significant at the 1% level for "G2" sample. Its coefficient is negative so GHG emissions for G2 biofuels are lower with a consequential approach compared to the attributional approach. The type of LCA approach thus influences GHG emission results for G2 biofuels. copval_alloc and copval_hyb variables are statistically significant at the 1% and 5% level, respectively (column (1aG2), Table 4). It confirms the influence of the method for taking into account coproducts on LCA GHG emission results as often mentioned in the literature [START_REF] Kaufman | Applying life-cycle assessment to low carbon fuel standards-How allocation choices influence carbon intensity for renewable transportation fuels[END_REF]. The coefficients of both variables are positive which means that GHG emissions are lower for G2 biofuels when using the system boundaries expansion method (copval_systexp) compared to allocation method and hybrid method. We observed, however, that most LCA authors recognize the importance of the method of taking into account burdens associated to coproducts. 91% of the studies in our database test alternative methods for allocation performing a sensibility analysis. luc_indir is statistically significant at the 1% level. It shall be noticed that all studies assessing indirect LUC (luc_indir) always assess direct LUC (luc_dir), so luc_indir is equal to 1 when the study assesses both direct and indirect LUC. Nevertheless luc_dir is not statistically significant. We can then conclude that assessing indirect LUC increases GHG emission results for G2 biofuels as luc_indir coefficient is positive. Nevertheless, the direct LUC (luc_dir) has an influence but it is linked with the type of biomass feedstock used, as mentioned before.

impcat_nev, impcat_nrc variables are both statistically significant at the 1% level. The type of other environmental indicators than GHG emissions assessed in the study thus could influence GHG emission results for G2 biofuels. According to our results, GHG emissions are statistically lower when the study assesses the Net Energy Value (impcat_nev) and are statistically higher when the study assesses the Non Renewable Energy consumption (impcat_nrc). This effect could not have been anticipated. Nevertheless, it could be interpreted as a quality indicator for the study: when these energy indicators are consistently assessed, the GHG emission result can be considered to be more robust.

Variables related to the methods for taking into account uncertainties (uncer_MC and uncer_SA) are statistically significant and impact positively the amount of GHG emissions emitted for G2 biofuels. This effect is unexpected. It means that GHG emissions for G2 biofuels are statistically higher when uncertainties are taken into account -via Monte Carlo method (uncer_MC) or Sensitivity analysis (uncer_SA) -than when there is no uncertainties assessment (uncer_ref). The fact to assess uncertainties could be interpreted also as a quality indicator of a study. It can be seen as an effort to establish the accuracy of the results but the tendency of the influence of these parameters in the e-s could not be anticipated nor explained afterwards.

Typological variables

Lastly, zlab_us variable has a negative impact on GHG emissions and is significant at the 1% level. Again, GHG emissions for G2 appear to be statistically lower when the authors are from North America (zlab_us) compared to authors from Europe (zlab_eu). Hence, the geographical location of the authors also influences GHG emission results for G2 biofuels.

Results for the Ethanol sample

Estimates results for the "G2-Ethanol" sample are presented in Table 5. Columns (1cEtha) and (2cEtha) correspond to the model without the inclusion of the technical variable that is the mass yield of the pathway (g2_mass_yield). Columns (1bEtha) and (2bEtha) test the existence of a linear effect of this variable (g2_mass_yield) whereas columns (1aEtha) and (2aEtha) test the existence of a non-linear effect of this variable by taking the logarithm of the g2_mass_yield variable (g2_mass_yield_ln). The AIC and the BIC both decrease from the first specification (columns (1aEtha) and (2aEtha)) to the last one (columns (1cEtha) and (2cEtha)). Therefore, the inclusion of a non-linear effect of the mass yield of the pathway appears more relevant to explain GHG emission variations. Thus, we choose to comment results presented in column (1aEtha).

Technical variables mat_cultxdluc variable is significant at the 5% level and has the same effect on GHG emissions for Ethanol as for G2 biofuels (See Section 4.2.2)

The mass yield of the pathway g2_mass_yield_ln impacts negatively GHG emissions for G2 Ethanol, which is an intuitive effect: the better the mass yield is, the less GHG are emitted all along the biofuel life cycle, ceteris paribus. It should be noticed that g2_mass_yield_ln traduces a non-linear effect of this variable.

We should also mention that variables related to other technical data, such as the type of biomass pretreatment, are not statistically significant for Ethanol. Indeed, 83% of observations are related to Ethanol produced using dilute sulfuric acid pretreatment and most of these observations use technical data from the same study (NREL) [START_REF] Aden | Lignocellulosic Biomass to Ethanol Process Design and Economics Utilizing Co-Current Dilute Acid Prehydrolysis and Enzymatic Hydrolysis for Corn Stover[END_REF]. Hence pretretament process variables for Ethanol are not really discriminatory, and this could explain why those variables are not statistically significant.

Methodological variables Among significant variables found for G2 biofuel sample, lca_cons, luc_indir, impcat_nev, impcat_nrc, uncer_MC and uncer_SA variables are also significant for the Ethanol sample and have the same impact as described for the G2 sample. So the type of LCA approach, the fact 'to assess indirect LUC', the type of other environmental indicators, the method for taking into account uncertainties influence GHG emission results for G2 Ethanol.

It can be noticed that copval_alloc and copval_sys variables are no longer statistically significant. This result is surprising regarding a previous lignocellulosic Ethanol LCA studies review [START_REF] Wiloso | LCA of second generation bioethanol: A review and some issues to be resolved for good LCA practice[END_REF] which concludes that the treatment of coproducts has a strong influence in the LCA results.

Typological variables zlab_us variable has a negative impact on GHG emissions and is significant at the 5% level. It means that GHG emissions for Ethanol are statistically lower when the authors are from North America (zlab_us) compared to authors from Europe (zlab_eu). Hence, the geographical location of the authors also influences GHG emission results for Ethanol.

Results for the BtL sample

Estimates results for the "G2-BtL" sample are presented in Table 6. Columns (1eBtL) and (2eBtL) correspond to the reduced model obtained for the "G2" sample. Columns (1dBtL) and (2dBtL) correspond to the new reduced model without any technical variables. Columns (1aBtL) to (2cBtL) correspond to the reduced model with technical variables. Columns (1aBtL) and (2aBtl) are the only one to test a non-linear effect of the mass yield of the pathway. The AIC and the BIC both decrease from the first specification (columns (1aBtL) and (2aBtL)) to the last one (columns (1eBtL) and (2eBtL)). Thus, we choose to comment results presented in column (1aBtL).

Technical variables mat_cultxdluc variable is significant at the 1% level and has the same effect on GHG emissions for BtL as for G2 biofuels (See Section 4.2.2)

Variables related to the type of conversion into fuel process (btl_pro_alng and btl_pro_alelec) are statistically significant. Using natural gas as a source of heat for an allothermic BtL unit leads to higher GHG emissions than producing BtL from an autothermic plant (biomass provides all process energy needs). Conversely using grid electricity as a utility for an allothermic BtL unit leads to lower GHG emissions than producing BtL from an autothermic plant. The source of electricity used could explain these results. Indeed, among the observations using grid electricity as a utility for an allothermic BtL unit, 57% of these observations use electricity provided by wind power plants [START_REF] Jungbluth | Life cycle assessment of BTL-fuel production: life cycle impact assessment and interpretation[END_REF]. The other studies do not precise the source of electricity used.

The mass yield of the pathway g2_mass_yield_ln impacts negatively GHG emissions for BtL, which is an expected effect: the better the mass yield is, the less GHG emissions are emitted all along the pathway for a G2 biofuel. It should also be noticed that g2_mass_yield_ln traduces a non-linear effect of this variable.

It should be noticed that variables related to other technical data, such as the type of biomass pretreatment or the inclusion of Carbon Capture and Storage (CCS) in the process, are not statistically significant for BtL. Indeed, 90% of observations in the econometric sample are related to BtL produced without biomass pretreatment (See Table C.4 in Appendix C). Hence pretreatment process variables for BtL are not really discriminatory, and this may be the reason why those variables are not statistically significant. Moreover, the variable btl_ccs is equal to zero for the econometric sample (See Table C.4 in Appendix C), therefore this variable could not have been tested. In fact, the variable in question appears in only three observations and all of them are considered outliers (see Table B.8 in Appendix B).

Methodological variables Among significant variables found for "G2" sample, only copval_alloc and lca_cons are significant for the "G2-BtL" sample. The method for taking into account coproducts (copval_alloc) has the same impact as described for "G2" sample (copval_hyb for BtL is equal to zero). However the influence of the type of LCA approach is not the same for G2 biofuel and for BtL: GHG emissions are higher with a consequential approach (lca_cons) compared to an attributional approach (lca_att). So the type of LCA approach and the method for taking into account coproducts influence GHG emission results for BtL.

Furthermore, the type of coproduct influence GHG emission results for BtL since cop_elec variable is statistically significant at the 1% level. So the coproduction of electricity for BtL decreases GHG emissions compared to other coproducts, ceteris paribus.

Typological variables zlab_us variable has a negative impact on GHG emissions and is significant at the 1% level. It means that GHG emissions for BtL are statistically lower when the authors are from North America (zlab_us) compared to authors from Europe (zlab_eu). Hence, the geographical location of the authors also influences GHG emission results for BtL.

(ref) copval_hyb - - - - - - - - - - luc_indir - - - - - - - - - - uncer_MC - - - - - - - - - - uncer_SA - - - - - - - - - - uncer_ref (ref) impcat_nev - - - - - - - - - - impcat_nrc - - - - - - - - - - impcat_other - - - - - - - - - - impcat_gwponly (ref)

WLS

We turn now to the analysis of the "G3" sample.

Results for the G3 sample

Estimate results for the "G3" sample are presented in Table 7. We begin by commenting the impact of g3_productivity and g3_oil as the influence of these two continuous technical variables will determine the final specification of the model for the "G3" sample.

Technical variables

First, a lin-lin model is specified in order to test the linear effects of both g3_productivity and g3_oil on the e-s. Table 7, columns (1dG3) and shows the reduced form of this specification. It could be noticed that g3_productivity variable is not statistically significant. This result is non intuitive as most part of the literature mentions that algae productivity could explain the variability of GHG emission results. The nonsignificance of this variable may be explained by the existence of a non-linear effect instead of a linear one. To test this hypothesis, two models are specified. In the first one (Table 7, column (1cG3)), the non-linear effect is modelled as a second-degree polynomial by introducing the variable g3_productivity and its squared value (g3_productivity_sq). In the second one (Table 7, column (1bG3)), the linear effect is modelled as a logarithmic function by introducing g3_productivity_ln instead of g3_productivity. In Table 7, column (1cG3), neither g3_productivity nor g3_productivity_sq are statistically significant at the 10% level. On the contrary, g3_productivity_ln is statistically significant at the 1% level (Table 7, column (1bG3)). As a conclusion, the variable g3_productivity does have an impact on GHG emission results for G3 biofuels but this effect is non-linear which can be captured by a logarithmic function, not a second degree polynomial. Regarding g3_oil, results presented in Table 7, column (1bG3) indicates a negative linear influence of this variable. Finally only g3_productivity_ln and g3_oil_ln variables are statistically significant at the 1% level and their coefficients are both negative (Table 7, column (1aG3)). Thus, we choose to comment results presented in column (1aG3).

Algae productivity value and the oil content -as proxies of the g3_productivity and g3_oil variables, respectively -influence GHG emission results for G3 biofuels. They have a negative impact on GHG emissions so the higher algae productivity or the algae content is, the lower GHG emissions are. In addition, these non-linear effects indicate that those parameters are more sensitive for low productivity or low oil content than for high ones.

The variable hvo is statistically significant at the 1% level. According to its coefficient estimate, GHG emissions for HVO from algae are higher than GHG emissions from FAME from algae by about 134 g CO 2 eq/MJ ceteris paribus. It indicates that the type of fuel conversion technology can explain the variability of GHG emission results for G3 biofuels. This result is difficult to be interpreted, especially due to the extent of its coefficient. In fact, the literature shows that upstream fossil energy consumption (including all inputs, notably methanol and hydrogen production) is similar in FAME and HVO processes [START_REF] Aatola | Hydrotreated Vegetable Oil (HVO) as a Renewable Diesel Fuel: Trade-off between NOx, Particulate Emission, and Fuel Consumption of a Heavy Duty Engine[END_REF] 15 . Vegetable oil consumption for both processes is also quite similar.

The coefficient of g3_Oppond is negative and significant at the 1% level. GHG emissions for G3 biofuels are thus statistically lower when microalgae are grown in an open-pound than in a photobioreactor. Hence the type of technology used for microalgae cultivation influences GHG emission results for G3 biofuels.

The type of technology used for microalgae cultivation, the algae productivity and the oil content of algae are often identified as key parameters in G3 biofuel LCA studies. So the fact that those variables are statistically significant confirms previous conclusions found in the literature. Jorquera et al. [START_REF] Jorquera | Comparative energy life-cycle analyses of microalgal biomass production in open ponds and photobioreactors[END_REF], in a microalgae LCA study (not included in this review because conversion into biofuel is not included), shows that culture in photobioreactors is more energy intensive than in open ponds. One of the conclusions of previous literature review on biofuel from microalgae technologies [START_REF] Brennan | Biofuels from microalgae-A review of technologies for production, processing, and extractions of biofuels and co-products[END_REF][START_REF] Mata | Microalgae for biodiesel production and other applications: A review[END_REF] is that microalgae strains presenting high biomass productivity are better for CO 2 emission mitigation.

Methodological variables

Concerning methodological variables, only lca_cons variable is statistically significant at the 1% level for G3 sample. Its positive coefficient indicates that GHG emissions for G3 biofuels are statistically higher when the study uses a consequential approach for LCA compared to the attributional approach. Hence the type of LCA approach influences GHG emission results for G3 biofuels. However, note that consequential LCA approach is only used by one study (that represents 9% of the observations for the econometric sample). Consequently the influence of the type of LCA approach for G3 biofuels should be interpreted with caution. Liu et al. [START_REF] Liu | Algae biodiesel has potential despite inconclusive results to date[END_REF], in an LCA harmonization exercise, show that different authors accounted for different microalgae coproducts and that it plays an important role in the final life cycle GHG emissions of the biofuel. However, in our meta-regression, variables related to the coproducts did not show themselves to be statistically significant. Still, the fact that lca_cons is statistically significant warns us about the importance of the definition of system boundaries and coproduct accounting methodology.

Typological variables

Regarding typological variables, the coefficient of zlab_us variable is significant at the 1% level and its sign is negative whereas zlab_other is not statistically significant. Thus, the previous result regarding the influence of geographical location is partly retrieved: GHG emissions of G3 biofuels are statistically lower when studies are from NA compared to ones from Europe. The non-significance of zlab_other indicates that there are no systematic differences between results drawn from European studies and other countries.

Harmonization

The MRA results presented in Section 4.2 are now used to adress the harmonization issue in the field of advanced biofuels GHG emissions thanks to the technique of benefits transfer using meta-regression models. As already demonstrated in the previous Section, the meta-regression framework allows the production of an estimation of the mean e-s weighted by the systematic influence of its main drivers. Once estimated, the meta-function can be used to deduce original values of the e-s by specifying new values for the main drivers identified corresponding to relevant case studies. This technique of benefits transfer using meta-regression models, as it is named in the MA literature, may be a particularly well adapted methodology to deal with the so-called harmonization issue specific to the LCA literature.

This section aims at providing an illustration of the potential for MRA to perform harmonization in the field of LCA through an application to advanced biofuels GHG emissions. To do so, predicted values of the e-s are computed using the meta-functions estimated in Section 4.2. The predicted values can be calculated using a combination of variables that already exists in the metadatabase: this type of prediction is called "in sample". In sample prediction enables the comparison of collected values (estimations of the e-s) and predicted values in order to check the accuracy of the metafunction in predicting the e-s. Furthermore, predicted values can be extrapolated for a combination of relevant variables that do not necessarily exist in the meta-database, hence the prediction is called "out of sample". Out of sample prediction could provide values for the e-s for case studies not assessed in the literature. In addition, out of sample prediction applied to quantitative variables can help to test how sensible the e-s is to these variables.

First, in sample predictions are presented and analyzed. Second, out of sample predictions are conducted assessing in particular the sensitivity of quantitative variables (algae productivity and oil content for G3 biofuels, mass yield for BtL and Ethanol).

Prediction in sample

Table 8 presents some characteristics of predicted values compared to collected values (estimations of the es in the meta-database) for each sample. The meta-models used to calculate these in sample predictions are those estimated in columns (1aAll), (1aG2), (1aEtha), (1aBtL) and (1aG3) for the "whole" sample, the "G2" sample, the"G2-Ethanol" sample, the "G2-BtL" sample and the "G3" sample, respectively (see Table 4, Table 5, Table 6 andTable 7).

First, we observe that mean values for predicted values are slightly different from those of collected values. Nevertheless the ranking between G2 and G3 biofuels, BtL and Ethanol in terms of contribution to the climate change (i.e. amount of GHG emissions emitted all along their life cycle) is still the same as depicted in the econometric analysis. Second, the range of variation is narrower for predicted values than for collected values, except for the G3 sample. Furthermore, these meta-models tend to overestimate predicted values compared to their corresponding collected values (53% to 56% of predicted values are overestimated depending on the samples) as depicted in Figure 6.

Prediction out of sample

Out of sample prediction enables the building of values of the e-s for combinations of variables that do not necessarily exist in the meta-database. Those values are calculated from the meta-function obtained by the meta-regression method. This harmonization method allows us to obtain mean values of the e-s and associated confidence intervals (CI) for each combination of statistically significant variables of a metamodel. For instance, using the meta-model for the "whole" sample presented in column (1aAll), Table 4, predicted values of the e-s can be calculated for G3 biofuel, BtL and Ethanol in Europe and North America. Table 9 and Table 10 illustrate the procedure. Table 9 reports coefficient estimates of the model (1aAll) (as presented in column (1aAll), Table 4) and the different values of the variable of this reduced model which have to be imputed to compute the predicted values of the e-s for G3 biofuel, BtL and Ethanol in Europe and North America. Table 10 shows the link between these imputed values and the corresponding predicted values of the e-s whereas Figure 7 offers an alternative view of Table 10 results. As depicted in the Figure 7, predicted values of GHG emissions for advanced biofuels in Europe are always higher than those in North America. In addition, GHG emissions are lower for BtL than Ethanol, and G3 biofuels always emit more GHG emissions than G2 biofuels. Those results are in line with the statistical description conducted in Section 3.2. Furthermore, the predicted value CIs are wider for G3 biofuels than for G2 biofuels, meaning that the model better estimates G2 biofuels GHG emissions than those of G3 biofuels.

It should be noted that predicted values of GHG emissions for advanced biofuels are always lower than GHG emissions for the reference fossil fuel even when considering CI, except for G3 biofuel in Europe.

The same type of analysis could be conducted for each meta-model. Out of sample prediction could also be used to test the sensitivity of results for quantitative variables. A range of values for quantitative variables could be tested by calculating mean predicted values for the e-s and associated CI, ceteris paribus.

For instance, the influence of oil content and algae productivity is tested for G3 biofuels (Figure 8 and Figure 9), by testing the range of values found in the meta-database. The same type of sensitivity analysis is conducted to test the influence of mass yield values of conversion process unit on BtL and Ethanol GHG emission values. As depicted in Figure 10 and Figure 11, mass yield value has a non linear effect on LCA GHG emissions of G2 biofuels, ceteris paribus. Variations for high values have less effect on the e-s than variations for low values. In addition, CIs are smaller for mass yield values around mean values than for extreme values, as previously described in the G3 sample.

Concluding remarks and discussion

This article aims at synthesizing the literature of LCA studies which have estimated GHG emissions of advanced biofuels. Our literature review showed a high variation among the results (Figure 1). Thus, one can wonder i) if there is a consensus about GHG emission benefits from advanced biofuels and ii) why there is so much variation among results. To do so, we have been chosen to apply a specific MA methodology (the "meta-regression anlysis", MRA) rather than a more classical narrative literature review approach. It provides a multivariate statistical analysis of previous estimated results to synthesize the available information. This assessment brings an extensive overview and contributes for a better understanding of the main factors inducing GHG emission variations. By using this original quantitative research framework, this article attempts to take the analysis of advanced biofuel GHG emissions one step further by complementing the qualitative surveys which have already been published [START_REF] Menichetti | Energy balance and greenhouse gas emissions of biofuels from a life-cycle perspective[END_REF][START_REF] Gnansounou | Life cycle assessment of biofuels: energy and greenhouse gas balances[END_REF][START_REF] Cherubini | Energy-and greenhouse gas-based LCA of biofuel and bioenergy systems: Key issues, ranges and recommendations[END_REF][START_REF] Sunde | Environmental Impacts and Costs of Hydrotreated Vegetable Oils, Transesterified Lipids andWoody BTL-A Review[END_REF][START_REF] Borrion | Environmental life cycle assessment of lignocellulosic conversion to ethanol: A review[END_REF][START_REF] Wiloso | LCA of second generation bioethanol: A review and some issues to be resolved for good LCA practice[END_REF]. We investigate -through an applicationthe potential for MRA to synthesize LCA literature by highlighting the main determinants of result variability in order to perform harmonization.

Our primary purpose was to identify and quantify which factors among i) technical data/characteristics, ii) author's methodological choices and iii) typology of the study under consideration have an impact on variations of the GHG emission estimates. Our results indicate a hierarchy between G3 and G2 biofuels: GHG emissions of G3 biofuels are statistically higher than those of Ethanol which, in turn, are superior to those of BtL. Moreover, whatever the type of advanced biofuel considered, North-American estimates are statistically higher than European estimates. Regarding author methodological choices, we have shown that some variables can influence the LCA results, such as the type of LCA approach (A-LCA vs. C-LCA), the method to account for coproducts and the fact of taking into account iLUC. Some technical variables appear to have an influence on GHG emission estimates. Concerning G2 biofuels, the mass yield has a negative and non-linear effect for both Ethanol and BtL whereas the type of process has a statistically significant effect only for BtL. For G3 biofuels, the algae productivity and its oil content have systematically a negative and non-linear effect. Finally, conclusions can be drawn also for some variables that have not been identified as variables influencing the final LCA result such as the type of biomass pretreatment in the Ethanol conversion process and the use of CCS in the BtL conversion process. The former is probably not statistically significant because most of the Ethanol technical data used in the different studies are derived from one single study [START_REF] Aden | Lignocellulosic Biomass to Ethanol Process Design and Economics Utilizing Co-Current Dilute Acid Prehydrolysis and Enzymatic Hydrolysis for Corn Stover[END_REF]. The latter is a variable expected to have a negative impact in the GHG emission results but that could not be tested because all observations with the use of CCS fell in the outliers category.

The secondary purpose of this study was to adress the harmonization issue in the field of advanced biofuel GHG emissions by using the technique of benefits transfer using meta-regression models. Our results may be summarized as follows. For each type of biofuel, a mean value of life cycle GHG emissions (expressed in g CO 2 eq / MJ of biofuel) weighted by the influence of its main drivers and its corresponding Confidence Interval is provided (Figure 5): about 60.0 (ranging from 43.3 to 76.7) for G3 biofuels; 19.7 (ranging from 17.4 to 22.0) for Ethanol; and 19.5 (ranging from 16.7 to 22.2) for BtL. Lastly, these values appear systematically higher for North-American estimates compared to those of Europe, ceteris paribus (Figure 7). Note that this range of values is lower than the fossil reference (about 83.8 in g CO 2 eq / MJ). However, only Ethanol and BtL do comply with the GHG emission reduction thresholds defined in both the US and EU directives.

Some results highlighted in this MRA have revealed some new information not previously assessed in this literature such as the existence of some non-linear effects regarding technical variables. Moreover, MRA provide i) a measure of the mean e-s and ii) a measure of the precision of this mean value estimate as provided by the corresponding Confidence Intervals.

Systematic reviews of LCA studies have gained interest due to their potential to clarify the impacts of particular products or services, producing more robust and policy-relevant results [START_REF] Brandão | What Can Meta-Analyses Tell Us About the Reliability of Life Cycle Assessment for Decision Support[END_REF]. Most of the published so-called LCA meta-analyses rely on a "harmonization" procedure adjusting other study estimates based on "more consistent methods and assumptions" [START_REF] Heath | Background and Reflections on the Life Cycle Assessment Harmonization Project[END_REF]. These studies typically harmonize technical parameters and methodological choices such as system boundaries, allocation procedures, impact calculation method, etc. [START_REF] Liu | Algae biodiesel has potential despite inconclusive results to date[END_REF][START_REF] Farrell | Ethanol can contribute to energy and environmental goals[END_REF][START_REF] Whittaker | Greenhouse gas reporting for biofuels: A comparison between the RED, RTFO and PAS2050 methodologies[END_REF][START_REF] Dolan | Life Cycle Greenhouse Gas Emissions of Utility-Scale Wind Power[END_REF][START_REF] Warner | Life Cycle Greenhouse Gas Emissions of Nuclear Electricity Generation[END_REF][START_REF] Burkhardt | Life Cycle Greenhouse Gas Emissions of Trough and Tower Concentrating Solar Power Electricity Generation[END_REF][START_REF] Kim | Life Cycle Greenhouse Gas Emissions of Thin-film Photovoltaic Electricity Generation[END_REF][START_REF] Hsu | Life Cycle Greenhouse Gas Emissions of Crystalline Silicon Photovoltaic Electricity Generation[END_REF]. All the cited studies are able to reduce variability in calculated outcomes representing a useful starting point for more precise estimates of LCA results. However, this does not mean that this "harmonization" procedure, which we will call "normalization", produces more accurate results since the "more consistent methods and assumptions" applied are subjective depending on an author choices (different authors can consider different methods and assumptions to be more consistent).

The MA approach applied in this study is quite different and follows the traditional practice in biomedical sciences or economics, based on in-depth application of statistical methods and analysis. To our knowledge, Bureau et al. [START_REF] Bureau | A quantitative assessment of the determinants of the net energy value of biofuels[END_REF] are the only authors to use this type of approach in LCA systematic reviews. In the same way as their study, our results show that this methodology can be consistently applied for the identification of parameters that influence a biofuel LCA result. Moreover, we have gone further by proposing a method to predict LCA results using a meta-model. This can be seen as a harmonization method alternative to the one applied currently in LCA meta-analysis ("normalization").

Our meta-model is obtained from a meta-regression and, therefore, it contains the parameters that were statistically proven to influence LCA results in a given sample. Our results show that, with this approach, we can provide more than a mean value and an interquartile range for the e-s as done in the "normalization" studies. We can calculate a real confidence interval for our predictions.

Among the LCA meta-analysis reviewed, the only meta-model built using regression techniques, is attempted in a work from Padey et al. [START_REF] Padey | A Simplified Life Cycle Approach for Assessing Greenhouse Gas Emissions of Wind Electricity[END_REF]. However, their wind turbine LCA meta-model is based on a limited number of parameters (lifetime and wind speed) and their regression method cannot account for qualitative parameters (dummy variables used in this study). Therefore, we observe that this is a field where significant progress can be made and we would recommend that the LCA community should work more closely with the Econometrics community so that more studies of this type could be conducted.

However, there are many limitations typically associated with MA. In the construction of the database, for example, there is always some exogenous information that has to be provided. Even if we avoid it as much as possible, in some cases it is necessary. This happened especially in the calculation of the e-s where the data required for the conversion of units (LHV, density, motor performance, etc.) was not always provided by the study in question.

Moreover, there is a compromise that has to be made between the number of studies that pass the screening process and the number of independent variables that are used in the description of an observation. In a MA database, all of the observations in a given sample have to be described with the same amount of independent variables. Theoretically, all the parameters that potentially influence the e-s have to be included. However, in LCA, the results are affected by hundreds of inputs and methodological choices, making it impossible to fully explain all the results of a big number of observations given the heterogeneity in LCA reporting. It was our judgement and experience in conducting LCA studies, but also previous narrative surveys, that determined which explanatory variables should be included in the database.

Finally, there may be some limitations regarding the statistical population of the MA sample. Heath and Mann [START_REF] Heath | Background and Reflections on the Life Cycle Assessment Harmonization Project[END_REF] highlight the fact that MA cannot make up for a lack of studies on a certain technology or methodological issue. In our case, for example, there are only 3 observations for BtL including CCS in its production pathway and these were coincidently discarded from the meta-regression sample as outliers. Therefore, no conclusions could be drawn from this technological parameter. Another example is the limited number of consequential LCAs, also limiting the conclusions we can reach concerning this methodological choice.

On our view, MA appear thus more as a complementary methodology than an alternative one to more classical narrative surveys.

Index of figures

Figure 1 -

 1 Figure 1 -GHG emissions extrema for bibliographic results of G2 and G3 biofuel LCA studies (47 studies, 593 observations)

Figure 2 -

 2 Figure 2 -Cumulative number of studies and observations per year of publication

Figure 3 -

 3 Figure 3 -Dispersion of LCA GHG emission results included in the database for the different types of biofuel

Figure 5 -Figure 4

 54 Figure 5 -Dispersion of LCA GHG emission results included in the database for G3 biofuels and for the different geographical location

Figure 6 -

 6 Figure 6 -Predicted and collected values of the e-s for meta-model (1a) distinguished by their geographical location

Figure 7 -

 7 Figure 7 -Predicted values of the effect size for the whole sample calculated from meta-model 1aAll

Figure 8 -Figure 9 -

 89 Figure 8 -Influence of oil content on predicted values of the e-s for G3 sample (1aG3 meta-model)

Figure 10 -Figure 11 -

 1011 Figure 10 -Influence of the mass yield on predicted values of the e-s for Ethanol sample (1aEtha meta-model)

Figure 1 -Figure 2 - 19 Figure 3 - 22 Figure 5 - 23 Figure 6 - 37 Figure 7 - 39 Figure 8 - 40 Figure 9 - 40 Figure 10 -

 121932252363773984094010 Figure 1 -GHG emissions extrema for bibliographic results of G2 and G3 biofuel LCA studies (47 studies, 593 observations) ............................................................................................................................................... 4 Figure 2 -Cumulative number of studies and observations per year of publication ....................................... 19 Figure 3 -Dispersion of LCA GHG emission results included in the database for the different types of biofuel .............................................................................................................................................................. 20 Figure 4 -Dispersion of LCA GHG emission results included in the database for G2 biofuels and for the different geographical location ........................................................................................................................ 22 Figure 5 -Dispersion of LCA GHG emission results included in the database for G3 biofuels and for the different geographical location ........................................................................................................................ 23 Figure 6 -Predicted and collected values of the e-s for meta-model (1a) distinguished by their geographical location ............................................................................................................................................................. 37 Figure 7 -Predicted values of the effect size for the whole sample calculated from meta-model 1aAll ........ 39 Figure 8 -Influence of oil content on predicted values of the e-s for G3 sample (1aG3 meta-model) .......... 40 Figure 9 -Influence of algae productivity on predicted values of the e-s for G3 sample (1aG3 meta-model) .......................................................................................................................................................................... 40 Figure 10 -Influence of the mass yield on predicted values of the e-s for Ethanol sample (1aEtha metamodel) .............................................................................................................................................................. 41 Figure 11 -Influence of the mass yield on predicted values of the e-s for BtL sample (1aBtL meta-model) 41 Figure A.1 -Main steps in the production of advanced biofuels .................................................................... 53

  is, the variance of the transformed error term,

	Let	σ	ε	,i	be the estimated standard error 7 of the i-th e-s estimate, i y , for any i. Knowing the i y 's
	heteroskedastic variances, 2 ,i ε σ , the WLS method of estimation takes this information into account explicitly
	by, first, dividing eq. (3) by the standard errors of i y , ,i
					* i ε , is now homoskedastic.

ε σ , giving:

-

Table 1 -List of categories and subcategories of variables included in the database

 1 The type of biofuel (Biomass To Liquid, Ethanol, Fatty Acid Methyl Ester or Hydrotreated Vegetable Oil) as well as the biofuel generation (G2 biofuel for BtL and Ethanol; G3 biofuel for FAME and HVO) are set as variables.

	Technical data	Methodological choices	Typology of the study
	Type of biofuel	Type of LCA approach	Type of study
	Type of biomass feedstock	System boundaries	Year of publication
	Type of coproducts	Method for taking into account coproducts	Geographical location of authors
	Type of technologies and associated yields	Carbon neutral
	Geographical location of the case study	Characterization method for impact assessment
		Method for assessing N2O emission from N input
		Method for taking into account Land Use Change
		Method for taking into account uncertainties
		Number and type of environmental impact indicator
		assessed in the study
	A brief description of all subcategories for all categories follows (See Table B.2 in Appendix B for a
	comprehensive variable description and their respective name):
	Technical data.

Table 2 -List of selected studies for the MA with a description of some of their characteristics

 2 (* MC=Monte Carlo analysis, SA=sensitivity analysis; ** PR= Peer review, OR= Official Report, Dir.= legislative text (Directive or Standard), WP= Working Paper)

			2009	34.45	G2 (87%) of which	A-LCA (97%),	MC (10%), SA	LUC (51%),	PR (65%), OR	North America
					BtL (26%) and	C-LCA (3%)	(38%), no	no LUC	(12%), Dir.	(45%), Europe
					ethanol (61%), G3		uncertainty	(49%)	(4%), WP	(53%), Other
					(13%)		analysis (52%)		(19%)	(2%)
	Mean and repartition	13 2009	23.07	G2 (87%) of which	A-LCA (98%),	MC (21%), SA	LUC (28%),	PR (65%), OR	North America
	(weighted by studies)				BtL (38%) and	C-LCA (4%)	(26%), no	no LUC	(12%), Dir.	(45%), Europe
					ethanol (70%), G3		uncertainty	(72%)	(4%), WP	(53%), Other
					(17%)		analysis (53%)		(19%)	(2%)
	Median (weighted by studies)	6	2010	15.53

Table 3 -Statistical description of GHG emission results included in the database for the different types of biofuel and for the different geographical location of authors

 3 (* expressed in g CO 2 eq/MJ)

	Mean*
	[Confidence Interval]	Min	Max	5th	95th

Dispersion of LCA GHG emission results included in the database for G2 biofuels and for the different geographical location

	G3 sample (mean: 88.87 gCO2eq/MJ)		G3 sample for Europe (mean: 175.25 gCO2eq/MJ)
	G3 sample for North America (mean: 2.02 gCO2eq/MJ)	5th Percentile
	95th Percentile				US threshold -60%
	EU threshold -60%				Fossil fuel reference
		80
		60
	Number of observations	40
		20
		0
	-200	0	200	400	600	800	1000	1200	1400	1600
					gCO 2eq /MJ

Table 4 -Results of MRA for the econometric samples Whole and G2 biofuels

 4

	Samples	Whole	Whole	G2	G2	G2	G2
	Model	1aAll	2aAll	1aG2	2aG2	1bG2	2bG2
	Constant	76.27***	271.74***	20.32***	27.24***	21.14***	28.43***
		(13.64)	(23.66)	(3.43)	(4.72)	(3.61)	(5.04)
	Technical data
	gen_3 (ref for Whole)
	etha	-41.39***	-220.92***	5.84***	-	5.83***	-
		(13.14)	(23.77)	(1.91)		(1.81)
	btl (ref for G2)	-52.12***	-215.57***
		(13.36)	(22.59)
	mat_cult					-9.47***	-11.56***
						(2.21)	(3.02)
	mat_cultxdluc			-7.94***	-13.67***
				(2.46)	(3.23)
	Methodological choices
	lca_att (ref)
	lca_cons			-33.66***	-40.41***	-34.04***	-39.09***
				(4.79)	(8.63)	(4.9)	(8.37)
	copval_alloc			8.96***	8.82**	8***	6.99*
				(1.91)	(3.62)	(1.94)	(3.84)
	copval_systexp (ref)
	copval_hyb			5.25**	-	5.41**	-
				(2.38)		(2.69)
	luc_dir					-	-
	luc_indir			29.97***	39.78***	29.62***	36.54***
				(6.32)	(7.27)	(6.34)	(7.2)
	uncer_MC			8.03**	16.68***	8.04**	17.25***
				(3.45)	(4.61)	(3.41)	(4.58)
	uncer_SA			7.78***	7.08*	7.32***	6.69**
				(2.4)	(3.63)	(2.39)	(3.39)
	uncer_ref (ref)
	impcat_nev			9.26***	-	7.71***	-
				(2.99)		(2.71)
	impcat_nrc			-15.01***	-7.31**	-12.65***	-
				(2.36)	(3.41)	(2.54)
	impcat_other			-	-	0.84*	-
						(0.49)
	impcat_gwponly (ref)
	Typology of the study
	zlab_us	-24.6***	-190.58***	-8.32***	-18.58***	-8.66***	-19.73***
		(3.97)	(25.05)	(2.1)	(3.66)	(2.12)	(3.2)
	zlab_eu (ref)
	zlab_other	-85.69***	-281.16***
		(15.6)	(24.85)
	Model information
	N	533	533	464	464	464	464
	Mean dep. Var.	28.64	17.62	24.15	25.04	24.15	25.01
	Adj. R-squ.	16.30%	68.76%	37.26%	30.95%	38.33%	30.94%
	Log-Likelihood	-2727.20	-3068.04	-1976.89	-2044.50	-1972.36	-2044.03
	F-stat.	18.93	32.82
	(P. value)	(0,0000)	(0,0000)
	Skewness	61.27		24.57		23.56
	(P. value)	(0,0000)		(0.017)		(0.0354)
	Kurtosis	8.75		1.6		3.06
	(P. value)	(0.0031)		(0.2062)		(0.0801)
	AIC	5464.39	6146.08	3977.78	4113.00	3970.72	4114.05
	BIC	5485.79	6167.47	4027.45	4162.68	4024.54	4167.87
	Wald Test (P. value) for	26.29	0.22
	etha=btl	(0,0000)	(0.6409)
		OLS		OLS		OLS
	Procedure	(White's	WLS	(White's	WLS	(White's	WLS
		HCCM)		HCCM)		HCCM)

Table 5 -Results of MRA for the econometric samples G2-Ethanol biofuels

 5

	Samples	Ethanol	Ethanol	Ethanol	Ethanol	Ethanol	Ethanol
	Model	1aEtha	2aEtha	1bEtha	2bEtha	1cEtha	2cEtha
	Constant	-5.88	31.9	46.39***	37.85***	32.11***	34.07***
		(14.8)	(31.58)	(8.33)	(13.52)	(2.64)	(3.95)
	Technical data
	mat_cultxdluc	-7.18**	-10.1**	-6.91**	-9.92**	-	-
		(3.26)	(4.85)	(3.28)	(4.79)
	g2_mass_yield			-73.57**	-
				(34.79)
	g2_mass_yield_sq
	g2_mass_yield_ln	-23.22**	-
		(9.3)
	Methodological choices
	lca_att (ref)
	lca_cons	-38.24***	-40.12***	-38.43***	-40.17***	-40.24***	-40.72***
		(5.53)	(11.37)	(5.46)	(11.33)	(4.72)	(9.9)
	luc_indir	29.01***	35.89***	27.48***	35.07***	19.85***	31.7***
		(7.49)	(8.59)	(7.41)	(8.43)	(7.29)	(7.78)
	uncer_MC	9.51**	20.32***	9.66**	20.43***	10.06**	18.67***
		(4.06)	(5.83)	(4.11)	(5.82)	(4.23)	(5.5)
	uncer_SA	12.5***	12.28**	11.53***	11.99**	12.09***	14.01***
		(3.68)	(5.71)	(3.59)	(5.57)	(2.72)	(4.08)
	uncer_ref (ref)
	impcat_nev	12.34***	-	11.05***	-	9.51**	11.15*
		(3.99)		(3.99)		(3.94)	(6.49)
	impcat_nrc	-17.09***	-14.16***	-17.24***	-14.18***	-22.53***	-20.14***
		(3.19)	(5)	(3.17)	(5)	(2.51)	(4.08)
	impcat_other	-	-	-	-	-1.09*	-
						(0.61)
	impcat_gwponly (ref)
	Typology of the study
	zlab_us	-7.29**	-28.56***	-8.22**	-29.23***	-11.26***	-23.84***
		(3.56)	(7.44)	(3.56)	(7.35)	(2.37)	(4.74)
	zlab_eu (ref)
	Model information
	N	209	209	209	209	321	321
	Mean dep. Var.	19.70	19.14	19.70	18.96	26.61	26.61
	Adj. R-squ.	31.21%	36.31%	30.32%	36.24%	40.13%	37.82%
	Log-Likelihood	-884.15	-919.42	-885.49	-919.54	-1364.10	-1412.35
	F-stat.	12.61	10.91	12.55	10.79	33.94	27.19
	(P. value)	(0,0000)	(0,0000)	(0,0000)	(0,0000)	(0,0000)	(0,0000)
	Skewness	18.14		16.84		18.16
	(P. value)	(0.0527)		(0.078)		(0.0333)
	Kurtosis	0.32		0.23
	(P. value)	(0.5729)		(0.6351)
	AIC	1790.30	1860.83	1792.98	1861.08	2748.21	2844.70
	BIC	1827.07	1897.60	1829.75	1897.85	2785.92	2882.42
	LR test (P. value)	959.9	985.87	957.22	985.62
	Nested model: model (c)	(0,0000)	(0,0000)	(0,0000)	(0,0000)
		OLS		OLS		OLS
	Procedure	(White's	WLS	(White's	WLS	(White's	WLS
		HCCM)		HCCM)		HCCM)

Table 6 -Results of MRA for the econometric samples G2-BtL biofuels

 6

	Samples	BtL	BtL	BtL	BtL	BtL	BtL	BtL	BtL	BtL	BtL
	Model	1aBtL	2aBtL	1bBtL	2bBtL	1cBtL	2cBtL	1dBtL	2dBtL	1eBtL	2eBtL
	Constant	43.23***	29.68	70.94***	75.11***	39.6***	32.19***	27.43***	29.03***	16.03**	24.5***
		(12.66)	(20.05)	(9.38)	(12.85)	(6.29)	(6.36)	(5.59)	(5.69)	(6.33)	(8.38)
	Technical data
	mat_cultxdluc	-14.41***	-19.53***	-15.41***	-20.33***	-15.16***	-18.1***	-16.24***	-17.02***	-11.64***	-13.28***
		(3.08)	(3.27)	(3.11)	(3.23)	(2.93)	(2.84)	(2.47)	(2.6)	(3.98)	(4.46)
	cop_elec	-44.56***	-35.68***	-43.99***	-35.94***	-19.4***	-	-	-
		(4.14)	(7.7)	(4.19)	(7.71)	(5.09)
	g2_mass_yield			-	-
	g2_mass_yield_sq
	g2_mass_yield_ln	-11.66*	-17.41**
		(7.04)	(8.52)
	btl_pro_autoth
	btl_pro_alng	17.04***	-	17.73***	-	13.85**	-
		(5.4)		(5.73)		(5.6)
	btl_pro_alelec	-	-	-	-	-	-
	btl_pro_alrenew	-	-	-	-	-	-
	btl_gasrecycl	-	-	-	-	-	-
	Methodological choices
	lca_att (ref)
	lca_cons	25.61***	-	26.23***	-	22.97***	-	18.1**	-	-	-
		(8.36)		(8.6)		(8.68)		(8.87)
	copval_alloc	9.6***	-	9.81***	-	13.73***	12.51***	16***	11.02**	11.7***	13.21***
		(3.37)		(3.4)		(3.05)	(4.33)	(2.96)	(4.65)	(2.79)	(4.31)
	copval_systexp

Table 7 -Results of MRA for the econometric samples G3 biofuels

 7

	Samples	G3	G3	G3	G3	G3	G3	G3	G3	G3	G3
	Model	1aG3	2aG3	1bG3	2bG3	1cG3	2cG3	1dG3	2dG3	1eG3	2eG3
	Constant	318.44***	550.41***	621.72***	916.55***	490.82***	640.23***	450.73***	585.43***	105.38***	237.46***
		(90.09)	(171.08)	(99.61)	(146.59)	(87.74)	(68.43)	(88.11)	(59.96)	(19.91)	(25.17)
	Technical data
	fame
	hvo	134.18***	185.12***	135.18***	181.47***	137.73***	178.64***	134.31***	176.78***
		(35.34)	(39.47)	(32.44)	(34.94)	(34.09)	(35.28)	(34.62)	(34.69)
	g3_productivity					-	-5.82***	-	-3.19***
							(1.86)		(1.2)
	g3_productivity_sq					-	0.02**
							(0.01)
	g3_productivity_ln	-65.31***	-124.8***	-64.46***	-127.33***
		(20.13)	(45.43)	(20.06)	(44.5)
	g3_oil			-434.74***	-521.06***	-425.28***	-522.41***	-430.6***	-527***
				(142.4)	(112.68)	(150.9)	(110.74)	(146.08)	(115.09)
	g3_oil_sq
	g3_oil_ln	-140.32***	-161.66***
		(42.3)	(39.17)
	g3_Oppond	-197.13***	-259.9***	-198.94***	-260.33***	-201.93***	-257.79***	-199.6***	-257.1***
		(34.6)	(24.28)	(36.92)	(24.35)	(38.32)	(24.13)	(38.46)	(23.73)
	Methodological choices
	lca_att (ref)
	lca_cons	172.72***	250.7***	174.8***	254.66***	196.92**	268.68***	187.41**	290.31***	-	-
		(61.08)	(70.3)	(65.98)	(73.36)	(79.77)	(81.63)	(84.67)	(86.21)
	Typology of the study
	zlab_us	-207.56***	-259.02***	-198.73***	-244.44***	-201.53***	-244.11***	-199.27***	-240.76***	-95.93***	-225.96***
		(31.01)	(26.35)	(29.55)	(25.73)	(30.19)	(26.09)	(30.8)	(25.61)	(26.17)	(31.21)
	zlab_eu (ref)
	zlab_other	-	-	-	-	-	-	-	-	-114.8***	-246.87***
										(21.87)	(26.35)
	Model information
	N	68	68	68	68	68	68	68	68	69	69
	Mean dep. Var.	59.97	68.95	59.97	67.95	59.97	67.85	59.97	66.53	58.84	126.49
	Adj. R-squ.	65.23%	80.63%	66.07%	81.32%	66.59%	81.92%	66.06%	81.34%	17.77%	48.39%
	Log-Likelihood	-373.01	-376.38	-372.18	-375.14	-371.08	-373.46	-372.19	-375.11	-410.22	-418.31
	F-stat.	11.11	24.7	11.67	25.07	10.96	22.62	13.53	27.17	11.17	31.42
	(P. value)	(0,0000)	(0,0000)	(0,0000)	(0,0000)	(0,0000)	(0,0000)	(0,0000)	(0,0000)	(0,0000)	(0,0000)
	Skewness	9.25		13.93		14.15		16.85		32.57
	(P. value)	(0.2352)		(0.0524)		(0.078)		(0.0184)		(0,0000)
	Kurtosis	0.06		0.32		0.47		0.41		6.01
	(P. value)	(0.8139)		(0.5694)		(0.4938)		(0.521)		(0.0142)
	AIC	762.02	768.75	760.36	766.29	760.17	764.92	760.37	766.23	828.44	844.62
	BIC	779.78	786.51	778.11	784.04	780.14	784.89	778.13	783.98	837.37	853.56
	LR test (P. value)	74.42	83.87	76.08	86.34	78.27	89.71	76.06	86.4
	Nested model: model (e)	(0,0000)	(0,0000)	(0,0000)	(0)	(0,0000)	(0,0000)	(0,0000)	(0,0000)
		OLS		OLS		OLS		OLS		OLS
	Procedure	(White's	WLS	(White's	WLS	(White's	WLS	(White's	WLS	(White's	WLS
		HCCM)		HCCM)		HCCM)		HCCM)		HCCM)

Table 8 -Characteristics of collected and predicted values of the e-s in g CO 2 eq/MJ (predicted values calculated from (1a) meta-models)

 8

	Samples	Whole	G3	G2	BtL	Ethanol
	Collected values
	Number of values	533	69	464	143	321
	Mean	28.64	58.84	24.15	18.65	26.61
	Min	-85.00	-85.00	-24.00	-24.00	-23.65
	Max	332.20	332.20	85.80	85.68	85.80
	NA values higher than -60%	7%	14%	5%	1%	7%
	GHG emission threshold
	EU values higher than -60%	25%	30%	24%	17%	27%
	GHG emission threshold
	Predicted values
	Number of values	533	68	464	132	209
	Mean	28.64	59.97	24.15	19.45	19.7
	[Confident Interval]	[25.19;32.09]	[43.29;76.65]	[22.56;25.74]	[16.67;22.23]	[17.37;22.03]
	Min	-9.42	-109.25	-15.82	-8.04	-20.86
	Max	76.27	230.82	47.91	56.31	47.49
	Underestimated values	44%	46%	44%	47%	47%
	Overestimated values	56%	54%	56%	53%	53%
	Collected values included in	12%	51%	22%	18%	37%
	the predicted value CI
	NA values higher than -60%	5%	9%	2%	1%	2%
	GHG emission threshold
	EU values higher than -60%	7%	28%	22%	8%	1%
	GHG emission threshold

Table 9 -Benefits Transfer for the "Whole" Sample (1aAll meta-model)

 9

	Samples	Whole
	Model:	1aAll			Imputed Values
	Parameter Estimate
	Constant	76,27***	1	1	1	1	1	1
		(13,64)
	Technical data
	gen_3 (ref for Whole)		0	0	0	0	0	0
	etha	-41,39***	0	1	0	0	1	0
		(13,14)
	btl (ref for G2)	-52,12***	0	0	1	0	0	1
		(13,36)
	Typology of the study
	zlab_us	-24,6***	0	0	0	1	1	1
		(3,97)
	zlab_eu (ref)		0	0	0	0	0	0
	zlab_other	-85,69***	0	0	0	0	0	0
		(15,6)
	Transfer Values		76,27 (13,64)	34,88 (1,75)	24,15 (1,88)	51,67 (12,35)	10,29 (2,98)	-0,44 (3,50)

Table 10 -Harmonized e-s (g CO 2 eq/MJ) for the "Whole" sample (1aAll meta-model))

 10

			Harmonized	95% Confidence Interval
			e-s	Min	Max
		G3	76,27	49,54	103,00
	Europe	G2 Ethanol	34,88	31,45	38,31
		G2 BtL	24,15	20,46	27,84
	North America	G3 G2 Ethanol G2 BtL	51,67 10,29 -0,44	27,47 4,45 -7,31	75,88 16,13 6,42
	In sample
	predicted	Mean	28,64	25,19	32,09
	value

  Results show that both variables have a non-linear effect on LCA GHG emissions, ceteris paribus. Furthermore, variations for high values of the algae productivity have less effect on the e-s than variations for low values. Moreover, CIs are smaller for oil content and algae productivity values around mean values than for extreme values.

		Min						Max
		Predicted value (for oil content mean value in G3 sample)	Predicted values
		95% Confident Interval (lower)				95% Confident Interval (upper)
		300
		250
		200
		150
	gCO2eq/MJ	50 100
		0
		-50	0%	10%	20%	30%	40%	50%	60%	70%	80%
		-100
		-150
							Oil content (%)

Table B .4 -Descriptive statistics for the effect size and variables of the original Whole sample

 B

		# of values	mean	std dev	min	max
	Descriptive statistics for the Effect Size
	es	593	34.45	89.34	-142.18	1377.90
	es_min	593	-11.25	70.81	-352.81	881.44
	es_max	593	80.18	155.52	-127.01	1874.37
	es_var	593	2264.65	9868.76	0.00	64159.87
	es_et	593	23.37	41.49	0.03	253.30
	Technical data
	gen_2	593	0.87	0.34	0	1
	gen_3	593	0.13	0.34	0	1
	etha	593	0.61	0.49	0	1
	btl	593	0.26	0.44	0	1
	fame	593	0.11	0.31	0	1
	hvo	593	0.03	0.16	0	1
	mat_algae	593	0.13	0.34	0	1
	mat_agrires	593	0.22	0.41	0	1
	mat_for	593	0.05	0.22	0	1
	mat_enercult	593	0.28	0.45	0	1
	mat_farmwood	593	0.10	0.30	0	1
	mat_other	593	0.23	0.42	0	1
	mat_cult	593	0.38	0.49	0	1
	coprod	593	0.91	0.29	0	1
	cop_gly	593	0.09	0.29	0	1
	cop_elec	593	0.63	0.48	0	1
	cop_heat	593	0.12	0.32	0	1
	cop_algmeal	593	0.10	0.30	0	1
	cop_biog	593	0.18	0.39	0	1
	cop_other	593	0.25	0.54	0	2
	cop_otherelec	593	0.48	0.50	0	1
	coprod_num	593	1.36	1.00	0	5
	mass_yield_exist	593	0.64	0.48	0	1
	g2_mass_yield	378	0.22	0.07	0.07	0.50
	eth_expl	361	0.08	0.28	0	1
	eth_ac	361	0.83	0.37	0	1
	eth_amm	361	0.08	0.28	0	1
	eth_other	361	0.00	0.00	0	0
	btl_pre_torr	153	0.07	0.25	0	1
	btl_pre_pyro	153	0.05	0.21	0	1
	btl_pre_none	153	0.89	0.32	0	1
	btl_pro_autoth	153	0.86	0.35	0	1
	btl_pro_alng	153	0.08	0.27	0	1
	btl_pro_alelec	153	0.03	0.18	0	1
	btl_pro_alrenew	153	0.03	0.16	0	1
	btl_gasrecycl	153	0.01	0.11	0	1
	btl_ccs	153	0.02	0.14	0	1
	g3_productivity	76	30.09	18.86	6.85	150.00
	g3_oil	77	0.41	0.11	0.15	0.70
	g3_Oppond	77	0.61	0.49	0	1
	zloc_us	593	0.34	0.47	0	1
	zloc_eu	593	0.64	0.48	0	1
	zloc_other	593	0.02	0.15	0	1
	Methodological choices
	lca_att	593	0.97	0.17	0	1
	lca_cons	593	0.03	0.17	0	1
	wtt	593	0.38	0.49	0	1
	wtw	593	0.62	0.49	0	1
	infrastruct	593	0.44	0.50	0	1
	copval_alloc_ener	593	0.26	0.44	0	1
	copval_alloc_mass	593	0.04	0.20	0	1
	copval_alloc_markval	593	0.12	0.32	0	1
	copval_alloc_exerg	593	0.01	0.07	0	1
	copval_alloc	593	0.42	0.49	0	1
	copval_systexp	593	0.55	0.50	0	1
	copval_hyb	593	0.07	0.26	0	1
	wtw*g3_carbneut	77	0.00	0.00	0	0
	gas_num	394	0.26	0.44	0	1
	ass_ipcc	573	0.37	0.48	0	1
	luc	593	0.51	0.50	0	1
	luc_dir	593	0.51	0.50	0	1
	luc_indir	593	0.03	0.18	0	1
	uncer_ref	593	0.57	0.50	0	1
	uncer_MC	593	0.10	0.30	0	1
	uncer_SA	593	0.38	0.49	0	1
	uncer_MCSA	593	0.48	0.50	0	1
	impcat_nev	593	0.31	0.46	0	1
	impcat_nrc	593	0.41	0.49	0	1
	impcat_nrcnev	593	0.50	0.50	0	1
	impcat_gwp	593	1.00	0.00	1	1
	impcat_other	593	1.09	2.28	0	9
	impcat_all	593	2.81	2.43	1	12
	Typology of the study
	lit_pr	593	0.63	0.48	0	1
	lit_or	593	0.09	0.29	0	1
	lit_dir	593	0.03	0.17	0	1
	lit_ordir	593	0.12	0.32	0	1
	lit_wp	593	0.25	0.44	0	1
	year	593	2009.38	1.31	2002	2011
	year_07	593	0.97	0.17	0	1
	year_09	593	0.90	0.30	0	1
	year_10	593	0.56	0.50	0	1
	zlab_us	593	0.32	0.47	0	1
	zlab_eu	593	0.67	0.47	0	1
	zlab_other	593	0.01	0.10	0	1
	58

Table B .5 -Descriptive statistics for the effect size and variables of the original G3 sample

 B

		# of values	mean	std dev	min	max
	Descriptive statistics for the Effect Size
	es	77	88.87	211.85	-96.47	1377.90
	es_min	77	-46.68	146.41	-352.81	881.44
	es_max	77	224.42	351.73	-7.55	1874.37
	es_var	77	11898.53	23739.99	265.09	64159.87
	es_et	77	69.16	84.91	16.28	253.30
	Technical data
	gen_2	77	0.00	0.00	0	0
	gen_3	77	1.00	0.00	1	1
	etha	77	0.00	0.00	0	0
	btl	77	0.00	0.00	0	0
	fame	77	0.82	0.39	0	1
	hvo	77	0.19	0.40	0	1
	mat_algae	77	1.00	0.00	1	1
	mat_agrires	77	0.00	0.00	0	0
	mat_for	77	0.00	0.00	0	0
	mat_enercult	77	0.00	0.00	0	0
	mat_farmwood	77	0.00	0.00	0	0
	mat_other	77	0.00	0.00	0	0
	mat_cult	77	0.00	0.00	0	0
	coprod	77	1.00	0.00	1	1
	cop_gly	77	0.71	0.45	0	1
	cop_elec	77	0.27	0.45	0	1
	cop_heat	77	0.40	0.49	0	1
	cop_algmeal	77	0.79	0.41	0	1
	cop_biog	77	0.00	0.00	0	0
	cop_other	77	0.95	0.93	0	2
	cop_otherelec	77	0.87	0.34	0	1
	coprod_num	77	2.99	1.71	1	5
	mass_yield_exist	77	0.05	0.22	0	1
	g3_productivity	76	30.09	18.86	6.85	150.00
	g3_oil	77	0.41	0.11	0.15	0.70
	g3_Oppond	77	0.61	0.49	0	1
	zloc_us	77	0.42	0.50	0	1
	zloc_eu	77	0.51	0.50	0	1
	zloc_other	77	0.08	0.27	0	1
	Methodological choices
	lca_att	77	0.92	0.27	0	1
	lca_cons	77	0.08	0.27	0	1
	wtt	77	0.65	0.48	0	1
	wtw	77	0.35	0.48	0	1
	infrastruct	77	0.51	0.50	0	1
	copval_alloc_ener	77	0.08	0.27	0	1
	copval_alloc_mass	77	0.00	0.00	0	0
	copval_alloc_markval	77	0.03	0.16	0	1
	copval_alloc_exerg	77	0.00	0.00	0	0
	copval_alloc	77	0.10	0.31	0	1
	copval_systexp	77	0.90	0.31	0	1
	copval_hyb	77	0.55	0.50	0	1
	wtw*g3_carbneut	77	0.00	0.00	0	0
	gas_num	77	0.45	0.50	0	1
	ass_ipcc	77	0.48	0.50	0	1
	luc	77	0.08	0.27	0	1
	luc_dir	77	0.08	0.27	0	1
	luc_indir	77	0.08	0.27	0	1
	uncer_ref	77	0.39	0.49	0	1
	uncer_MC	77	0.00	0.00	0	0
	uncer_SA	77	0.61	0.49	0	1
	uncer_MCSA	77	0.61	0.49	0	1
	impcat_nev	77	0.30	0.46	0	1
	impcat_nrc	77	0.40	0.49	0	1
	impcat_nrcnev	77	0.70	0.46	0	1
	impcat_gwp	77	1.00	0.00	1	1
	impcat_other	77	0.66	1.13	0	5
	impcat_all	77	2.36	1.38	1	7
	Typology of the study
	lit_pr	77	0.73	0.45	0	1
	lit_or	77	0.00	0.00	0	0
	lit_dir	77	0.08	0.27	0	1
	lit_ordir	77	0.08	0.27	0	1
	lit_wp	77	0.19	0.40	0	1
	year	77	2009.88	0.32	2009	2010
	year_07	77	1.00	0.00	1	1
	year_09	77	1.00	0.00	1	1
	year_10	77	0.88	0.32	0	1
	zlab_us	77	0.42	0.50	0	1
	zlab_eu	77	0.51	0.50	0	1
	zlab_other	77	0.08	0.27	0	1

Lignocellulosic biomass refers to annual crop residues (e.g. corn stover), forest residues, herbaceous energy crops (e.g. switchgrass, miscanthus) and woody biomass (e.g. poplar, eucalyptus).

So defined, MRA may be viewed as a subset of MA in the literature.

Six meta-analyses were published at the same time in the field of economics[START_REF] Stanley | Meta-regression analysis: A quantitative method of literature surveys[END_REF][START_REF] Jarrell | A meta-analysis of the union-nonunion wage gap[END_REF][START_REF] Smith | Signals or noise? Explaining the variation in recreation benefit estimates[END_REF][START_REF] Smith | What have we learned since Hotelling's letter? A meta-analysis[END_REF][START_REF] Walsh | Issues in nonmarket valuation and policy applications: A retrospective glance[END_REF][START_REF] Weitzman | Profit sharing and productivity[END_REF]. See for instance Stanley[START_REF] Stanley | Wheat from chaff: Meta-analysis as quantitative literature review[END_REF] for a more comprehensive presentation. Standard references for technical aspects of meta-analysis are[START_REF] Hedges | Statistical Methods for Meta-Analysis[END_REF][START_REF] Hedges | Fixed effects models[END_REF][START_REF] Hedges | Meta-analysis[END_REF][START_REF] Lipsey | Practical Meta-Analysis[END_REF].

The MA literature distinguishes primary studies from secondary ones. Compared to the latter, the former presents original research results. Litterature reviews are the typical example of secondary studies. In order to avoid double counting, only results drawn from primary studies are included in a meta-database.

Only studies following the ISO 14044 guidelines to conduct an LCA were included[START_REF]:2006 Environmental management -Life cycle assessment -Requirements and guidelines[END_REF]

Studies on other biomass derived fuels such as methanol, DME, ETBE, biogas, heat, power, CHP were not included.

To be more precise, only the WTW studies with consumption of pure biofuel (E10, B10, etc) have been included. No study with a bi-functional unit was included.

The following presentation is partly inspired from Ready[START_REF] Ready | Do landfills always depress nearby property values?[END_REF].

Thompson & Sharp [115] provide an overview of various estimators that allow for random-effects variation.

In the EcoInvent database[START_REF] Dones | Life Cycle Inventories of Energy Systemsௗ: Results for Current Systems in Switzerland and other UCTE Countries Data v2.0 ecoinvent report[END_REF], the cumulative fossil energy demand for the production of 1 kg of hydrogen from cracking natural gas is 70, 9 MJ. The same indicator for 1 kg of methanol also produced from natural gas is 36.9 MJ. FAME contains around 10% of methanol and HVO around 4% of hydrogen (mass). The selected processes for this example are the most commonly used for these products.

Acknowledgements:

The authors thank the DDEEP-seminar's participants of EconomiX-CNRS, University of Paris Ouest for their helpful comments. The authors are grateful to Anthony Hua for his valuable help to build the database. The usual disclaimers apply.

G2 (Ethanol) A-LCA Yes (SA) No PR Europe GonzalesG2 (Ethanol) A-LCA Yes (MC & SA) Yes PR North America Spatari G2 (Ethanol) A-LCA Yes (MC) Yes PR North America Stephenson

Appendices Appendix A. Technical description of advanced biofuels

Figure A.1 represents the main steps involved in the production of second and third generation biofuels (G2 and G3 biofuels respectively) discussed in this paper and the following text contain a brief description of their production processes. Second generation Ethanol is obtained from the biochemical conversion of annual crop residues (e.g. corn stover) and perennial crops (e.g. miscanthus). A pretreatment of the biomass is necessary to separate the cellulose from hemicellulose and lignin. Once the cellulose is accessible, enzymes are used to hydrolyze these molecules, transforming them into sugars that can be fermented. The product of fermentation needs to be distilled and dehydrated for obtaining pure Ethanol [START_REF] Aden | Lignocellulosic Biomass to Ethanol Process Design and Economics Utilizing Co-Current Dilute Acid Prehydrolysis and Enzymatic Hydrolysis for Corn Stover[END_REF][START_REF] Dwivedi | Cellulosic ethanol production in the United States: Conversion technologies, current production status, economics, and emerging developments[END_REF].

Synthetic diesel from biomass is also known as BtL (Biomass to Liquids) or biomass FT-diesel. It is produced by the thermochemical conversion of forest residues, herbaceous energy crops (e.g. switchgrass) and woody biomass (e.g. poplar), which is a promising second generation pathway. A pretreatment of the biomass is necessary so that it can be loaded into the gasifier. In the gasifier, the biomass suffers a thermal treatment into what is known as "syngas", composed mainly of H 2 and CO. Impurities are removed from the "syngas" during a gas cleaning step, due to the high sensibility of the Fischer-Tropsch (FT) reaction catalyst. The synthetic diesel is obtained after the upgrading (hydrocracking) of the products from the FT unit [START_REF] Cheng | Biomass to renewable energy processes[END_REF][START_REF] Hamelinck | Outlook for advanced biofuels[END_REF].

Biodiesel can be produced from conventional transesterification of oil extracted from microalgae that have a higher theoretical productivity per hectare than conventional vegetable oil crops (e.g. soybeans, palm). Microalgae can be cultivated in open ponds or photobioreactors (PBR) and the technologies for harvesting, drying and extracting oil still require considerable research effort. Various pathways are studied in order to reduce costs and energy consumption in the production process. The use of power plant flue gas as a CO 2 source for growing algae or wastewater as a source of nutrients are potential options for this biodiesel pathway [START_REF] Brennan | Biofuels from microalgae-A review of technologies for production, processing, and extractions of biofuels and co-products[END_REF][START_REF] Pienkos | The promise and challenges of microalgal-derived biofuels[END_REF].

Studies about hydrotreated vegetable oil (HVO) from the hydrogenation of microalgae oil were also included in this literature review. It has different characteristics than biodiesel but the most important life cycle steps involving microalgae growth, harvesting and oil extraction are the same. HVO, as well as BtL, are being studied as renewable alternatives not just for road transportation but also for the aviation industry. The "Cahiers de l'Économie" Series

Appendix B. Complements on the database

Index of tables

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