Cédric Decarpigny

Rudina Bleta
email: rudina.bleta@univ-artois.fr

Anne Ponchel

Eric Monflier

silica. The critical role of pore characteristics on the catalytic performance

Keywords: cyclodextrin, mesoporous silica, Stöber process, enzyme, biocatalysis, 2diformyfuran, 2, 5-furandicarboxylic acid

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Introduction

Enzymes are versatile biocatalysts produced by living cells and also rightly called the catalytic machinery of living systems as they are responsible for catalyzing a multitude of chemical reactions in a variety of biological processes [START_REF]Enzymes in the Environment. Activity, Ecology, and Applications[END_REF][START_REF] Prescher | Chemistry in living systems[END_REF]. For several decades, enzymes from microorganisms have occupied an important place in a range of industrial relevant processes such as wine fermentation [START_REF] Yoshizumi | Process for producing alcohol by fermentation without cooking[END_REF][START_REF] Claus | Enzymes for wine fermentation: Current and perspective applications[END_REF], cheese manufacture [START_REF] Fox | Enzymes in cheese technology[END_REF], glucose production from starch [START_REF] Kunamneni | Response surface optimization of enzymatic hydrolysis of maize starch for higher glucose production[END_REF], as well as detergent and textile industries [START_REF] Kirk | Industrial enzyme applications[END_REF]. Over the past few decades, the rapid progress in enzyme engineering has strongly encouraged chemical industries to embrace enzyme technology [START_REF] Van Beilen | Enzyme technology: an overview[END_REF], a trend supported by the current environmental issues [START_REF] Tournier | An engineered PET depolymerase to break down and recycle plastic bottles[END_REF] and the sustainable development goals [START_REF] Thomas | Designing catalysts for clean technology, green chemistry, and sustainable development[END_REF][START_REF] Scrutton | Enzymes make light work of hydrocarbon production[END_REF].

One of the major concerns in industrial application of enzymes is their limited operational stability with regard to reaction conditions, their high cost, as well as the difficulty in recovering and reusing the biocatalyst [START_REF] Sheldon | Enzyme immobilization: the quest for optimum performance[END_REF]. To overcome some of these limitations and make a balance between cost and benefits of enzyme applications, immobilization procedures in a solid support can be used [START_REF] Sheldon | Enzyme immobilization: the quest for optimum performance[END_REF][START_REF] Tran | Perspective of recent progress in immobilization of enzymes[END_REF][START_REF] Garcia-Galan | Potential of different enzyme immobilization strategies to improve enzyme performance[END_REF][START_REF] Hanefeld | Understanding enzyme immobilization[END_REF]. Several immobilization strategies have been proposed in literature, including the multipoint covalent attachment to increase enzyme rigidity [START_REF] Hernandez | Control of protein immobilization: Coupling immobilization and site-directed mutagenesis to improve biocatalyst or biosensor performance[END_REF], the multisubunit immobilization to reduce subunit dissociation [START_REF] Fernandez-Lafuente | Stabilization of multimeric enzymes: Strategies to prevent subunit dissociation[END_REF], the introduction of suitable functional groups to create a favorable surrounding microenvironment [START_REF] Li | Fabricating Covalent Organic Framework Capsules with Commodious Microenvironment for Enzymes[END_REF], or the confinement into the pores of the carrier to minimize protein aggregation [START_REF] Mateo | Improvement of enzyme activity, stability and selectivity via immobilization techniques[END_REF]. Nevertheless, in some cases, immobilization may also cause deactivation of the biocatalyst due to conformational changes of the surface bound enzyme with respect to its native state [START_REF] Secundo | Conformational Changes of Enzymes Upon Immobilization[END_REF]. In this sense, the design of supporting materials with adequate pore architecture that can provide sufficient free space to preserve conformational freedom of the protein and avoid blocking of the active site, while reducing enzyme leakage, is of fundamental importance for an efficient immobilization strategy.

Porous materials prepared by template-directed approaches have emerged as promising carriers for the immobilization of enzymes [START_REF] Hartmann | Immobilization of enzymes on porous silicas -benefits and challenges[END_REF][START_REF] Bayne | Effect of pore size on the performance of immobilized enzymes[END_REF][START_REF] Xiao | Constructing a Continuous Flow Bioreactor Based on a Hierarchically Porous Cellulose Monolith for Ultrafast and Nonstop Enzymatic Esterification/Transesterification[END_REF]. As demonstrated by several studies, pores not only improve the biochemical stability of the enzyme [START_REF] Gao | Monodisperse coreshell magnetic organosilica nanoflowers with radial wrinkle for lipase immobilization[END_REF], but they also have a relevant importance in the diffusion of reactants and products during the catalytic process [START_REF] Du | Enzyme nanocapsules armored by metal-organic frameworks: A novel approach for preparing nanobiocatalyst[END_REF]. Among the solid carriers, mesoporous silica has attracted much interest owing to its high thermal and pH stability, functionalizable surface, as well as ease of preparation [START_REF] Hartmann | Immobilization of enzymes on porous silicas -benefits and challenges[END_REF]. Soft-template methods using block copolymers with different geometries and block lengths as template, in combination or not with swelling agents (e.g., alkyl-substituted benzenes) [START_REF] Huang | Synthesis of ultralarge-pore FDU-12 silica with facecentered cubic structure[END_REF][START_REF] Fan | Low-temperature strategy to synthesize highly ordered mesoporous silicas with very large pores[END_REF], as well as the supramolecular assemblies formed between nonionic polymers and native cyclodextrins in water [START_REF] Bleta | Evidence for the existence of crosslinked crystalline domains within cyclodextrin-based supramolecular hydrogels through sol-gel replication[END_REF] have been shown to be particularly effective in a fine tuning of the pore size of silica.

Cyclodextrins (CDs) are water-soluble cyclic oligosaccharides with a toroidal shape composed of α-(1,4)-linked glucopyranose subunits. They possess an exterior hydrophilic surface covered by primary and secondary hydroxyl groups and an internal hydrophobic cavity containing CH2 groups, which make them particularly attractive for construction of supramolecular architectures through host-guest interactions [START_REF] Szejtli | Introduction and general overview of cyclodextrin chemistry[END_REF][START_REF] Breslow | Biomimetic reactions catalyzed by cyclodextrins and their derivatives[END_REF]. The most common CDs are alpha-, beta-and gamma-CDs having respectively six, seven and eight glucopyranose subunits in the ring and among them, β-CD has received the greatest attention due to its high binding affinity and cost effectiveness [START_REF] Szejtli | Introduction and general overview of cyclodextrin chemistry[END_REF][START_REF] Breslow | Biomimetic reactions catalyzed by cyclodextrins and their derivatives[END_REF]. Randomly methylated β-CD (RaMeβCD) is one of the most widely used β-CD derivatives with a degree of substitution of 12.6 and a particular molecular structure conferring to this CD surface-active properties and very high solubility in water (>500 mg/mL) (Figure S1, ESI).

Over the last two decades, CD-containing polymers and dendrimers, as well as metallic and metal oxide surfaces capped with terminal CD moieties have been widely utilized as supports for the supramolecular attachment of proteins by host-guest interactions [START_REF] Villalonga | Supramolecular Chemistry of Cyclodextrins in Enzyme Technology[END_REF][START_REF] David | Coupling of antibodies to β-cyclodextrincoated gold surfaces via an intermediate adamantyl-modified carboxymethylated dextran layer[END_REF][START_REF] Holzinger | Biotin-β-Cyclodextrin: A New Host-Guest System for the Immobilization of Biomolecules[END_REF]. In materials science, CDs have also been explored for the synthesis of silica nanostructures with various pore architectures [START_REF] Polarz | From cyclodextrin assemblies to porous materials by silica templating[END_REF][START_REF] Han | Cyclodextrin-based pseudopolyrotaxanes as templates for the generation of porous silica materials[END_REF][START_REF] Han | Towards porous silica materials via nanocasting of stable pseudopolyrotaxanes from alpha-cyclodextrin and polyamines[END_REF], but the practical applications of those materials are still limited. Our group has recently shown that these oligosaccharides may be employed efficiently as soft templates to direct the synthesis of hierarchically structured porous silica [START_REF] Bleta | Evidence for the existence of crosslinked crystalline domains within cyclodextrin-based supramolecular hydrogels through sol-gel replication[END_REF] and mesoporous metal oxides [START_REF] Bleta | Coassembly of block copolymer and randomly methylated β-cyclodextrin: From swollen micelles to mesoporous alumina with tunable pore size[END_REF][START_REF] Bleta | Understanding the role of cyclodextrins in the self-assembly, crystallinity, and porosity of titania nanostructures[END_REF] with enhanced activity in photocatalysis [START_REF] Lannoy | Cyclodextrin-directed synthesis of gold-modified TiO2 materials and evaluation of their photocatalytic activity in the removal of a pesticide from water: Effect of porosity and particle size[END_REF], heterogeneous catalysis [START_REF] Bleta | Robust mesoporous CoMo/γ-Al2O3 catalysts from cyclodextrin-based supramolecular assemblies for hydrothermal processing of microalgae: Effect of the preparation method[END_REF][START_REF] Bleta | Mesoporous RuO2/TiO2 composites prepared by cyclodextrin-assisted colloidal self-assembly: towards efficient catalysts for the hydrogenation of methyl oleate[END_REF] and biocatalysis [START_REF] Decarpigny | Confinement of Candida antarctica lipase B in a multifunctional cyclodextrin-derived silicified hydrogel and its application as enzymatic nanoreactors[END_REF].

Here, we report a simple and efficient RaMeβCD-modified Stöber approach for the fabrication in aqueous phase of mesoporous silica with tunable pore size and demonstrate its use as an efficient carrier for the immobilization of lipase B from Candida antarctica (CALB). Lipases (triacylglycerol acylhydrolases EC 3.1.1.3) are versatile biocatalysts catalyzing hydrolysis, esterification and transesterification reactions and are widely used in food, pharmaceutical, detergent and chemical industries [START_REF] Schmid | Lipases: interfacial enzymes with attractive applications[END_REF]. The catalytic activity of lipases is greatly enhanced at lipid/water interfaces by a phenomenon known as "interfacial activation". Hence, the active site of lipases is naturally covered by a polypeptide chain called "lid" and in the presence of a lipid/water interface, the lid opens exposing a large hydrophobic surface of the active site to the substrate. CALB is probably one of the most important lipases currently used in many industrial applications owing to its high selectivity towards secondary alcohols and secondary amines [START_REF] Basso | Industrial applications of immobilized enzymes -A review[END_REF][START_REF] Anderson | One biocatalyst-Many applications: The use of Candida antarctica lipase B in organic synthesis[END_REF], as well as its high resistance towards hydrogen peroxide [START_REF] Tzialla | Lipase immobilization on smectite nanoclays: characterization and application to the epoxidation of αpinene[END_REF][START_REF] Hernandez | Lipase B from Candida antarctica immobilized on octadecyl Sepabeads: A very stable biocatalyst in the presence of hydrogen peroxide[END_REF]. In this study, we evaluate the activity of immobilized CALB in the oxidation of 2,5-diformylfuran (DFF) to 2,5furandicarboxylic acid (FDCA), which is listed as one of the 12+2 most important biomassderived platform chemicals. FDCA has also been identified as a highly promising substituent for the terephtalic acid, the precursor of polyethylene terephthalate (PET) used in the production of plastic bottles, films and fibers [START_REF] Sheldon | Green and sustainable manufacture of chemicals from biomass: state of the art[END_REF][START_REF] Fei | Biobased poly(ethylene 2,5-furancoate): No longer an alternative, but an irreplaceable polyester in the polymer industry[END_REF]. The oxidation of DFF to FDCA proceeds via a chemoenzymatic cascade reaction involving two consecutive reaction steps [START_REF] Decarpigny | Confinement of Candida antarctica lipase B in a multifunctional cyclodextrin-derived silicified hydrogel and its application as enzymatic nanoreactors[END_REF][START_REF] Krystof | Lipase-mediated selective oxidation of furfural and 5-hydroxymethylfurfural[END_REF]. First, the lipase CALB catalyzes the reversible formation of peracetic acid from ethyl acetate and hydrogen peroxide. Then, the peracid generated in-situ oxidizes the aldehyde group of DFF to carboxylic acid yielding the 5-formylfuran-2-carboxylic acid (FFCA), which is ultimately converted to FDCA (Scheme 1). We show for the first time that CALB incorporated into the pores of a RaMeβCD-templated mesoporous silica prepared by a modified Stöber process may present enhanced catalytic activity and stability with respect to the lipase immobilized on the surface of CD-free silica particles. Scheme 1. Chemo-enzymatic selective oxidation of DFF to FDCA.

Results and discussion

Method for the preparation of the supported biocatalysts

Two types of silica particles with different sizes and pore diameters were prepared and further utilized as supports for the immobilization of CALB (Figure 1). In a first synthesis, bimodal sized particles with 6 nm and 75 nm mean diameters and two sets of pores (3.4 nm and 33 nm diameters) were prepared by conventional Stöber process in an alkaline medium using tetraethyl orthosilicate (TEOS) as silica source. In a second synthesis, RaMeβCD was employed as structure directing agent yielding 8 nm-sized particles with uniform 11.2 nm-sized pore diameters and almost twice higher pore volume. DLS results revealed formation of large aggregates of RaMeβCD with 106 nm hydrodynamic radius (RH) coexisting with non-associated oligosaccharides (RH = 0.95 nm) (Figure S5, ESI). On the other hand, the surface tension measurements indicated a decrease in the surface tension of water from 72 mN/m to 58.4 mN/m at 20 mM RaMeβCD reflecting the surface-active properties of this cyclodextrin which would be beneficial for the self-assembly of silica particles (Figure S6, ESI). In both syntheses, silica surface was further modified with glutaraldehyde (GAH)-activated amine groups derived from the 3-aminopropyltrimethoxysilane (APTMS) used for the covalent anchoring of the lipase, as well as hydrophobic trimethyl groups derived from the chlorotrimethylsilane (CTMS), necessary for its interfacial activation. Based on the study of Monsan 51 who has proposed a glutaraldehyde reaction mechanism involving two molecules of GAH per amino group in Spherosil silica at pH 7, the amount of GAH used in our study was in excess to that required for activation (GAH/APTMS molar ratio = 6.7). The excess of GAH was then washed off before enzyme coupling. The catalytic performance of the immobilized lipase was then evaluated in the oxidation of 2,5-diformylfuran (DFF) to 2,5-furandicarboxylic acid (FDCA) and was correlated to the pore characteristics of the supports.

Characterization of the supports.

TG-DSC analysis in flowing air were performed to estimate the amount of cyclodextrin incorporated within the silica matrix (Figure S7, ESI). To minimize the effect of solvent adsorbed into the pores, the weight loss below 180 °C was not taken into consideration.

In the temperature range between 180 and 700 °C, the template-free sol-gel SiO2 (Figure S7 A, ESI) displayed a total weight loss of 6.5 wt.% corresponding mainly to polycondensation and dehydration reactions [START_REF] Ayral | Skeletal density of silica aerogels determined by helium pycnometry[END_REF]. The exothermic peak at 360 °C assigned to the oxidation of the ethoxy groups [START_REF] Kondo | The surface structure of ethoxylated silica gel[END_REF] indicates that TEOS is not completely hydrolyzed and residual -OCH2CH3 groups still remain on the particle surface. In comparison, the RaMeβCD-templated material (Figure S7 B,ESI) displayed an additional exothermic peak at 470 °C, which may be assigned to the decomposition of the oligosaccharide. The weight loss recorded in the temperature range of 180-700°C was 8.7 % and the remaining amount of cyclodextrin, calculated by the difference between the mass loss of RaMeβCD-SiO2 minus the mass loss of SiO2, was estimated to be 2.2%.

The adsorption isotherms and corresponding pore size distributions of SiO2 and RaMeβCD-SiO2 materials are depicted in Figure 2. Both isotherms present an hysteresis loop once a threshold relative pressure is reached, highlighting the presence of mesopores (Figure 2 A). At low relative pressures (P/P0 < 0.4), the amount of nitrogen adsorbed is almost identical in both materials indicating similar surface areas; however at higher relative pressures (P/P0 > 0.4), the rapid increase of the N2 uptake recorded on RaMeβCD-SiO2 solid points out an enhancement of the pore volume. Indeed, the BET surface areas (SBET) were measured to be 450 and 432 m 2 /g for SiO2 and RaMeβCD-SiO2 respectively, whereas the total pore volume (Vp) was almost doubled, from 0.487 to 0.969 cm 3 /g, when RaMeβCD was used as structure directing agent (Table 1).

The pore size distribution curves determined from the BJH method further illustrate the contrasting pore characteristics of these two solids (Figure 2 B). Indeed, the SiO2 material showed a broader and less well-defined pore size distribution with two types of mesopores of approximately 3.4 nm and 33 nm diameters (Figure 2 B inset). Macropores were also present, as revealed by the continuous increase of the adsorbed volume at high relative pressures (P/P0 ≈ 1).

In a quite different way, the material prepared from RaMeβCD exhibited a sharper pore condensation step, indicative of pores with uniform diameters. Accordingly, the pore size distributions of RaMeβCD-SiO2 were unimodal with an average pore diameter of 11.2 nm, occupying a much larger pore volume with respect to SiO2. The micropore volumes obtained from the t-plot represented 6.2% and 1.8% of the total pore volume of SiO2 and RaMeβCD-SiO2 respectively (Table 1). TEM images revealed that the SiO2 material was composed of round-shape particles with an average diameter of 75 nm decorated on their surface with small-sized particles of approximately 6 nm diameter (Figure 3 A). Mesopores were build-up by primary particles, while macropores resulted from the packing of primary particles in agglomerates. Conversely, the RaMeβCD-SiO2 From the small angle X-ray scattering diagrams (Figure S8, ESI), it can be seen that the RaMeβCD-SiO2 solid displayed a well-defined correlation peak at 2Ө = 1.62° corresponding to a d-spacing of 2.7 nm (dBragg = nλ/2sinθ). This means that some local organization of the mesopores exists within the silica network although the absence of high order peaks suggests a lack of overall long-range ordering. Moreover, the shift of the diagram of RaMeβCD-SiO2 to higher 2Ө values with respect to SiO2 is consistent with a decrease in the interparticular separation, in agreement with TEM observations. Taken together, these characterization results confirm that RaMeβCD plays an important role in improving both the structural and textural characteristics of the silica particles, which in turn can affect the activity and stability of the enzyme.

Silanization of the support and enzyme immobilization.

Prior to lipase grafting, the assynthesized silica particles were modified with hydrophobic trimethyl groups derived from the chlorotrimethylsilane (CTMS) and chemically reactive amine groups derived from the 3aminopropyltrimethoxysilane (APTMS). Functionalization with APTES was followed by activation of aminated silica support with a bifunctional spacer, i.e. the glutaraldehyde (GAH), which provides an aldehyde group that reacts with the amino groups of lysine residues, resulting in the formation of an imine bond (Schiff base). To identify the different functional groups anchored on the silica surface, attenuated total reflectance Fourier transform infrared spectroscopy (ATR-FTIR) and thermogravimetric (TG) analyses were carried out.

ATR-FTIR spectra of non-functionalized SiO2 and RaMeβCD-SiO2 (Figure 4 A-a, B-a) displayed two intense bands at 1061 and 800 cm -1 ascribed to the asymmetric and the symmetric stretching vibrations respectively of the Si-O-Si bond [START_REF] Vansant | Characterization and chemical modification of the silica surface[END_REF]. Upon surface modification, the attenuation of the vibration band at 959 cm -1 arising from the symmetric stretching of the Si-OH groups confirmed successful functionalization of surface silanols. Indeed, the strong vibration bands at 1566 cm -1 and 1417 cm -1 are consistent with the N-H bending of the primary amine and the symmetric CH2 bending of Si-CH2 groups respectively ((Figure 4 A-b, B-b). Furthermore, the Si-C stretching vibration at 856 cm -1 from the -O-SiCH3 end groups is indicative of effective surface functionalization with trimethylsilyl groups. The covalent anchoring of the enzyme on SiO2@CAG and RaMeβCD-SiO2@CAG supports was confirmed by the vibration band at 1640 cm -1 characteristic of the imine bond (C=N) resulting from the interaction between the aldehyde groups of the glutaraldehyde and the primary amine groups of the lysine ((Figure 4 A-c, B-c).

Moreover, the increase in the intensity of the vibration at 1566 cm -1 corresponding to the N-H bending of free amines is another indication of successful protein grafting. It is worth noting that as the immobilization of lipase was carried out at pH 4.6, that is in the interval between the isoelectric point of CALB (pI = 6.0) and the point of zero charge of silica (PZC = 2.0), ionic binding and hydrophobic interactions are also likely to occur, therefore facilitating the rapprochement of lipase to the activated support before its covalent attachment.

The amount of functional groups anchored on the silica surface was estimated from the thermogravimetric analysis by the difference between the mass loss of the functionalized matrix minus the mass loss of the bare matrix in the temperature range between 180 °C and 700 °C (Figure S9 ESI). The loadings of surface functional groups measured on SiO2@CAG (Figure S9 A,b ESI) and RaMeβCD-SiO2@CAG (Figure S9 1). Nevertheless, RaMeβCD-SiO2 solid exhibited a higher grafting density of trimethyl groups compared to SiO2 (60 mg/g vs. 38 mg/g), but presented a lower weight loss in the temperature range of 40-180°C (26 mg/g vs. 57 mg/g) consistent with its higher degree of hydrophobicity (Figure S10, Table S1, ESI). Using equation 1 (ESI), the corresponding surface coverages (Scov) were determined to be 0.66 chain/nm 2 and 1.02 chain/nm 2 for SiO2@C and RaMeβCD-SiO2@C respectively. Considering that organosilanes form a monolayer on the silica surface and that each trimethyl ligand occupies a surface of 0.43 nm 2 , the maximum grafting densities (Dg max ) for SiO2@C and RaMeβCD-SiO2@C were determined to be 189 mg/g and 181 mg/g respectively (equation 2, ESI). As can be noted, the grafting densities determined from TG analysis are much lower than those estimated from the surface areas, suggesting that the surface of silica particles can be only partially covered by the hydrophobic trimethyl groups. a BET specific surface area determined in the relative pressure range 0.1-0.25, b cumulative pore volume (BJH), c pore diameter calculated from BJH method, d % micropores = (Vmicro/VP)*100 where Vmicro is the micropore volume determined from the t-plot, e weight loss between 180 and 700 °C, f weight loss corrected by the decomposition profile of sol-gel silica before surface functionalization.

Despite their different pore characteristics, these two materials presented were very similar enzyme loading capacities i.e. 6.4 wt.% for SiO2 and 7.4 wt.% for RaMeβCD-SiO2 (Figure S9 ESI, Table 1). However, notable differences were evidenced on the location of the protein, which was found either to bind on the surface of SiO2@CAG particles or to be incorporated within the pore structure of RaMeβCD-SiO2@CAG. Indeed, as revealed by N2-adsorption analysis (Figure 5), the surface area of SiO2 decreased drastically from 450 m 2 /g to 39 m 2 /g upon grafting of trimethyl and aminopropyl groups and further activation with glutaraldehyde. Similarly, the pore volume was also reduced by almost one-third (from 0.487 to 0.178 cm 3 /g) (Table 1), while the smallest pores at 3.4 nm totally disappeared. This suggests that the distribution of grafted amino groups is most likely non-uniform, leading to pore blocking effects that result from the preferential reaction of these groups with the exposed surface of the small particles decorating the larger ones. Similar observations were made previously by Ritter et al. [START_REF] Ritter | Accessibility of amino groups in postsynthetically modified mesoporous silica[END_REF] that led to conclusion that the small pore diameters facilitate the pore blockage upon functionalization with APTMS due to the preferential location of amino groups at the pore entrances. However, in our bimodal material, we also noticed a broadening of the pore size distributions related to the largest mesopores, indicating that some silanes could also be located at the surface of particles [START_REF] Reber | Mesoporous hybrid materials by simultaneous pseudomorphic transformation and functionalization of silica microspheres[END_REF]. A similar trend on the evolution of pore size distributions was observed upon lipase immobilization, suggesting higher grafting density of the protein at the outer surface of the carrier. On the other hand, the RaMeβCD-SiO2@CAG support displayed a different behavior with regard to the binding of CALB, showing a progressive decrease in the pore diameter and pore volume indicative of the filling of pores with the functional groups and the protein (Figure 5 D, Table 1). Such changes are consistent with the higher pore accessibility of this material and its more uniform internal pore structure, in agreement also with TEM observations (Figure 3). Moreover, it is worth noting that the porosity and pore size distributions of our materials are measured under dried conditions, which usually involve contraction of the pore space, thus underestimating the pore diameter of silica in water.

Although the pore size cannot be fairly compared with the real dimensions of the enzyme, it is assumed that the hydrated surface of silica under immobilization conditions could further facilitate the diffusion of the protein through the silica framework due to the expansion of its pore structure in water.

Confocal laser scanning microscopy observations provided further evidence for the different spatial distribution of the enzyme within the two supports (Figure S11, ESI). Thus, a diffuse fluorescence of relatively high intensity, localized mainly on the particle surface, was obtained upon illuminating the FITC-labelled CALB immobilized on CD-free SiO2. Several large asymmetric fluorescent spots were present all over the sample, which are probably derived from inter-protein interactions on the surface of the densely packed fractal aggregates. In contrast, RaMeβCD-SiO2 displayed more homogeneous fluorescence signal and the bright luminescent spots observed in this sample were smaller and appeared more regular in size and shape, consistent with a higher degree of uniformity in the distribution of enzyme within the particles.

Catalytic activity.

In our experiments, the oxidation of DFF to FDCA was assessed by adding 2.0 equivalents of aqueous H2O2 (30% v/v) in a mixture of ethyl acetate (EtOAc) and tertbutanol (tBuOH) (1:1 v/v) containing 10 mM DFF.

As expected from our characterization results, the overall activity of the immobilized lipase was dependent on the immobilization procedure and the type of support (Table 2). Indeed, while the free lipase was inactive after 7 hours of reaction at 40 °C (entry 1), the DFF conversion reached 87% when 2 mg CALB was grafted on the surface of SiO2@CAG particles (entry 2). However, the FDCA yields were still low (29%), FFCA being the major product (58%). The specific activity achieved was 14.4 µmol g -1 min -1 , while the total turnover number (TTN) accumulated after 7 hours of reaction was 199 mol mol -1 , corresponding to a turnover frequency (TOF) of 0.475 min -1 . Interestingly, full conversion of DFF was achieved with the RaMeβCD-SiO2@CAG@CALB biocatalyst under the same reaction conditions, which resulted in more than 2-fold increase in the FDCA yield (69%, entry 3). Similarly, the specific activity, TTN and TOF were almost 2.4 times higher than those obtained with SiO2@CAG@CALB. Nevertheless, upon increasing the reaction time to 24 hours, both biocatalysts gave total DFF conversion with quantitative FDCA yields (>99%), resulting in accumulated TTN higher than 660 (entries 4, 5).

It is worth noting that the activities obtained with our catalysts were higher than those reported in previous research with the commercial Novozym 435 [START_REF] Qin | Enzyme-catalyzed selective oxidation of 5-hydroxymethylfurfural (HMF) and separation of HMF and 2, 5-diformylfuran using deep eutectic solvents[END_REF], where the maximum FDCA yield that could be obtained after 24 hours reaction was 88%, corresponding to a TTN of 293.

For comparison, the activity of CALB adsorbed on RaMeβCD-SiO2@C or grafted on RaMeβCD-SiO2@AG was also evaluated. Under identical reaction conditions, RaMeβCD-SiO2@C@CALB was not active (entry 6), while a DFF conversion of 63% was achieved with RaMeβCD-SiO2@AG@CALB without any formation of FDCA (entry 7). This result confirms that although the hydrophobic interactions with the trimethyl groups from CTMS are not strong enough to maintain the protein anchored to the support, the hydrophobic microenvironment that these groups create is crucial for the interfacial activation of the lipase [START_REF] José | Influence of the nature of the support on the catalytic performance of CALB: experimental and theoretical evidence[END_REF]. Indeed, as shown by Manoel et al. [START_REF] Manoel | Immobilization of lipases on hydrophobic supports involves the open form of the enzyme[END_REF] immobilization on hydrophobic surfaces implies the open form of the lipase. It is well known that CALB does not have a lid domain, but presents an interfacial hyperactivation upon contact with hydrophobic surfaces, exposing its active site towards the substrate [START_REF] Zisis | Interfacial activation of Candida antarctica lipase B: Combined evidence from experiment and simulation[END_REF]. On the basis of our previous findings [START_REF] Decarpigny | Confinement of Candida antarctica lipase B in a multifunctional cyclodextrin-derived silicified hydrogel and its application as enzymatic nanoreactors[END_REF], the CTMS/SiO2 molar ratio was fixed at 0.3. Increasing or reducing the CTMS/SiO2 ratios caused a decrease in the FDCA yield due to denaturation of lipases in highly hydrophobic surfaces and strong water-surface interactions on hydrophilic ones that tend to shield the protein, causing its desorption [START_REF] Firkowska-Boden | Controlling protein adsorption through nanostructured polymeric surfaces[END_REF]. 3(see experimental part ESI), c CTMS/SiO2 molar ratio = 0.33, APTMS/SiO2 molar ratio = 0.17 and GAH/APTMS molar ratio = 1.1, d 2 mg CALB in 20 mg support (1.33 mg/mL CALB in the immobilization solution), e reaction time = 24 hours, f specific activity was calculated as µmol of product formed (two µmol peracid per µmol of FDCA) per g of protein in one minute, g TTN = moles of FDCA formed divided by moles of protein, h TOF = TTN divided by reaction time.

To evaluate the recyclability of the two biocatalysts, 10 mM DFF was incubated in the EtOAc/t-BuOH (1:1 v/v) mixture for oxidation at 40 °C for 24 hours for each reaction cycle. The immobilized lipase was collected by centrifugation after each cycle, rinsed three times with the EtOAc/tBuOH (1:1, v/v) mixture and subsequently dried under vacuum before being reused for the next reaction cycles.

As shown previously [START_REF] Karich | Enzymatic preparation of 2,5furandicarboxylic acid (FDCA)-A substitute of terephthalic acid by the joined action of three fungal enzymes[END_REF], the furanic compounds formed during this reaction are likely to create pH-gradients in the immediate vicinity of the lipase due to the carboxylic acid groups that they bear in their cycle, provoking a complete inhibition of the enzyme activity. Moreover, under acidic conditions, protein leakage could also occur due to the very favorable hydrolysis of the Schiff base. Indeed, after the first reaction cycle, the FTIR spectra indicated a reduction in the intensity of the imine vibration at 1640 cm -1 for the RaMeβCD-SiO2@CAG@CALB catalyst and total disappearance of this band for the SiO2@CAG@CALB one (Figure S12 ESI). However, although the levels of enzyme leakage were different, complete deactivation of the lipase occurred in both systems due to the drop of the pH below 3.0.

To circumvent those limitations, a shell of a pH-sensitive polymer, the poly(4-vinylpyridine) (P4VP), was deposited on the biocatalyst surface. P4VP has a pKa equal to 4.5 and can interact with the functional groups available on the protein surface through its pyridine units. When the pH of the reaction mixture decreases below 4.5, P4VP undergoes protonation, causing swelling of the polymer chain and a reduction of the pH-gradient created near the biocatalyst surface [START_REF] Wang | A general method to determine ionization constants of responsive polymer thin films[END_REF][START_REF] Nie | One-pot synthesis of amphiphilic polymeric Janus particles and their self-assembly into supermicelles with a narrow size distribution[END_REF]. Therefore, to some extent, the polymer shell acts as a solid buffer protecting the lipase from denaturation [START_REF] Virgen-Ortiz | Polyethylenimine: a very useful ionic polymer in the design of immobilized enzyme biocatalysts[END_REF].

With 20 wt.% surface coverage of P4VP, the activities obtained with both biocatalysts across five consecutive runs are shown in Figure 6. Whilst SiO2@CAG@CALB caused the DFF conversion to drop by approximately one half (52%), almost full conversion (>90%) was achieved with RaMeβCD-SiO2@CAG@CALB, which exhibited also higher selectivity for the FDCA formation. Thus, the FDCA yield was almost quantitative (> 99%) in the first two cycles, but it decreased to 72% after the third cycle, FFCA being the only intermediate (28%). In the last two cycles, FDCA was present as approximately 39% of the reaction mixture, while the yield obtained with the SiO2@CAG@CALB biocatalyst was twice lower (19%). The rapid decrease in the FDCA yield from the third cycle can be related to the loss of the smallest particles along successive rinsing steps that caused a decrease in the amount of enzyme remaining in the reaction mixture. Indeed, after the fifth cycle, we were able to recover only 30% of the initial amount of solid (6.4 mg vs. 20.2 mg). However, the rinsing solution was able to catalyze efficiently the DFF oxidation giving 100% conversion. This is an indication that the enzyme was held tightly on the surface of functionalized silica particles and was not released into the rinsing solution. Further work in this direction is still necessary to reduce losses of fine particles and improve the biocatalyst separation efficiency.

Taken together, our results indicate that incorporation of CALB within the pores of the RaMeβCD-templated matrix followed by subsequent deposition of a poly(4-vinylpyridine) shell appears as a promising tool to bypass problems associated with lipase degradation under acidic conditions. Moreover, owing to its peculiar physicochemical properties (Figure S6 ESI), the methylated cyclodextrin may also provide a benign surrounding microenvironment for the protein. Thus, its high degree of hydrophobicity may contribute to the interfacial activation of CALB and its unique surface-active properties may be beneficial for reducing the steric constraints, maintaining the immobilized lipase in a flexible conformation [START_REF] Griebenow | Improved enzyme activity and enantioselectivity in organic solvents by methyl-β-cyclodextrin[END_REF][START_REF] Mine | Enhanced enzyme activity and enantioselectivity of lipases in organic solvents by crown ethers and cyclodextrins[END_REF]. Figure 6. Catalytic recyclability of SiO2@CAG@CALB@P4VP (A) and RaMeβCD-SiO2@CAG@CALB@P4VP (B) biocatalysts. Reaction conditions: 10 mM DFF, 2 mL EtOAc/tBuOH (1:1 v/v), sequential addition of 2.0 eq. H2O2 (30% v/v) every hour for seven hours, temperature 40°C, reaction time 24 hours.

Conclusions

In summary, we have prepared and characterized two types of silica particles -one by conventional Stöber process in alkaline medium using the tetraethyl orthosilicate (TEOS) as silica source and the other by a modified Stöber process using the randomly methylated βcyclodextrin (RaMeβCD) as structure directing agent. The first material consisted of 75-nm sized particles decorated on their surface with 6-nm sized nanoparticles and presented a bimodal pore size distribution with average pore diameters of 3.4 nm and 33 nm. Differently, the second material was composed of unimodal 8 nm-sized particles showing 11.2 nm-sized mesopores and a pore volume that was twice as high as that of the CD-free material (0.969 cm 3 /g vs. 0.487 cm 3 /g). In both syntheses, lipase B from Candida antarctica (CALB) was immobilized on the pre-functionalized supports by covalent bonding. Results revealed differences on the location of the enzyme, which was found either to anchor on the outer peripheral surface of CD-free particles or to be incorporated inside the pores of RaMeβCD-templated material. The catalytic activity of the immobilized biocatalysts was then evaluated in the oxidation of 2,5-diformylfuran (DFF) to 2,5-furandicarboxylic acid (FDCA). While the free enzyme was not active under the employed reaction conditions, interfacial activation was observed upon immobilizing lipase on the functionalized supports. Incorporation of CALB into the pores of RaMeβCD-templated material resulted in enhanced enzyme properties as compared to immobilization on surface. Thus, full DFF conversion was achieved after 7h at 40°C and the FDCA yields were two-fold higher with respect to the reference catalyst. Notably, CALB incorporated into the pores could be recycled five times, retaining more than 90% of its initial activity compared to 52% activity for the surface-bound lipase. This work can provide useful insights into the design of cyclodextrin-

Figure 1 .

 1 Figure 1. Schematic illustration of the immobilization of CALB on silica particles prepared by

Figure 2 .

 2 Figure 2. N2-adsorption isotherms (A) and corresponding pore size distributions (B) of SiO2

  (w) Pore Volume (cm³/g•Å)Pore width (nm) (w) Pore Volume (cm³/g•Å) P ore wid th (nm )3.4 nm33 nm a material consisted mainly of small-sized particles with uniform 8 nm diameter assembled in a sponge-like porous network (Figure3 B). The white areas in the TEM micrographs are representative of mesopores originating from the interstitial spaces between primary particles.

Figure 3 .

 3 Figure 3. TEM images and corresponding particle size distribution of SiO2 (A) and

Figure 4 .

 4 Figure 4. ATR-FTIR spectra of silica supports prepared without (A) and with RaMeβCD (B):

Figure 5 .

 5 Figure 5. N2 adsorption isotherms and corresponding pore size distributions of functionalized

  B,b ESI) were almost equal, i.e. 22.3 wt% and 22.2 wt% respectively, because both supports have nearly the same surface area, i.e. 450 m 2 /g and 432 m 2 /g respectively (Table

Table 1 .

 1 Parameters deduced from N2-adsorption and TG analysis for the silica materials before and after modification with different functional groups and lipase immobilization.

			N2-adsorption		TG analysis
	Sample	SBET a (m 2 .g -1 )	Vp b (cm 3 .g -1 )	Dp c (nm)	% µpore d	total weight loss (%) e	effective weight loss (w%) f
	SiO2	450	0.487	3.4 and 33	6.2	6.5	-
	RaMeβCD-SiO2	432	0.969	11.2	1.8	8.7	2.2
	SiO2@CAG	39	0.178	39	0.2	28.8	22.3
	RaMeβCD-SiO2@CAG	278	0.628	8.1	4.8	30.9	22.2
	SiO2@CAG@CALB	17	0.246	45	0.3	35.5	6.7
	RaMeβCD-SiO2@CAG@CALB	212	0.474	6.5	4.1	38.3	7.4

Table 2 .

 2 Catalytic performance of immobilized lipase CALB in the oxidation of DFF to FDCA. a

	Entry	Catalyst	Enzyme loading (mg)	Immobilization efficiency (%) b	DFF conversion (%)	Yield (%) FFCA FDCA (%) (%)	Specific activity (µmol g -1 min -1 ) f	TTN (mol mol -1 ) g	TOF (min -1 ) h
	1	Free CALB-7h	-	-	0	0	0	0	0	0
	2	SiO2@CAG c @CALB d -7h	1.92	96	87	58	29	14.4	199.4	0.475
	3	RaMeβCD-SiO2@CAG@CALB-7h	1.98	99	100	31	69	33.2	460.0	1.095
	4	SiO2@CAG@CALB-24h e	1.92	96	100	<1	>99	>49.1	>680.6	>1.621
	5	RaMeβCD-SiO2@CAG@CALB-24h	1.98	99	100	<1	>99	>47.6	>660.6	>1.571
	6	RaMeβCD-SiO2@C@CALB-7h	1.38	69	0	0	0	0.0	0.0	0.000
	7	RaMeβCD-SiO2@AG@CALB-7h	1.74	87	63	63	0	0.0	0.0	0.000
	a Reaction conditions: 10 mM DFF, 2 mL EtOAc/tBuOH (1:1, v/v), sequential addition of 2.0 equivalents aqueous H2O2 (30% v/v)
	every hour for seven hours, temperature 40 °C, reaction time 7 hours, b Calculated from Equation

Acknowledgments

Chevreul Institute (FR 2638), Ministère de l'Enseignement Supérieur, de la Recherche et de l'Innovation and FEDER are acknowledged for supporting and funding this work. C.D. is grateful to the Région Hauts-de-France and the University of Artois who funded his PhD grant.

We thank Dr E. Richard for access to Confocal Laser Scanning Microscope and technical advices, as well as the Research Federation FRABio (Univ. Lille, CNRS, FR 3688) for providing the scientific and technical environment conducive to achieving this work. We are grateful to D. Prevost, J. Ternel, A. Addad and L. Burylo for technical assistance with the reactor setup, NMR, TEM and SAXS respectively, as well as N. Kania for help with HPLC and TG analyses. The TEM facility in Lille is supported by the Conseil Regional des Hauts-de-France and the European Regional Development Fund (ERDF).

based materials for efficient immobilization of other lipases and improvement of their functionality.


Dionisis Philippas
email: dionisis.philippas@essca.fr.

Catalin Dragomirescu-Gaina
email: catalinflorinel.dragomirescugaina@unicatt.it.

Emilios Galariotis
email: egalariotis@audencia.com.

Chasing the 'green bandwagon' in times of uncertainty

Keywords: dynamic herding, pricing dynamics, green energy, crude oil. JEL classification: C24, G14, G15, Q40

la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

An increasing number of institutional investors are divesting1 from fossil fuel stocks and shifting billions of dollars into alternative assets belonging to a new sector, which claims to promote a green (i.e. environmental-friendly) investment agenda (Kaminker and Steward, 2012). Attracted by the allure of wide media coverage, many smaller investors are jumping onto this same bandwagon for fear of missing out on an investment opportunity that seems to align better with the ongoing shifts in social preferences [START_REF] Bassen | Climate information in retail investors' decision-making: Evidence from a choice experiment[END_REF]. According to Morningstar, net inflows into the sustainable sector during 2019 stand at USD 20.6 bn., which is nearly four times the USD 5.5 bn. record that was registered for the previous year. 2 A trending market can enable investors to gain more from trading rather than from acting on their private information signals, particularly when prices do not efficiently incorporate all available information. This raises the probability of information cascades, speculative bubbles and herding behaviour [START_REF] Cipriani | Herd behavior and contagion in financial markets[END_REF]. In mid-2000, a trending market in German renewable energy stocks led to speculative patterns, which only worked to amplify the market collapse after a shift in government policies [START_REF] Bohl | From hero to zero: Evidence of performance reversal and speculative bubbles in German renewable energy stocks[END_REF]. Because herding is usually associated with information frictions and volatility spikes, its impact on financial markets and prices can be substantial and persistent [START_REF] Dasgupta | Institutional trade persistence and long-term equity returns[END_REF][START_REF] Schmitt | Herding behaviour and volatility clustering in financial markets[END_REF].

Energy markets are currently lying at the crossroads between operating with an old technology that relies heavily on fossil fuels, and embracing a new, greener one. As with every technological transition, this implies higher levels of risk as well as uncertainty, so investors face bigger challenges regarding their strategic portfolio allocations to different energy asset classes. 3Our aim here is to analyse changes in investors' group behaviour with respect to U.S. energy equities on the back of the ongoing greening in investment preferences, whose shifts can contribute to large market fluctuations, especially when reacting to changes in policies, social attitudes, or information sets. Consequently, we outline policy directions that might help investors in energy equities to navigate through wide swings in uncertainty and overcome the existing information barriers that characterise green energy investing today.

Given the growing hype around climate change topics, investors considering green asset allocations should account for potential price distortions that are known to arise in markets characterised by informational frictions and barriers. In the case of green investing, access to relevant information is often costly or limited due to the high uncertainty surrounding the longterm economic viability prospects of many green technologies (Kaminker and Steward, 2012).

As long as this type of uncertainty prevails, investing in an old technology (i.e. oil-dependent assets) can be regarded as less risky4 than investing in a new (i.e. green) technology. This happens because information frictions increase uncertainty that delays the necessary learning process of identifying the most profitable market opportunities evaluated in risk-adjusted terms.

A different but equally important type of uncertainty arises from regulations and government policies that greatly impact on the innovation process on which the economic success of these new (particularly green) technologies depends upon. Where public financial institutions invest in higher risk technologies, they create a direction for change that can help reducing this uncertainty [START_REF] Mazzucato | Public financing of innovation: new questions[END_REF]2018). Wustenhagen and Menichetti (2012), [START_REF] Andersson | Hedging climate risk[END_REF], and [START_REF] Pliousis | A multicriteria assessment approach to the energy trilemma[END_REF] discuss in detail how changes in various government policies and regulations affect the trade-offs associated with investing in the green energy sector.

Our broader approach on uncertainty allows us to disentangle between drivers of changes in behaviour (i.e. social learning) originating from asset-specific sources. With different motivations to hold different assets, changes in information type, availability and cost can have a great impact on investors' behaviour. Green assets are considered for portfolio diversification motives (Miralles-Quiros and Miralles-Quiros, 2019) and as a way to attract more client inflows.

Different motives apply to crude oil portfolio allocations, particularly in the current social context in which awareness on social, environmental and governance (ESG) criteria and climate change have increased substantially. 5 Crude oil allocations serve investors in other ways, and thus can affect their behaviour for different reasons. For example, [START_REF] Andersson | Hedging climate risk[END_REF], [START_REF] Batten | Addressing COP21 using a stock and oil market integration index[END_REF] and [START_REF] Engle | Hedging climate change news[END_REF] suggest risk management techniques to hedge climate-related risks with allocations to crude oil, along with (global) stocks. For [START_REF] Chkili | Instabilities in the relationships and hedging strategies between crude oil and US stock markets: do long memory and asymmetry matter?[END_REF] and [START_REF] Omar | Diversifying away the risk of war and crossborder political crisis[END_REF], crude oil can serve as a hedge against uncertainty stemming from the (geo-)political realm.

With no certainty regarding the long-term prospects of the new green technologies and 5 Much of the current hype in green investing seems to be driven by the idea that renewable assets can be a substitute for fossils, neglecting therefore any possible technologic complementarity (e.g. due to an intermittent provision of energy from some renewable sources). Yet, neglecting only adds to the information noise that investors must deal with in their investment decisions. [START_REF] Bassen | Climate information in retail investors' decision-making: Evidence from a choice experiment[END_REF] provide experimental evidence on how presentation format and climate label designs can nudge retail investors into more climate-friendly investments. We thank an anonymous reviewer for pointing to us the importance of complementarity between the two technologies. without a coherent global policy response (to which the United States withdrawal from the Paris climate accord is the latest proof), the efficiency of the financial markets remains key to directing our society's responses to climate-related challenges (Kaminker and Steward, 2012). We frame this problem from the perspective of investors in energy equity markets, for whom market efficiency represents a first-order concern. The danger is that investors' own behavioural biases interact with this multidimensional uncertainty, complicating the social learning process and raising market volatility that further obscures price discovery [START_REF] Avery | Multidimensional uncertainty and herd behavior in financial markets[END_REF]. 6 Within a market environment characterised by costly or limited information and constant regulatory challenges, this multidimensional uncertainty affects investors' allocations to U.S. energy equities. But what type of new information do investors trading in energy equity markets need to learn before they can abandon an established investment strategy into oil-dependent assets and start chasing for newer, greener opportunities? Herding 7 arises when individuals choose to suppress their own private information and instead mimic the actions of others [START_REF] Bikhchandani | A theory of fads, fashion, custom, and cultural change as informational cascades[END_REF]. This change in behaviour, implying social learning, can lead to higher market volatility, deviations of prices from their fundamental values, and thereby asset booms and busts [START_REF] Avery | Multidimensional uncertainty and herd behavior in financial markets[END_REF][START_REF] Schmitt | Herding behaviour and volatility clustering in financial markets[END_REF]. Our set of energy equities belongs to some of the biggest oil and gas companies, not only in U.S., but globally (e.g. 6 Avery and Zemsky (1998) discuss financial investors' herding behaviour in relation with three main types of uncertainty. The first type refers to price signals that bring in value uncertainty but do not foster herding behaviour.

The second type refers to event uncertainty, which makes herding possible but is also supportive for price discovery.

The third type, the proportion of informed versus uninformed investors, denotes composition uncertainty, which works by incentivising herding behaviour that obscures rather than supports price discovery. 7 A 2015 survey conducted by the CFA Institute amongst professional portfolio managers places herding on top of a list featuring several behavioural biases that can affect market outcomes.

Source: https://blogs.cfainstitute.org/investor/2015/08/06/the-herding-mentality-behavioral-finance-and-investorbiases.

Chevron, Exxon Mobil, ConocoPhillips), so the market implications of mispricing are potentially large. Some of these companies are already positioning themselves as leaders in the transition towards greener energy sources [START_REF] Pickl | The renewable energy strategies of oil majors-From oil to energy?[END_REF], but investors can be faster in shifting their desired portfolio allocations towards greener assets. Although we focus exclusively on financial investors' behaviour, herding is an overarching phenomenon with substantial consequences on various energy market segments. 8 Our empirical results show evidence that investors as a group herd more in response to positive shocks in crude oil returns but not to shocks in crude oil volatility. Therefore, investing in an old technology requires little besides information on its returns. In contrast, investors in energy equity markets herd less in response to positive green volatility shocks but not to shocks in green returns. Therefore, opting for a newer technology requires a better information set. To some extent, one can interpret this difference in responses along the narrow line separating rational from irrational herding, particularly when investors face structural market (or policy) changes that can trigger sizable portfolio reallocations [START_REF] Devenow | Rational herding in financial economics[END_REF][START_REF] Avery | Multidimensional uncertainty and herd behavior in financial markets[END_REF].

Our findings offer new evidence in support for recent theories where volatility spikes might shift investors' attention [START_REF] Kacperczyk | A rational theory of mutual funds' attention allocation[END_REF][START_REF] Andrei | Dynamic attention behavior under return predictability[END_REF] and thus incentivise social learning in a positive way by reducing herding incidence. We therefore suggest a new interpretation for herding as a temporary failure by investors in energy equity markets to allocate attention towards the most information-revealing sources. From this perspective, it is important 8 For example, managers' herding behaviour can have positive effects, like speeding up innovation adoption in reference to cutting CO2 emissions [START_REF] Egmond | Target group segmentation makes sense: If one sheep leaps over the ditch, all the rest will follow[END_REF]. It can also lead to overinvestment in firms operating in the renewable energy sector, resulting in financial vulnerability and requiring strong policy interventions from the government [START_REF] Bohl | From hero to zero: Evidence of performance reversal and speculative bubbles in German renewable energy stocks[END_REF]Zhang et al., 2016). that policymakers minimize the uncertainty flow stemming from the policy realm, given its higher portfolio impact today, on the back of raising allocations towards greener assets.

The rest of this paper is organised as follows. Section 2 details the dataset used in the analysis.

Section 3 describes the empirical methodology and Section 4 discusses the main results. Section 5 concludes with policy implications. More detailed results of our analyses are provided in the accompanying Supplement.

DATA

Our dataset brings together several different sources, which we discuss in detail in this section.

The full sample spans from January 2011 to December 2018, covering several events with potential impact on the US energy industry, including a series of declarations and political actions by President Trump on the Iranian nuclear deal, OPEC agreements with Russia to limit oil supply, political upheaval in the Middle East related to the Syrian war, and so on. All our indicators are constructed as weekly averages of daily observations to balance the higher frequency needed for identifying herding behaviour with the lower frequency at which strategic portfolio reallocations occur (i.e. in sync with phases of the economic cycle or swings in risk appetite; see [START_REF] Batten | Addressing COP21 using a stock and oil market integration index[END_REF]). Herding behaviour is more likely to be identified with highfrequency data, but (intra-) daily figures would capture too much of the trading noise. Moreover, significant changes in the strategic reallocations (e.g. from oil-related to green energy assets) are not visible on a high frequency basis. Our results should be viewed, therefore, as being rather conservative in terms of herding detection. 9 9 While possible extensions of our analysis can consider different frequencies and uncover stronger herding behaviour, the link between strategic portfolio allocations and herding might also weaken, along with the policy implications of such an analysis.

We examine herding behaviour by focusing on the U.S. energy sector as represented in the S&P 500 Index. Data on closing prices for all the 31 constituents of this sector come from Thomson Reuters Eikon. Yet, to adequately explain changes in investors' behaviour towards energy equities, we need a broader perspective that includes information sources spanning beyond the immediate investable universe of these investors, considered as a group. This is an essential aspect of our approach because in large markets, such as the U.S., imperfect information aggregation, which is central to explaining information cascades in the herding literature, can only arise due to strong information barriers and exogenous frictions.

At the end of 2018, the S&P energy sector had a market representation of 5.3% in the total S&P 500 index, which was significantly down from its high of 14.3% reached in March 2009. In general, the market valuation share is a function of the capitalisation of the constituent stocks, which may depend on the economic cycle, geopolitics, risk appetite, and so on. Empirical research shows that the energy sector's performance mainly depends on the oil price [START_REF] Baffes | The great plunge in oil prices: Causes, consequences, and policy responses[END_REF][START_REF] Ahmadi | Global oil market and the US stock returns[END_REF][START_REF] Gkillas | International announcements and WTI crude oil futures: A case study of the 2008 global financial crisis[END_REF], which is the most relevant reference as well as a leading indicator of the global economic cycle. We use the average weekly spot prices of the WTI crude oil as the main proxy for investments in oil-dependent energy assets in the following sections.

To reflect the performance of green assets, we rely on various available indexes, which can be separated in two broad groups. First, we use 16 green Exchange Traded Funds (ETFs), which are some of the most representative ETFs in this sector and are traded on the New York Stock Exchange and Nasdaq. 10 The ETFs are an attractive option for investors because they offer diversification benefits and indirect access to (illiquid or inaccessible) international equities or exotic asset classes. ETFs generally have low fees, high transparency and liquidity, and trade similarly to stocks (i.e. throughout the day), meaning that investors can employ leverage and/or short selling to take advantage of market moves in real time. Several empirical papers focusing on the energy sector use green ETFs to study the transition to a low-carbon economy [START_REF] Andersson | Hedging climate risk[END_REF][START_REF] Miralles-Quiros | Are alternative energies a real alternative for investors?[END_REF]. To summarise the performance of the 16 ETFs with a single aggregate indicator, we use returns derived from an equally weighted (in US dollar terms) portfolio based on all 16 ETFs. For robustness, we derive a time-series of synthetic returns from the first principal component of the weekly returns of the 16 ETFs. 11 As additional robustness checks, we use four indexes that are commonly employed in empirical studies on financial aspects of climate change [START_REF] Rahdari | Designing a general set of sustainability indicators at the corporate level[END_REF]. These indexes are available from Thomson Reuters Eikon and serve to monitor the financial performance of companies, whose investing and operating principles are sensitive to environmental and climaterelated risks. Two of the four indexes are based on the S&P500 -the leading U.S. stock market index, but with different allocations: (i) the S&P500 ESG Index over-(under-)weights companies that have high (low) ESG scores; and, (ii) the S&P500 Carbon Efficient Index over-(under-)weights companies with a low (high) carbon footprint. The last two indexes are: (iii) the S&P Global Clean Energy Index, which provides investors with exposures to 30 global companies with businesses in clean energy production and equipment; and (iv) the S&P Global Water Index, which tracks a portfolio of about 50 global companies that do water-related businesses in utilities, infrastructure, and equipment.

To proxy for general sources of information frictions that might be relevant to understanding information cascades and herding in the U.S. energy sector, we use the CBOE Volatility index (VIX), and the Economic Policy Uncertainty (EPU) index12 that was developed in [START_REF] Baker | Measuring economic policy uncertainty[END_REF] and can be viewed as a proxy for Knightian uncertainty. VIX is a traded index and the most widely used indicator of financial risk in the empirical literature, and therefore a relevant proxy for information frictions. EPU is a composite index based on the frequency of some relevant keywords appearing in leading U.S. newspapers and available as a daily time-series. To refine the content of the index, several categorical sub-indexes that pertain to different policy domains (e.g. fiscal, trade etc.) are available. As a robustness check for the more general EPU index, we use the EPU Regulation index which includes several climate-and regulation-related terms, such as carbon tax, drilling restrictions, offshore drilling, pollution controls, environmental restrictions, Clean Air Act, and Clean Water Act.

Finally, we capture asset-specific sources of information frictions by looking at the returns and conditional volatilities of oil and green assets. For investors, returns convey information that is relevant from a short-term perspective, particularly in trending markets, while volatility proxies carry information about the medium-to long-term portfolio implications. For each asset, we derive its conditional volatility from a GARCH (1,1) model specified in weekly returns, allowing us to capture the forward-looking dynamic of volatility. While volatility can be measured in different ways, most of these measures are backward-looking and/or less predictable and hence less relevant to explain changes in behaviour, which inevitably entails some form of persistence in information processing.

EMPIRICAL DESIGN

This section derives a dynamic herding metric that can effectively summarise the relevant changes in investors' behaviour towards energy equities, from a time perspective. We then propose a non-parametric analysis to check the properties of this metric in relation with a wide set of determinants, encompassing various information sources and frictions. Finally, we employ a multivariate analysis to examine herding behaviour in a context where investors in energy equities face two outside options when dealing with policy-and climate-related challenges: allocate more funds to crude oil or to green energy assets.

Dynamic herding detection as a metric

The common approach in the empirical literature to detect herding towards the market consensus has followed the seminal paper of [START_REF] Chang | An examination of herd behavior in equity markets: An international perspective[END_REF]. 13 This literature uses the crosssectional absolute deviation (CSAD) as a proxy for the asset's return dispersion:

= ∑ , -, -1 (1)
where , is the return of asset at time , , is the return at time on the market portfolio constructed as an equally-weighted portfolio of all the assets traded on that market, which in our case is the U.S. energy equity sector. [START_REF] Chang | An examination of herd behavior in equity markets: An international perspective[END_REF] demonstrate that in the presence of herding, the linear relationship that capital asset pricing models (CAPM) predict between the dispersion of individual asset returns and the market portfolio return would be violated. Herding behaviour introduces nonlinearities because some investors may fail to differentiate among individual assets and thus trade closer to 13 Alternative model specifications and extensions are included in [START_REF] Chiang | An empirical analysis of herd behavior in global stock markets[END_REF] who add spill-overs from international markets, [START_REF] Galariotis | Herding on fundamental information: A comparative study[END_REF] and Hwang and Salmon (2014) who separate between fundamental and non-fundamental factors, [START_REF] Demirer | Does the stock market drive herd behavior in commodity futures markets?[END_REF] who include volatility persistency.

the market consensus (i.e. low CSAD values) when faced with extreme market moves (i.e. extreme values). Therefore, herding can be detected in the following model:

= + , + , + (2)
where , denotes the absolute value of market returns, , denotes the squared market returns, , and are coefficients to be estimated, and is an error term.

The mathematical derivation of Eq. ( 2) implies that the first derivative of CSAD with respect to the market portfolio return is a constant term, while the second derivative is null. 14 Therefore, in the absence of herding, the CAPM-based model predicts that variations in market returns (in either direction) should be linearly associated with CSAD; that is, there must be a positive and statistically significant coefficient. If herding exists, then investors will ignore private information and switch from following their own strategies to following the market consensus, thus pulling individual asset returns towards the market returns. This type of behaviour occurs in the non-linear relationship between CSAD and squared market returns, and it is reflected in a statistically significant and negative coefficient [START_REF] Chang | An examination of herd behavior in equity markets: An international perspective[END_REF].

Some of the main issues associated with the herding model given in Eq. ( 2) stem from the fact that herding has repeatedly been shown to be market-dependent, non-linear, asymmetric and therefore time-varying. Given these characteristics, we can relax the constant coefficient assumption implicit in Eq. ( 2) and employ a Kalman filter to estimate it. We only allow to be time-varying and we keep the other two coefficients as time-invariant to reflect the linear 14 Under the CAPM, the expected cross-sectional absolute deviation of stock returns (ECSAD) at t can be expressed as = ( ) ∑ -, , -!, , from which we can derive:

" #$%&' ( "# ) *,( = + , ∑ -, > 0 and

" / #$%&' ( "# ) *,( / = 0.
relationship between CSAD and market returns embedded in the CAPM theory. We re-specify Eq. ( 2) in state-space form as a system: 0123 45 0 36 5 0 : = ′ + ′ , + , , + 3

(3) 2 5 3 36 5 0 : , = , 9 + : where 3 ~<(0, = ), ′ and ′ are coefficients, while : ~<(0, = > ). The filtered time-varying , will be denoted as our dynamic herding metric in the rest of this paper because it reflects the time-varying nature of the non-linear relation between cross-sectional dispersion and market extreme returns, , . A continuous and time-varying herding metric provides more insights without additional a-priori assumptions that impose a rigid model structure during its estimation.

Therefore, estimating a time-varying , balances the need for a dynamic herding proxy with the mathematical consistency of the original model proposed by [START_REF] Chang | An examination of herd behavior in equity markets: An international perspective[END_REF].15

Non-parametric analysis

In this subsection, we explore the properties of the dynamic herding metric using the nonparametric filter introduced by Ratto and Pagano (2010), denoted as ANOVA, which combines a Kalman filter with a fixed interval smoothing. Intuitively, any model output denoted as ? can be seen as a mapping on a set of inputs, @ , = @ , , @ , , … . Allowing for both first-order and second-order interactions between these inputs, the output can be specified as:

? = B(C ) = B + B D@ , E + B D@ , E + B F D@ , * @ , E + ⋯ (4)
where B are unknown functions of the inputs @ , that need to be identified. In our case, we let ?

be the dynamic herding metric, and then analyse a wide set of explanatory inputs, @ , that encompass both general and asset-specific information sources and frictions.

The main advantages of this filter come from the ease of interpreting its results, improved fitness, and the flexibility of the estimation approach. Using this filter, we are able to expose the inputs (and inputs' non-linear interactions) that make the biggest contribution to explaining the time-series characteristics of herding metric. While the ANOVA filter can offer a model-free characterisation of the herding metric, the strength of the interactions can suggest an endogeneity potential between output and inputs.

A multivariate analysis of herding

Much of the empirical literature uses volatility metrics to proxy for information frictions, which influence strongly on herding behaviour in theoretical models [START_REF] Bikhchandani | Does herding affect volatility? Implications for the Spanish stock market[END_REF]. Using an intraday measure of herding intensity, Blasco et al. (2012) find that herding impacts positively on the volatility of Spanish stocks. However, [START_REF] Holmes | Herding in a concentrated market: a question of intent[END_REF] show that market volatility impacts negatively on herding, while BenSaida (2017) find evidence from U.S.

that herding reduces aggregate volatility due to the presence of inactive stocks. Given this lack of consensus on the transmission links between herding and volatility, we propose an unrestricted vector autoregressive (VAR) model that can naturally account for any (bi-)directional influences.

The VAR model allows for an unrestricted interaction between herding and the other information proxies, exposing the most important linkages, while at the same time remaining flexible in including a larger number of variables without compromising on its inference efficiency. Hence, our main insights are based on unrestricted VAR models, which include partial Granger causality tests and impulse response analysis.

Without loss of generality, consider a multivariate process IJ K L of dimension . An unrestricted VAR formulation specifies the dynamics of J K as:

M(N)J = (5)
where N is the lag operator, M is a polynomial matrix in the lag operator, M(0) = O being the identity matrix, ( ) = 0 and a variance-covariance matrix 45 ( ) = P with dimension × . In our application, = 3 and we specify the endogenous vector J as having the general form:

J = -, , B3 3 5S T UV, , 5223 _2X3Y Z Y T UV, ′ (6)
where the dynamic herding metric is taken with a negative sign in the VAR model to facilitate interpretation, implying that an increase in -, reflects more (not less) herding. The component B3 3 5S T UV denotes general information proxies (i.e. VIX and EPU), which are included as a way to filter out market-related and policy-related dynamics, and thus better identify assetspecific information frictions. By 5223 _2X3Y Z Y T UV , we refer to oil-related and green-related returns and their conditional volatility proxies. By including both general and asset-specific components, we aim to capture all the relevant sources of information frictions that affect herding behaviour. Therefore, we seek to understand herding in a broader market context where investors are facing two investment strategies, i.e. oil versus green assets. We also fill a gap in the literature by including Knightian uncertainty, a broader concept encompassing volatility, while also paying particular attention to uncover the main interactions between herding and various proxies of information frictions.

Even if we are only interested in analysing the main interactions between these groups of variables, there is still a risk that our VAR model does not include all the relevant variables. To account for any exogenous and latent (endogenous) factors that can produce inaccurate causal inferences in a multivariate setting, we apply the partial Granger causality (GC) approach set in the time domain [START_REF] Philippas | Exposing volatility spillovers: A comparative analysis based on vector autoregressive models[END_REF]. 16 This approach allows us to isolate all traces of common exogenous and latent factors, assuming they all have simultaneous effects on all the observed components of the system.

Based on specification (6), we estimate several unrestricted VAR models that differ along the set of proxies used to reflect information components. We perform standard checks on each model's stability and then derive the generalised impulse response functions (GIRFs) to a onestandard deviation shock at time on expected values of J at horizon + ℎ [START_REF] Koop | Impulse response analysis in nonlinear multivariate models[END_REF][START_REF] Pesaran | Generalized impulse response analysis in linear multivariate models[END_REF]. Using GIRFs in our case is more appropriate given that it is hard to use other decomposition methods that impose a-priori restrictions, e.g. on contemporaneous responses (thus effectively enforcing a specific ordering or sequencing) in a VAR model featuring fast-moving variables.

EMPIRICAL RESULTS

Individual returns of the constituent shares of the S&P 500 Energy Index are computed by taking the log-differences of the weekly average price levels. The equally-weighted market portfolio returns are calculated as a simple average of all stocks' returns, at a weekly frequency. CSAD is then computed using Eq. ( 1) based on weekly stocks' returns.

4.1 Dynamic herding as metric 16 More technical details are provided in Appendix B in the Supplement.

To derive the dynamic herding metric, we apply a Kalman filter to the state-space specification of the herding model from Eq. (3). 17 Figure 1 displays the time-varying , along with a confidence interval set at +/-2 standard deviations.

Figure 1. 'Dynamic herding metric', S&P 500 Energy Index and spot WTI oil prices 17 The preliminary OLS estimate of in Eq. ( 2) was found to be positive and statistically insignificant, offering no evidence of herding behaviour within the constituent stocks of the S&P 500 Energy Index. Estimation by Maximum Likelihood of Eq. ( 3) leads to statistically significant ′ and ′ that are very close to the previous OLS estimates of and from Eq. ( 2). These results are not reported to save space, but are available by request from the authors.

Notes:

The figure displays the estimate of dynamic herding metric, i.e. , , as a solid black line along with a confidence interval of +/-2 standard deviations depicted in grey. The upper panel includes the S&P 500 Energy Index in red, while the bottom panel includes the crude oil prices in USD/barrel in red.

At this point, it is important to see our metric reflecting real market phenomena rather than being a statistical construct. The dynamic herding metric is seen to display mostly negative values, except for some short periods of time concentrated at the end of 2015 and beginning of 2016. It has highly negative values during most of 2013 and 2014, which coincides with a time period when the energy market was peaking, and the oil prices were hovering above 100 USD per barrel. Overall, this suggests herding in U.S. energy equities is more prevalent during rising (or peak) energy equities and oil prices, an observation that seems to confirm previous findings in [START_REF] Brunetti | Herding and speculation in the crude oil market[END_REF][START_REF] Benmabrouk | Cross herding between American industries and the oil market[END_REF][START_REF] Benmabrouk | Cross herding between American industries and the oil market[END_REF].

The literature has converged around several explanations for the abrupt fall in oil prices in the late 2014, among which: the U.S. shale boom, a global economic slowdown (led by China and the Eurozone), production ramp-ups in several countries, and OPEC shifts in market strategy (see [START_REF] Behar | OPEC vs US shale: Analyzing the shift to a market-share strategy[END_REF]. Leaving global factors aside, the most important domestic driver for U.S. investors appears to be related to developments in the oil shale industry. Given the overlaps observed in Figure 1 between the oil price, energy equities and our herding metric, it looks highly probable that investors in U.S. energy equities were in a rush to profit from the boom in U.S. shale oil in late 2013 and early 2014, making thus irrational and herding behaviour more likely to be observed [START_REF] Teti | Effects of oil price fall on the betas in the Unconventional Oil & Gas Industry[END_REF]. However, a more causal analysis would be required before drawing definite conclusions.

Non-parametric filter

Armed with a dynamic herding metric that can efficiently summarise investors' group behaviour, we must now frame our research questions in a wider market context where portfolio allocations span the entire investable universe, ranging from oil to green assets. We employ the ANOVA non-parametric filter and consider two different sets of determinants that reflect information frictions relevant for investors in U.S. energy equities. The first input set includes VIX and EPU (in logs), along with weekly returns for the WTI crude oil and the green assets proxy. The second set of inputs replaces returns with conditional volatilities of the two alternative investments considered, but keeps both VIX and EPU indices as general information sources. As green proxy, we use the equally-weighted portfolio built out of 16 green ETFs, denoted as ETF_EQW, while for oil we reserve the CRUDEOIL label.

Results are displayed in Table 1. Main effects are computed as percentage of variance explained by the first-order terms, while second-order effects reflect the percentage of variance explained by the interactions. Total effects include both the first-and the second-order effects.

Notes:

The table presents the percentage of variance in the 'dynamic herding metric' explained by each input, its interactions and the total explained by all inputs in each of the two sets.

The first observation we derive from Table 1 is that conditional volatilities perform better than returns at explaining the time-series properties of our herding metric. The second observation is that interactions between the inputs improve the model fit significantly, especially when conditional volatilities are used as inputs. Taken together, these observations suggest a more complex relationship between information proxies and herding, whereby the presence of strong interactions hints at undetected endogeneity within the model variables.

Herding in a multivariate framework

To address the main research questions, we seek to understand herding in a broader market context, though still centred on U.S. energy equity segment which comprises some of the biggest energy companies in the world. Energy equity markets are at the crossroads of the current energy transition phase between the old and the new. Within the energy sector, and with given portfolio constraints derived from strategic decisions, investors might steer their allocations towards more or less greener assets. Such shifts in portfolio allocations can have large price impacts, depending on investors' learning behaviour in response to changes in policies and regulations, perceived social attitudes, market trends etc. All these possible sources of information frictions might affect investors' behaviour in the energy equities market segment. Given the lack of consensus in the empirical literature and the strong interactions uncovered in previous sub-sections, we set up an unrestricted VAR model including: (i) herding (which here we proxy using the negative of the dynamic metric), (ii) two asset-specific information proxies (i.e. one for each investment option), and (iii) two general information proxies, for which we use (log) VIX and (log) EPU. Depending on the asset-specific information considered, we estimate one VAR model for returns and one VAR model for conditional volatilities. We first apply the partial GC tests to get an overview of the existing causality influences, and then perform the impulse response analysis.

Three main findings emerge from Table 2, which reports the partial GC test results. First, oil returns do Granger-cause herding in energy equities, in contrast to oil conditional volatility.

Second, green assets' conditional volatility Granger-causes herding but not the green returns.

Finally, VIX Granger-causes both oil and green assets' returns but not their conditional volatilities.

Notes:

The table presents the results for partial GC. The first column displays the "senders" while the first row displays the "receivers". Each cell displays the label "Yes" whenever we cannot reject the existence of Granger causality (using 10% as a confidence level) and "No" otherwise, with the p-value in parenthesis.

In terms of identification, we follow [START_REF] Koop | Impulse response analysis in nonlinear multivariate models[END_REF], and [START_REF] Pesaran | Generalized impulse response analysis in linear multivariate models[END_REF] and employ generalised impulse responses, or GIRFs, to derive our main insights. Our GIRFs only provide the average impact expected after a shock to the multivariate system (6). [START_REF] Kilian | Not all oil price shocks are alike: Disentangling demand and supply shocks in the crude oil market[END_REF] and [START_REF] Bastianin | How does stock market volatility react to oil price shocks?[END_REF] employ structural identification methods to study oil and market volatility in VAR model's settings. In contrast, we focus on understanding what type of information sources might be more relevant for investors who must cope with their own behavioural biases, which usually get amplified during periods of market turmoil. Two main results emerge from the analysis of GIRFs, confirming previous insights from the partial GC tests. We find that herding does not respond to shocks in green returns, but increases in response to positive shocks in oil returns. With oil portraying an investment strategy into an industry reliant on old production technologies, no more than information on returns is required.

Our dynamic herding metric responds (albeit with a lag that reflects learning process) only to shocks in green (but not oil) volatility, which can be best related to the medium-and long-term prospects and the quality of the information set available for green assets and technologies.

The evidence we provide in Figure 2 implies that unexpected negative oil returns and/or positive spikes in green volatility might reduce herding intensity among investors in energy equities. These results offer a perspective on what type of information is required to resolve uncertainty and ease information frictions that are conducive to herding in the first place. [START_REF] Kacperczyk | A rational theory of mutual funds' attention allocation[END_REF] and [START_REF] Andrei | Dynamic attention behavior under return predictability[END_REF] suggest that skilled investors allocate more attention and thus prefer to learn more about the most uncertain outcomes. In our case, high volatility in green assets could incentivise (at least) some investors to learn more about 'greener opportunities'. As the group of investors following the market consensus becomes smaller now, the incidence of herding behaviour would obviously reduce. From this perspective, we can interpret herding as a temporary failure in allocating attention. In other words, neglecting alternative, though valuable, information sources for the sake of following others reduces market efficiency, as well as profit opportunities. While much of the previous literature suggests that higher volatility drives more herding, we uncover an opposite transmission channel, where higher volatility pushes (at least those skilled) investors towards more learning and therefore less herding. 18 This can have implications for cross-market efficiency, whereby the information quality in one market can affect investors' group behaviour in other markets.

Appendix C in the Supplement includes the full set of GIRF from the two VAR models discussed above. They provide additional evidence in line with the partial GC insights where we observe that green assets (but not oil) are sensitive to policy uncertainty. We find that unexpected shocks in EPU lead to higher volatility and lower returns in the case of green assets but not in the case of crude oil. At the same time, unexpected VIX shocks drive higher volatility and lower returns in both oil and green assets. Policy uncertainty is therefore a better indicator than financial risk proxies, such as VIX, in reflecting the multidimensional nature of risks associated with green investing.

ESG criteria are gaining in popularity among investors and companies alike. However, despite this euphoria, 8 of the 10 biggest ESG funds in the United States report substantial equity shares in big oil companies (e.g. ExxonMobil). Our findings help to explain this (seemingly) puzzling allocation strategy by providing empirical evidence for the lack of sensitivity for crude oil to policy uncertainty shocks, which instead highly affect green portfolio allocations. This result is in line with the recent discussion from [START_REF] Andersson | Hedging climate risk[END_REF], [START_REF] Batten | Addressing COP21 using a stock and oil market integration index[END_REF] and [START_REF] Engle | Hedging climate change news[END_REF] regarding the role of oil allocations for financial portfolios that aim to reduce climaterelated risks.

While our analysis can have its drawbacks, several extensions remain possible. Future studies can employ different datasets, at a different frequency, or covering a different sample -e.g.

extended to more recent periods to include the COVID-19 pandemic. Different herding metrics to allow for stochastic volatility can also be employed with different results and policy implications.

Robustness checks

To overcome concerns regarding our specifications, we implement a series of robustness checks to the multivariate framework, which we report in detail in the Supplement. In all these cases, results are similar. We first replace the equally-weighted ETFs portfolio (our benchmark for green assets) with each of the green proxies discussed in the data section. Next, we use futures oil prices instead of spot prices, since Avery and Zemsky (1998) claim that derivatives are better at reflecting multidimensional uncertainty. We also replace EPU with one of its domain-specific sub-indexes i.e. EPU-Regulation, which is more relevant for the green sector given the strong feedbacks between policy regulation, innovation and investing [START_REF] Mazzucato | Financing renewable energy: Who is financing what and why it matters[END_REF].

Lastly, we extend our VAR model with a new variable to reflect mass media coverage of climate-related topics -an indicator that complements the market information available to investors from returns or volatility proxies. Based on data from Fernández-Reyes et al. ( 2020), we find a negative response of herding to a positive shock in media coverage. This new result aligns with our previous discussion about the quality of the information required by investors in green assets.

CONCLUSIONS AND POLICY IMPLICATIONS

The current hype growing around green energy investing poses substantial challenges for investors trading in U.S. energy equity markets. Whether and how these investors as a group learn to deal with different information frictions, to navigate through wide swings in market risk appetite and uncertainty, and to deal with sudden changes in energy policies and regulations, is of great importance for their investment choices.

We derive a metric of dynamic herding in energy equities towards the market consensus based on the time-varying version of herding detection model [START_REF] Chang | An examination of herd behavior in equity markets: An international perspective[END_REF]. We then set up a VAR model and use tools such as partial Granger Causality tests and impulse responses to draw conclusions on how herding interacts with energy equities' returns, policy uncertainty and volatility proxies. We find that herding among investors in U.S. energy equities responds to green volatility shocks but not to green return shocks. In contrast, herding responds to shocks in oil returns but not in oil volatility. Therefore, opting for strategies that invests in assets reliant on old technologies would require little besides information on returns, but newer investment opportunities require a better information set. Consequently, the better information quality needed to alter behaviour of investors' in energy equity markets with respect to greener opportunities shows that the old discussion on rational versus irrational herding in the face of structural market changes remains relevant today [START_REF] Devenow | Rational herding in financial economics[END_REF][START_REF] Avery | Multidimensional uncertainty and herd behavior in financial markets[END_REF].

Our findings that crude oil allocations are largely insensitive to policy uncertainty shocks suggest a possible hedging strategy similar to those proposed in [START_REF] Andersson | Hedging climate risk[END_REF], and [START_REF] Batten | Addressing COP21 using a stock and oil market integration index[END_REF]. However, this strategy would run against current market trends favouring greener allocations, which we have seen that, unfortunately, might amplify portfolios' vulnerability in the face of sudden policy changes and uncertainty spikes emerging from the policy realm.

Policymakers should reduce policy uncertainty that can stimulate irrational herding behaviour among investors, with negative consequences on energy equity market valuations and mispricing dynamics. There are many ways to achieve this goal, including better transparency of the policy decision-making process, or better engagement with all relevant stakeholders before substantial policy changes are decided. By contrast, high policy uncertainty would incentivise firms to engage in lobbying to gain government support or collect more information on future policy initiatives, leading to a situation that profits the insiders and creates more information frictions, asset bubbles and mispricing. 19Speculative episodes and irrational behaviour usually feed on easy money and large credit availability. While green bonds (both private and institutional) issuance has increased several times over the last decade, providing thus ample investment opportunities, there is a lack of adequate regulatory tools to properly address climate-related risks in general. In this context, investors should welcome the recent admission from the Federal Reserve, in its November 2020 report on financial stability, 20 that it is considering climate change as a potential threat to the stability of the U.S. financial system and that an evaluation process is underway; meanwhile, ECB is moving ahead and planning for its 2022 stress testing exercise to include climate change risk in the evaluation. Apart from central bankers, policymakers would often reverse course due to fiscal constraints and/or political motivations (e.g. U.S. withdrawal from the Paris accord). A better outcome can be achieved if such high transparency (i.e. low policy uncertainty) displayed by central banks (and financial institutions) would be matched by political and regulatory authorities that oversee the energy sector -the key responsible for a large part of critical infrastructure.

Figure 2

 2 Figure 2 illustrates how herding responds to asset-specific information shocks in the two

Figure 2 .

 2 Figure 2. Herding responses to energy asset-specific information shocks

Table 1 .

 1 Non-parametric filter

	% of	Main	Total	Graphs

Table 2 .

 2 Partial Granger Causality influences

	Component	→ Herding	→ VIX	→ EPU	→ Crude Oil (returns)	→ ETF EQW (returns)
	Herding→	-	Yes (0.0544)	No (0.1960)	Yes (0.0118)		No (0.3356)
	VIX→	No (0.1116)	-	Yes (0.02531)	Yes (0.0011)		Yes (0.0029)
	EPU→	No (0.8113)	Yes (0.000)	-	No (0.79914)		No (0.7389)
	Crude Oil (returns)→	Yes (0.0447)	Yes (0.0002)	Yes (0.0009)	-		Yes (0.0071)
	ETF EQW (returns)→	No (0.5081)	Yes (0.0203)	No (0.9989)	No (0.3684)		-
	Component	→ Herding	→ VIX	→ EPU	→ Crude Oil (volatility)	→ ETF EQW (volatility)
	Herding→	-	Yes (0.0544)	No (0.1960)	No (0.9988)		No (0.998)
	VIX→	No (0.1116)	-	Yes (0.0253)	No (0.9988)		No (0.998)
	EPU→	No (0.8113)	Yes (0.000)	-	No (0.9988)		No (0.998)
	Crude Oil (volatility)→	No (0.9988)	Yes (0.0003)	No (0.997)	-		Yes (0.000)
	ETF EQW (volatility)→	Yes (0.0090)	Yes (0.000)	Yes (0.000)	No (0.998)		-

As of December

2019, various institutions ranging from NGOs, educational institutions to corporations have publicly announced and committed to divest from at least one type of fossil fuel almost $11.94 trillion. Source: http://gofossilfree.org/commitments, accessed on February 20, 2020.2 Source: "Sustainable Fund Flows in 2019 Smash Previous Records", Morningstar, January 10, 2020, see https://www.morningstar.com/articles/961765/sustainable-fund-flows-in-2019-smash-previous-records.

Many institutional investors (representing the biggest investors in energy equity markets) operate under tight mandates, which often imply tracking a benchmark index with low appetite for large variations in the optimal portfolio weights. Our analysis proceeds under the assumption of a fixed allocation to energy assets, and although extensions to including all asset classes remain possible, this is beyond the scope of the present paper.

During the transition to a low-carbon economy, green investing entails dealing with higher uncertainty, not just higher risks.Thoma and Chenet (2017) differentiate between uncertainty and risk when discussing the financial implications of climate change.

The data source is Bloomberg. More details regarding the green ETFs used in this paper are provided in TableA1, in the Supplement.

The main goal of principal component analysis (PCA) in our case is to summarize the 16 green ETFs returns with a smaller set of linear combinations. Since the correlation between the returns of any two ETFs in our list is above 0.4 and statistically significant, the PCA is an efficient aggregation tool.

Data and methodological details are available from www.policyuncertainty.com.[START_REF] Baker | Measuring economic policy uncertainty[END_REF] show that EPU is orthogonal to market volatility and risk indexes such as VIX, despite some overlaps and correlation.

We differentiate from other alternatives(Chiang et al., 2013;[START_REF] Balcilar | Does speculation in the oil market drive investor herding in emerging stock markets?[END_REF]) that estimate herding models with time-varying coefficients. Using complex estimation techniques that allow all parameters to be time-varying might compromise on estimation efficiency, while imposing too much of a rigid structure on the estimated herding proxy, which can bias the subsequent analysis.

Similarly, in Bikhchandani and Sharma (2000) the arrival of better-informed investors can break the information cascade and reduce herding incidence.

Many firms from the U.S. oil and gas industry are engaged in lobbying activities. Although lobbying can be an optimal response to policy uncertainty by firms and their managers, we have focussed our analysis only on investors' behaviour, since in their case market efficiency is a first-order concern.

Source: https://www.federalreserve.gov/publications/financial-stability-report.htm.

ACKNOWLEGEMENTS

We would like to thank two anonymous reviewers for helpful comments and suggestions that helped us streamline the analysis and the discussion of the paper. We are also grateful to Emanuele Bacchiocchi, Andrea Bastianin, Rosario Crino, Giulio Palomba, Eduardo Rossi, and Costas Siriopoulos for their many comments and suggestions. The usual disclaimer applies.