Luz Zavala-Sanchez

Xavier Portier

Françoise Maugé

Laetitia Oliviero
email: laetitia.oliviero@ensicaen.fr

Formation and stability of CoMoS nanoclusters by the addition of Citric Acid: a study by High resolution STEM-HAADF microscopy

Keywords: HR STEM-HAADF, CoMoS, Citric acid, CO adsorption, IR spectroscopy, Sulfide nanoparticles morphology, used catalyst. Graphical

In this work, we present atomic-scale images of Co promoted MoS2 slabs supported on γ-Al2O3 obtained by High Resolution Scanning Transmission Electron Microscopy equipped with High Angular Annular Dark Field detector (HR STEM-HAADF). These images allow to study the effect of citric acid (CA) addition during preparation, on the slab length and its stability during thiophene hydrodesulfurization (HDS) reaction.

Thus, the observations, obtained for sulfide catalysts prepared without or with citric acid as chelating agent, evidenced strong decrease in size of the CoMoS nano-slabs as detected indirectly by the adsorption of CO followed by Infrared spectroscopy (IR/CO). Quantitative dispersion values were calculated from the images taking into account the true shape of the particles instead of the classical hexagonal shape hypothesis. Characterization of the used catalyst shows that these nanoclusters are stable under model thiophene HDS reaction.. Such observations allow a better understanding of the effect of chelating agent addition on promoted MoS2 samples in order to explain their catalytic activity.

Introduction

The increasing demand for low sulfur fuels puts pressure on the development of more active catalysts for the production of clean transportation fuels. However, Used CoMo (CA/Mo=2) current oil deposits have higher sulfur concentration [START_REF]Sulfur production report by the United States Geological Survey[END_REF] and, strict fuel regulations are being established in both developed and developing countries [START_REF]EIA, Annual Energy Outlook 2019 with projections to 2050[END_REF]. To meet environmental standards, the oil industry is producing ultra-low sulfur diesel fuel (ULSD), a cleaner fuel containing a maximum of 10 parts per million (ppm) of sulfur.

This level is likely to be further decreased by environmental legislation in subsequent years. Hydrodesulfurization (HDS) catalysts are mainly based on supported transition-metal disulfides (TMS) [START_REF] Alphazan | Highly Active Nonpromoted Hydrotreating Catalysts through the Controlled Growth of a Supported Hexagonal WS2 Phase[END_REF]. The TMS active phase is usually composed of molybdenum (Mo) or tungsten (W), promoted by cobalt (Co) or nickel (Ni). Although the non-promoted MoS2 (WS2) catalysts do not present high catalytic activity, a very significant increase in activity can be achieved by adding Co or Ni [4,[START_REF] Topsøe | Situ Mössbauer Emission Spectroscopy Studies of Unsupported and Supported Sulfided Co-Mo Hydrodesulfurization Catalysts: Evidence for and Nature of a Co-Mo-S Phase[END_REF]. Then a bimetallic sulfide phase is formed, typically called the CoMoS, NiMoS, or NiWS phase, whose structure corresponds to a two-dimensional (2D) nanolayer of Mo(W)S2 decorated by the promoter at its edges, as described in the so-called

CoMoS model [4][START_REF] Topsøe | Situ Mössbauer Emission Spectroscopy Studies of Unsupported and Supported Sulfided Co-Mo Hydrodesulfurization Catalysts: Evidence for and Nature of a Co-Mo-S Phase[END_REF][START_REF] Besenbacher | Recent STM, DFT and HAADF-STEM studies of sulfide-based hydrotreating catalysts: Insight into mechanistic, structural and particle size effects[END_REF][START_REF] Topsøe | Importance of Co-Mo-S Type Structures in Hydrodesulfurization[END_REF]. The sulfide phase presents a lamellar structure, formed by layers of MS2 (M = W, Mo). These particles are often supported on high specific surface area carriers such as γ-alumina (γ-Al2O3). Co-promoted MoS2 nanostructured catalysts are traditionally used for hydrotreatment reactions. CoMo catalysts are some of the most used catalyst for reaching ULSD levels. They have been the subject of research in numerous studies to determine their structure and to identify their active sites [START_REF] Byskov | Edge termination of MoS2 and CoMoS catalyst particles[END_REF][START_REF] Baubet | Quantitative Two-Dimensional (2D) Morphology-Selectivity Relationship of CoMoS Nanolayers: A Combined High-Resolution High-Angle Annular Dark Field Scanning Transmission Electron Microscopy (HR HAADF-STEM) and Density Functional Theory (DFT) Study[END_REF][START_REF] Krebs | Mixed sites and promoter segregation: A DFT study of the manifestation of Le Chatelier's principle for the Co(Ni)MoS active phase in reaction conditions[END_REF]. Active sites in sulfided CoMoS catalysts are associated to the nano-slabs exposed edges, i.e. M-edge and S-edge. Lowtemperature CO adsorption followed by infrared spectroscopy (IR/CO) is a technique that gives access to the site dispersion and then to their intrinsic activity. It has been intensively used to probe the edges sites of MoS2 slabs on MoS2/Al2O3 catalysts.

Previous results of our group [START_REF] Chen | IR spectroscopy evidence of MoS2 morphology change by citric acid addition on MoS2/Al2O3 catalysts -A step forward to differentiate the reactivity of M-edge and S-edge[END_REF][START_REF] Chen | On the morphology of MoS 2 slabs on MoS 2 /Al 2 O 3 catalysts: the influence of Mo loading[END_REF][START_REF] Travert | Parallel between infrared characterisation and ab initio calculations of CO adsorption on sulphided Mo catalysts[END_REF], have demonstrated that the S-edge is more active than the M-edge in thiophene HDS reaction and is also more favored in being promoted, therefore, the increase of S-edge/M-edge ratio leads to an increase of HDS activity. In this way, CoMoS slabs morphology can be expected to be related to the catalytic activity. The concentration of S-and M-edge sites and the distinction of the promoted sites is essential to accurately explain their activity and their selectivity. In addition, parameters of preparation of these catalysts as effect of support, conditions for the preparation of the initial oxide phase, sulfidation conditions among others, play an important role in the final result in catalytic performance.

Recent advances in high-resolution scanning transmission electron microscopy (HR STEM) imaging have opened up the possibility of studying two-dimensional materials with atomic-level resolution and sensitivity. In addition to conventional TEM-based modes, a very useful alternative to characterize materials at a subnanometer scale is HR STEM-HAADF. In this STEM mode, the annular detector collects high angle scattered electrons and the intensity of the image depends on the atomic number within the sample and is approximately proportional to Z 1.7 [START_REF] Girleanu | HAADF-STEM highresolution study of nanometric MoS2 inside mesoporous SBA-15[END_REF][START_REF] Nellist | Direct Imaging of the Atomic Configuration of Ultradispersed Catalysts[END_REF]. Due to its high sensitivity to heavy metal atoms (such as Mo, W and even Co and Ni), a -STEM-HAADF analysis is the best alternative to evaluate parameters such as slab shape and structural characteristics.

Improving the dispersion degree of active metals is another crucial idea to enhance the activity of sulfided catalysts. Various methods have been developed to prepare well-dispersed catalysts. The addition of chelating agents have a special and efficient role in increasing the dispersion degree of Co(Ni)-Mo-S active phases [START_REF] Al-Dalama | A Comparative Study of the Influence of Chelating Agents on the Hydrodesulfurization (HDS) Activity of Alumina and Silica-Alumina-Supported CoMo Catalysts[END_REF][START_REF] Cattaneo | The Relationship between the Structure of NiMo/SiO2 Catalyst Precursors Prepared in the Presence of Chelating Ligands and the Hydrodesulfurization Activity of the Final Sulfided Catalysts[END_REF][START_REF] Badoga | Beneficial influence of EDTA on the structure and catalytic properties of sulfided NiMo/SBA-15 catalysts for hydrotreating of light gas oil[END_REF] by interacting with the precursor ions and the support surface. However, the effect of the addition of citric acid in the preparation of promoted catalysts is always somewhat controversial since both increase [START_REF] Chen | Role of Citric Acid in Preparing Highly Active CoMo/Al 2 O 3 Catalyst: From Aqueous Impregnation Solution to Active Site Formation[END_REF] and decrease [START_REF] Zavala-Sanchez | High-resolution STEM-HAADF microscopy on a γ-Al2O3 supported MoS2 catalyst-proof of the changes in dispersion and morphology of the slabs with the addition of citric acid[END_REF] in dispersion have been reported. Moreover, while in the non-promoted catalysts the variation of morphology with the addition of citric acid was indirectly observed by IR/CO method, that is, the S-edge/M-edge ratio was closer to one after CA addition, for the promoted systems this is still inconclusive. In particular, a better distinction of the nature of the promoted sites by IR/CO is required. But, the results of catalytic activity, as well as those of IR spectroscopy obtained from non-promoted and promoted samples, have certain consistency: citric acid addition provokes a considerable increase in catalytic activity and in total site concentration.

In this work, the aim is to observe by direct image characterization the slab morphology of sulfided Al2O3 supported CoMo catalysts prepared at the same conditions of synthesis and sulfidation that the ones for the catalytic application.

Then a parallel study of the effect of citric acid by means of HR STEM-HAADF and IR/CO spectroscopy method is carried out. Finally, the effect of using the CoMo catalyst prepared with CA in model thiophene HDS reaction is studied to check the stability of the observed slabs.

Experimental

Catalyst preparation

CoMo/Al2O3 catalysts, without and with citric acid (CA), were prepared by a one-step pore volume impregnation method. The aqueous impregnation solutions were prepared by dissolving a fixed amount of ammonium heptamolybdate tetrahydrate ((NH4)6Mo7O24•4H2O MERCK) and cobalt (II) nitrate hexahydrate (Co(NO3)2•6H2O Alfa Aesar) in deionized water at room temperature. Citric Acid (CA) was incorporated at this stage by dissolving the required amount (C6H8O7•H2O PROLABO) to obtain a CA/(M) = 0 or 2, (M=Mo+Co). Afterwards, the solution was added to the pretreated γ-Al2O3 support (SASOL, specific surface area of 252 m 2 ·g - 1 and pore volume of 0.84 mL·g -1 , precalcined in air at 723 K for 2 h), strongly shaken and left for maturation during 2 h. Finally, the catalysts were dried at 383 K for 16 h.

Note that these catalysts were not calcined in order to keep the chelating agent if present in its initial form. Hereinafter, the CoMo/Al2O3 catalysts are denoted CoMo(CA/M=x)/Al2O3. X refers to the molar ratio of CA to Mo; x = 0 or 2.0. For these two CoMo(CA/M = x)/Al2O3 catalysts, the content of Mo was fixed to 3.2 Mo atoms per nm 2 , and the Co/(Co + Mo) ratio was equal to 0.3.

The CoMo(CA/M=2)/Al2O3 catalysts was then tested in thiophene hydrodesulfurization (HDS) reaction. A mass of 50 mg of catalyst (20-40 meshes, precisely weighed) was first sulfided with 30 mL•min -1 10% (v/v) H2S/H2 at 623 K (3 K•min -1 ) for 2 h. Then, the catalytic activity of thiophene HDS was tested at 623 K using a 90 mL•min -1 gas mixture consisting of 7.9% thiophene, 90.0% H2, and 2.1% H2S. The sample was left under these conditions during 72 h.

Low-Temperature CO Adsorption Followed by IR Characterization (IR/CO).

The CoMoS edge sites of these catalysts were in-situ characterized by lowtemperature CO adsorption followed by IR spectroscopy [START_REF] Chen | On the morphology of MoS 2 slabs on MoS 2 /Al 2 O 3 catalysts: the influence of Mo loading[END_REF][START_REF] Chen | Role of Citric Acid in Preparing Highly Active CoMo/Al 2 O 3 Catalyst: From Aqueous Impregnation Solution to Active Site Formation[END_REF][START_REF] Garcia | New insight into the support effect on HDS catalysts: evidence for the role of Mo-support interaction on the MoS 2 slab morphology[END_REF][START_REF] Chen | On the morphology of MoS 2 slabs on MoS 2 /Al 2 O 3 catalysts: the influence of Mo loading[END_REF]. First, the dried catalytic precursor in oxidic form was grounded and pressed into a self-supported wafer (10 mg for a disc of 2.01 cm 2 ) precisely weighted and positioned into a quartz IR cell with CaF2 windows. Then, the catalyst pellet was sulfided at 623 K (3 K•min -1 ) at atmospheric pressure under 30 mL•min -1 10% H2S/H2 for 2 h. After that, the reactor was flushed by Ar for 10 min and evacuated during 1 h at 623 K.

Finally, after being cooling down to room temperature, the sulfided pellet was transferred to the IR optical path. Prior to the adsorption experiments, the sample was sulfided in situ in the IR cell. For this, the catalysts was sulfided in a gas mixture containing 10% H2S/H2 (30 mL·min -1 ) at 623 K for two hours with a heating rate of 3 K·min -1 . After sulfidation, the cell was flushed with Ar and evacuated up to P<1·10 -4 Pa until the catalyst reached room temperature. Then, CO adsorption was performed at low temperature (~100 K) to avoid any reaction with the catalysts surface. Small calibrated doses of CO were introduced into the IR cell until equilibrium pressure of 133 Pa. After each CO introduction, FTIR spectra were recorded with 256 scans and a resolution of 4 cm -1 using Nicolet Nexus FT-IR spectrometer equipped with a MCT Detector.

HRTEM and High-resolution Scanning Transmission Electron Microscopy -High Angular Annular Dark Field (HR STEM-HAADF).

All presented TEM images were taken using a double corrected JEOL ARM 200F cold FEG microscope operated at 200 kV. First, slab length and stacking degree distributions of sulfide slabs were determined manually by measuring around 300 slabs per sample from HRTEM images. The image treatment was performed using the commercial software from GATAN (DIGITALMICROGRAPH). The nanostructure and morphology of the MoS2 slabs were analyzed by high resolution scanning transmission electron microscopy (HR STEM) using a high angle annular dark field (HAADF) detector. The catalyst precursors were firstly sulfided at 623 K (heating rate of 3 K·min -1 ) and 0.1 MPa for 2 h under a 30 mL·min -1 flow of 10% H2S/H2. Then, to limit detrimental exposure to air, the sulfided catalysts were unloaded from the sulfidation reactor under argon flow and deposited into absolute ethanol. A few drops of the suspension of catalyst were put on a 300 mesh copper grid with holey carbon film. The STEM images presented in this manuscript were obtained in HAADF mode and the acquisition of an image lasted about 30 s with a resolution of 1024 pixels x 1024 pixels, (30 μs of exposure time for each spot in the scanning mode). The possible damage associated with the heating effects caused by the incident beam in the nanolayers is always a factor to consider. In this study, it was not observed significant changes during the acquisition of the images at 200 kV with a beam current value of about 12 μA. Observations at 80 kV were also performed, but no significant differences in terms of slab stability were noticed. Therefore, it was concluded that the operation with an acceleration of 200 kV is compatible with our purpose of morphological analysis.

Following an approach similar to that of our recent work [START_REF] Zavala-Sanchez | High-resolution STEM-HAADF microscopy on a γ-Al2O3 supported MoS2 catalyst-proof of the changes in dispersion and morphology of the slabs with the addition of citric acid[END_REF], a set of 20 individual nanoparticles (observed on HAADF mode) of samples CoMo(CA/M=0)/Al2O3, CoMo(CA/M=2)/Al2O3 and CoMo(CA/M=2)/Al2O3 after catalytic reaction (used catalyst), was taken through contrast optimization of the images. This in order to obtain statistical information about the morphology of the Co promoted MoS2 slabs. In these individual nanoparticles, the outline of the shape was drawn and the corresponding particle lengths were measured, as well as the area of the particle with the help of the Mesurim Pro software. The limited number of particles analyzed by STEM-HAADF compared to HRTEM is explained by the difficulty to observe isolated specimens with faceted edges in these realistic samples. This is associated to the high metal loading present in this type of catalysts. Considering that for each slab, the dispersion is the ratio of edge atoms per total atoms, the calculated dispersion (D) values were obtained through the measurement of slab area and perimeter with the following equation ( 1):

𝐷 = 𝑎𝑡𝑜𝑚𝑠 𝑎𝑡 𝑡ℎ𝑒 𝑒𝑑𝑔𝑒 𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑎𝑡𝑜𝑚𝑠 𝑝𝑒𝑟 𝑠𝑙𝑎𝑏 = 𝑃 𝑑 ⁄ -𝑁 𝑐 𝐴 𝑑 2 ⁄ (1)
Where: D = dispersion P = particle perimeter (nm) d = atomic diameter Mo (nm) Nc = number of corner atoms in the slab A = particle area (nm 2 )

Calculating a numeric value of dispersion will more directly reflect the effect of citric acid in the morphology of the studied catalysts than simple observation.

Results and discussion

IR/CO Characterizations of Sulfided CoMo(CA/M =0 and 2)/Al2O3 Catalysts.

Low-temperature (liquid nitrogen temperature) CO adsorption followed by in situ IR spectroscopy (IR/CO) allows distinguishing non-promoted (MoS2) sites and promoted (CoMoS) sites [START_REF] Chen | Role of Citric Acid in Preparing Highly Active CoMo/Al 2 O 3 Catalyst: From Aqueous Impregnation Solution to Active Site Formation[END_REF][START_REF] Travert | CO Adsorption on CoMo and NiMo Sulfide Catalysts: A Combined IR and DFT Study[END_REF][START_REF] Maugé | FT-IR Study of CO Adsorption on Sulfided Mo/Al2O3 Unpromoted or Promoted by Metal Carbonyls: Titration of Sites[END_REF] on the supported CoMo catalyst. Figure 1 reports the IR/CO spectra obtained on the CoMo(CA/M = x)/Al2O3 catalysts. The two bands located around 2189 and 2156 cm -1 are ascribed respectively to CO interaction with Lewis acid sites and hydroxyl groups of the Al2O3 support.

The strong band at around 2072 cm -1 is attributed to the CO adsorption on Copromoted MoS2 edges (the so-called CoMoS sites), while the small shoulder at 2115 cm -1 is attributed to CO adsorption on unpromoted MoS2 sites [START_REF] Travert | Parallel between infrared characterisation and ab initio calculations of CO adsorption on sulphided Mo catalysts[END_REF][START_REF] Chen | Role of Citric Acid in Preparing Highly Active CoMo/Al 2 O 3 Catalyst: From Aqueous Impregnation Solution to Active Site Formation[END_REF]. In addition in CoMo(CA/M = 2)/Al2O3 sample, a second band in the promoted massive is observed at 2060 cm -1 , assigned by Dominguez et al. [START_REF] Garcia | Effet du support sur la morphologie et l'activité des catalyseurs d'hydrodésulfuration[END_REF] to partially promoted S-edge. It was observed that the CO adsorption bands at 2072 cm -1 and 2060 cm -1 increase with the addition of citric acid, demonstrating that citric acid favors strongly the formation of CoMoS sites. This effect on promoted edge site concentration has previously been reported with other chelating agents such as ethylene diaminotetraacetic acid (EDTA) [START_REF] Lélias | Effect of EDTA addition on the structure and activity of the active phase of cobaltmolybdenum sulfide hydrotreatment catalysts[END_REF] and nitrilo triacetic acid (NTA) [START_REF] Lélias | Effect of NTA addition on the formation, structure and activity of the active phase of cobalt-molybdenum sulfide hydrotreating catalysts[END_REF][START_REF] Lélias | Effect of NTA addition on the structure and activity of the active phase of cobalt-molybdenum sulfide hydrotreating catalysts[END_REF].

Length and stacking degree determined by HRTEM analysis

A careful process of measuring the length of the slabs present in each sample was carried out by modifying the contrast to make sure to see the smallest particles. The addition of citric acid leads to a decrease of the average slab length from 2.90 ± 0.12 nm to 1.95 ± 0.10 nm. The length distribution is given in Figure 2. catalysts and ascribed to the reduced interaction between the (Co)MoS slabs and the support due to the addition of citric acid [START_REF] Cattaneo | The Relationship between the Structure of NiMo/SiO2 Catalyst Precursors Prepared in the Presence of Chelating Ligands and the Hydrodesulfurization Activity of the Final Sulfided Catalysts[END_REF].

Effect of citric acid addition in the 2D-morphology of CoMo(CA/M=x)/Al2O3

Figure 3 presents the HR STEM-HAADF micrographs of sulfided CoMo(CA/M=0)/Al2O3 (Figure 3A-C) and CoMo(CA/M=2)/Al2O3 (Figure 3D-F) respectively. As expected for the HAADF mode, the observed particles have a good quality contrast and, therefore, the acquisition parameters used are suitable for revealing the 2D morphology of the slabs in these industrial grade catalysts. On a large field of view, sample CoMo(CA/M=0)/Al2O3 consist of CoMoS slabs that are distributed over the alumina support in the form of plates. Higher contrast in some zones of both set of images are attributed to an increase of metal density. This is observed more in sample CoMo(CA/M=0)/Al2O3 and is related to agglomerated or stacked slabs. On the other hand, striking changes are observed for the sample that was prepared in presence of citric acid. The particles observed in the CoMo(CA/M=2)/Al2O3 sample are characterized by their considerable small size compared to the ones observed in CoMo(CA/M=0)/Al2O3, and in many occasions, what resembles groups of a few atoms and even individual atoms dispersed all over the support are observed. Such groups and individual atoms were also visible in the images of sulfided CoMo (CA/M=0)/Al2O3 sample but in much lesser extent. The zoom-in in figure (3-E), puts in evidence a particle with dispersion of 1, this is, all the atoms of the slab are exposed. Their interatomic distances, that are of the order of 3.1 Å, are in good agreement with the ones expected for Mo-Mo interatomic distances of MoS2 disulfide [START_REF] Baubet | Quantitative Two-Dimensional (2D) Morphology-Selectivity Relationship of CoMoS Nanolayers: A Combined High-Resolution High-Angle Annular Dark Field Scanning Transmission Electron Microscopy (HR HAADF-STEM) and Density Functional Theory (DFT) Study[END_REF][START_REF] Deepak | Direct Imaging and Identification of Individual Dopant Atoms in MoS2 and WS2 Catalysts by Aberration Corrected Scanning Transmission Electron Microscopy[END_REF]. Recently, we reported a similar observation for non-promoted MoS2 prepared as well with and without citric acid as a chelating agent [START_REF] Zavala-Sanchez | High-resolution STEM-HAADF microscopy on a γ-Al2O3 supported MoS2 catalyst-proof of the changes in dispersion and morphology of the slabs with the addition of citric acid[END_REF]. To better understand the improvement of the dispersion degree, measurements of the length and perimeter were carried out in each one of the samples, and using the Eq. 1, it was found that the addition of citric acid decreases the average length from 2.60 ± 0.50 to 1.32 ± 0.50 nm. The calculated particle dispersion (D) value passes from 48% for CoMo (CA/M=0)/Al2O3 to 78% for CoMo (CA/M=2)/Al2O3. Table 1 gathers together the measured and calculated parameters for each of the analyzed samples. Since the catalytic HDS reaction activity is ascribed to the coordinatively unsaturated sites (CUS) of the slabs, located in the edges of the slab, an increase of dispersion is therefore associated to an increase in activity.

Observation of CoMo/Al2O3 used catalyst.

Very often TMS catalysts are analyzed after the sulfidation stage, nevertheless, the fact that during the catalytic reaction stage the catalyst is contacted with hydrogen and also with H2S is sometimes overlooked. One question that arises is the stability of the very small agglomerates observed in particular in the sulfided CoMo (CA/M=2)/Al2O3 catalyst. If we take into account that during the catalytic reaction the catalyst is in contact with H2 and with H2S present as a byproduct, could there be a subsequent transformation or reorganization of such agglomerates? To answer this, the sulfided CoMo (CA/M=2)/Al2O3 sample was analyzed after being subjected for 72 hours of catalytic test in order to know if the nanoslabs undergo any alteration.

Therefore, this analysis is a way to observe their stability against prolonged reaction conditions. The sulfided CoMo (CA/M=2)/Al2O3 was chosen as used sample since it For the three samples, the mean length value obtained from the HR STEM-HAADF images is lower than the one obtained from the HRTEM ones, underlying that it can be hard to distinguish the smallest particles in HRTEM. Moreover, the length distribution from both techniques also differ: more homogeneous lengths are observed in HR STEM-HAADF than in HRTEM. Similar results were previously reported in [START_REF] Zavala-Sanchez | High-resolution STEM-HAADF microscopy on a γ-Al2O3 supported MoS2 catalyst-proof of the changes in dispersion and morphology of the slabs with the addition of citric acid[END_REF]. Note that the point to point resolution for STEM-HAADF technique (0.78 Å) is also better than that for HRTEM (1.0 Å).

The dispersion value obtained from the STEM-HAADF slab images is closer to the theoretical dispersion obtained with hexagonal shape in absence of citric acid while with citric acid it tends to be closer to the theoretical dispersion calculated for triangular slabs. Compared to the Mo/Al2O3 sample, it seems that the effect of citric acid on the slab shape occurs in the opposite direction. Nevertheless, this result could also indicate that these triangular particles are exposing S-edges, i. e. that citric acid still favors S-edge exposition. Future work along with spectroscopy is presently being carried out in order to understand better and confirm this hypothesis.

Conclusion

HR STEM-HAADF unequivocally demonstrates that adding citric acid in the preparation of CoMo catalysts significantly reduces the size of CoMoS nano-slabs.

This result goes hand in hand with the infrared spectra results observed, where the band associated with the active CoMoS sites increases considerably. Numerous agglomerates formed by a few atoms with a high degree of dispersion are detected in the sulfide sample CoMo(CA/M=2)/Al2O3. These clusters are proved to be stable after being subjected to a thiophene HDS reaction for 72 hours in the same way as the nanometric ones. This demonstrates that the catalysts retain their integrity during the catalytic reaction process and therefore that analyzing the catalyst after sulfidation is relevant to understand the catalyst under HDS operational conditions.

Next step is to study the variation of atomic contrast in several slabs of CoMo catalysts in order to verify the decoration model as it has been reported recently for NiW catalysts.

Figure 1 .

 1 Figure 1. IR spectra of CO adsorption (-173 °C and 133 Pa CO at equilibrium) on CoMo(CA/M = 0)/Al2O3 and CoMo(CA/M = 2)/Al2O3 catalysts sulfided with 10% (v/v) H2S/H2 at atmospheric pressure and 350 °C for 2 h.

Figure 2 .

 2 Figure 2. HR-TEM analysis of slab length distribution: images of CoMo(CA/M=0)/Al2O3, CoMo(CA/M=2)/Al2O3 and CoMo(CA/M=2)/Al2O3 after 72 h of thiophene reaction.

  /M = 2)/Al 2 O 3

Figure 3 .

 3 Figure 3. HR STEM-HAADF micrographs of CoMoS particles of CoMo(CA/M=0)/ Al2O3 (A-C) and CoMo(CA/M=2)/Al2O3 (D-F) of different areas. Inset E: zoom in of particle with dispersion degree of 1.0.

Figure 4 . 2

 42 Figure 4. HR STEM-HAADF micrographs of CoMoS particles of CoMo(CA/M=2)/Al2O3 after 72 h of thiophene HDS reaction at 623K. The arrows indicate that the few atoms agglomerates observed in CoMo(CA/M=2)/Al2O3 after sulfidation are still present.

Figure 5

 5 Figure 5 allows the comparison of the three sulfided promoted samples,

Figure 5 .

 5 Figure 5. Distribution of the measured length and STEM-HAADF images of the particles of CoMo(CA/M=0)/Al2O3, CoMo(CA/M=2)/Al2O3 and CoMo(CA/M=2)/Al2O3 after thiophene HDS reaction (72h).

Table I .

 I Parameters calculated from the HR TEM and HR STEM-HAADF images for the γ-Al2O3 supported Catalyst.

					CoMo(CA/M=2)
	Mode	Parameters	CoMo(CA/M=0) CoMo(CA/M=2)	after 72 h HDS
					reaction
	TEM	Average length (nm) Stacking	2.90 ± 0.12 1.80 ± 0.04	1.95 ± 0.10 2.20 ± 0.05	1.94 ± 0.12 2.26 ± 0.05
	HAADF	Average length (nm)	2.60 ± 0.50	1.32 ± 0.50	1.36 ± 0.50
		Dispersion (measured)	0.48 ± 0.08	0.78 ± 0.08	0.76 ± 0.08
		*Theoretical Dispersion (triangle)	0.58	0.86	0.8
		*Theoretical Dispersion (hexagon)	0.43	0.7	0.63

*Calculated from the model Kasztelan for triangular and hexagonal slabs

[START_REF] Kasztelan | Preparation of Co-Mo-γAl2O3 and Ni-Mo-γAl2O3 catalysts by pH regulation of molybdenum solution. characterization of supported species and hydrogenation activities[END_REF]

.

Acknowledgements

L. Zavala-Sanchez acknowledges the Mexican National Council for Science and Technology (CONACYT) for the Ph. D. grant. The authors acknowledge LABEX EMC3 for the financial support to MIMOSA project.


Christian Bordes

Samuel Maveyraud
email: samuel.maveyraud@u-bordeaux4.fr

The Friedman's and Mishkin's hypotheses (re)considered

Keywords: JEL classi…cation: E52, E31, E32 in ‡ation, uncertainty, output growth, GARCH, CF …lter

This paper o¤ers to investigate both the Friedman's and Mishkin's hypotheses on the consequences of in ‡ation on output growth. To this end, we …rst base these hypotheses in a uni…ed framework. Second, in an empirical work based on OECD countries, we distinguish between short-medium and long run and between headline and core in ‡ation.

We get two main results. First, nominal uncertainty and in ‡ation are positively linked. Second, headline in ‡ation negatively Granger causes output gap (US, Japan, France) but has no e¤ect on potential output growth (US excepted) whereas core in ‡ation impacts potential output growth (UK, Germany) but not output gap (US excepted).

Introduction

Negative e¤ects of in ‡ation on output growth are well known at least in the long run. For [START_REF] Friedman | From New Deal banking reform to World War II in ‡ation[END_REF]: "In ‡ation, particularly highly variable in ‡ation, interferes with growth by (a) introducing static into the messages transmitted by the price system, increasing the uncertainty facing individuals and business enterprises, which encourages them to divert attention from productive to protective activities, and (b) inducing governments to adopt such counterproductive false cures as price controls and incomes policy. These adverse e¤ects have sometimes been more than o¤set by other forces, so that high in ‡ation has not prevented rapid growth" (Friedman and Schwartz, 1980, pp. 55-6). Conversely, the stabilization of in ‡ation rate at a low level is able to improve output growth. This friedmanite hypothesis was carefully scrutinized and related econometric studies undertaken can be classi…ed into the following three surrounding issues. The …rst one relates to whether high in ‡ation rates might result in more variable in ‡ation and to, subsequently, create more unpredictability in future in ‡ation. However, there appears contradictory evidence of the causal relationship between in ‡ation levels and in ‡ation uncertainty and this leaves macroeconomists uneasy whether the Friedman-Ball [START_REF] Friedman | Nobel lecture: in ‡ation and unemployment[END_REF][START_REF] Ball | Why does high in ‡ation raise in ‡ation uncertainty?[END_REF] hypothesis really holds (see [START_REF] Davis | The level and uncertainty of in ‡ation: results from OECD forecasts[END_REF][START_REF] Fountas | The relationship between in ‡ation and in ‡ation-uncertainty in the UK: 1885-1998[END_REF][START_REF] Fountas | In ‡ation and output growth uncertainty and their relationship with in ‡ation and output growth[END_REF][START_REF] Grier | The asymmetric e¤ects of uncertainty on in ‡ation and output growth[END_REF][START_REF] Kontonikas | In ‡ation and in ‡ation uncertainty in the United Kingdom: Evidence from GARCH modeling[END_REF][START_REF] Thornton | High and variable in ‡ation: further evidence on the Friedman hypothesis[END_REF]. The second issue relates to the welfare loss associated with in ‡ation so that unpredictable future in ‡ation tends to distort the e¢ cient allocation of resources through the price mechanism and, hence, to lower total output. Studies that tested the link between the in ‡ation variability and the output growth include [START_REF] Grier | The e¤ects of real and nominal uncertainty on in ‡ation and output growth: some GARCH-M evidence[END_REF], [START_REF] Hayford | In ‡ation uncertainty, unemployment uncertainty and economic activity[END_REF], Fountas 2 et al. (2002), Aspergis (2004) and [START_REF] Grier | The asymmetric e¤ects of uncertainty on in ‡ation and output growth[END_REF]. The results found in these studies are mixed. And …nally, the last issue investigates the link between the level and the variability of both in ‡ation and growth (refer to [START_REF] Wilson | On measuring the response of real GDP growth to changes in in ‡ation volatility[END_REF][START_REF] Grier | The asymmetric e¤ects of uncertainty on in ‡ation and output growth[END_REF][START_REF] Wilson | The links between in ‡ation, in ‡ation uncertainty and output growth: New time series evidence from Japan[END_REF][START_REF] Fountas | In ‡ation, output growth, and nominal and real uncertainty: Empirical evidence for the G7[END_REF], which addresses the simultaneous feedback between the variables of interest. The results derived are also mixed and depend on the samples and econometric methodologies employed.

In the short run, [START_REF] Mishkin | Does Stabilizing In ‡ation Contribute to Stabilizing Economic Activity?[END_REF] hightlights in a seminal paper that in ‡ation also negatively impacts output growth. Both demand and supply shocks can lead to unstable in ‡ation and a diminution of output growth below its potential level.

For example, a negative shock to aggregate demand (a decline of consumer or …rm con…dence) implies a cut of households or …rms spendings. As a result, future in ‡ation and output gap will decrease. Supply shocks can also lead to in ‡ation unstability and a fall of output gap. For New Keynesian models, this negative correlation between in ‡ation and growth is mainly due to misalignment of employment to its e¢ cient level [START_REF] Blanchard | Comment on 'The new Neoclassical synthesis and the role of monetary policy[END_REF], Ercberg, Henderson and Levin (2000)) and ine¢ ciencies in labor market search [START_REF] Blanchard | A new Keynesian model with unemployment[END_REF], Galí, Gertler and Lopez-salido (2007)). On its side, the New Neoclassical Synthesis shows that, as some prices move sluggishly, in ‡ation distorts relative prices between goods and services [START_REF] Goodfriend | The new Neoclassical synthesis and the role of monetary policy[END_REF], [START_REF] Rotemberg | An optimization-based econometric framework for the evaluation of monetary policy[END_REF], [START_REF] Woodford | Interest and prices: foundations of a theory of monetary policy[END_REF]) and thus reduces ouput growth.

Hence, according to both Friedman's and Mishkin's hypotheses, we must expect a signi…cant causality of in ‡ation on output gap and potential output growth. Furthermore, as the increase of in ‡ation must lead to a diminution of output growth, we must observe that nominal variables negatively explain real variables.

In this paper, we o¤er to evaluate the impacts of in ‡ation on both output gap and potential output growth for main OECD countries. Implicitely based on the Friedman's and Mishkin's hypotheses, the mandate assigned to Central Bank is to achieve price stability at a medium-long run. In this perspective, we may expect that in ‡ation in ‡uences both the output gap and the medium-long run output growth.

Moreover, we distinguish between headline in ‡ation and core in ‡ation, measured by CPI less food and energy. The concept of core in ‡ation, developed in the early 1970s by Eckstein (see [START_REF] Eckstein | Core In ‡ation[END_REF], can be de…ned as the in ‡ation rate for which the employment of labor and capital would be stabilized. According to [START_REF] Catte | Assessing the value of indicators of underlying in- ‡ation for monetary policy[END_REF], core in ‡ation "is connected to the fundamental drivers of the in ‡ation process: excess demand for goods and services, changes in unit labour costs and, ultimately, monetary policy" and is assimilated to "the generalised component of in ‡ation -that is, with the common factor (or a set of common factors) driving all CPI components". These de…ntions imply that in ‡ation.can be decomposed in two components: core in ‡ation and a transient component. This distinction between these two components of in ‡ation must be associated with the distinction made by [START_REF] Friedman | In ‡ation. Causes and consequences[END_REF] "between a steady in ‡ation, one that proceeds at a more or less constant rate, and an intermittent in ‡ation, one that proceeds by …ts and starts". Most Central Banks base their in ‡ation calculations on consumer price index (Hereafter CPI) rather than on Producer Price Index because CPI well re ‡ects reductions in economic e¢ ciency [START_REF] Rich | A review of core in ‡ation and an evaluation of its measures Federal Reserve Bank of New York[END_REF]: …rst, CPI variations capture the component of aggregate price movements of goods and services and second, CPI variations imply indexing arrangements that involve somewhat arbitrary reallocations of income across group.

The more familiar core in ‡ation measure as aggregate price growth excluding food and energy was …rst analyzed by Robert Gordon [START_REF] Gordon | The impact of aggregate demand on prices[END_REF] and was then adopted by most Central Banks. However, this measure of core in ‡ation is subject to debates among Central Bankers. Reserve Federal shifted from CPI less food and energy in February 2000 toward Personal Consumption Expenditures (PCE) de ‡ator less food and energy as measure of core in ‡ation in order to take into account the quarter modi…cations of consumption baskets. CPI and PCE indexes are both based on consumer prices but the latter one is calculated as a chained index. Note, however, that these two measures of core in ‡ation both exclude food and energy prices. For [START_REF] Mishkin | Headline versus core in ‡ation in the conduct of monetary policy, speech delivered at the Business Cycles[END_REF], member of the Board of the Reserve Federal System, core in ‡ation has many limitations, even if it cannot take into account all possible shocks, is valuable for the conduct of monetary policy as it "provides some greater signal about persistent movements in in ‡ation than does headline in ‡ation itself". On its side, J.C. [START_REF] Trichet | Globalisation, in ‡ation and the ECB monetary policy[END_REF], the ECB governor , worries about the exclusion of energy and food prices in the calculation of European core in ‡ation:

"ECB research has in particular shown that for the euro area standard measures of core in ‡ation, excluding energy and unprocessed food prices, do not have desirable leading indicator properties" [START_REF] Trichet | Globalisation, in ‡ation and the ECB monetary policy[END_REF]. This concern is explained by the recent rise in world prices of raw materials and their possible e¤ects on mediumlong run price stability inside the Euro area and hence on output growth.

This paper provides several contributions. First, we base both the Friedman's and Mishkin's hypotheses in a theroretical macroeconomic framework. More precisely, we develop a uni…ed model to highlight all possible origins of uncertainty.

Second, we implement a Christiano and Fitzgerald …lter (hereafter CF …lter) to decompose output series in potential output growth, output gap and real uncertainty.

Moreover, as Fountas and Karanasos (2007), we extract in ‡ation variability using a threshold-GARCH or TGARCH model where asymmetric e¤ects of good news and bad news are possible but contrary to them, we use both headline in ‡ation and core in ‡ation to extract uncertainty.

The paper is organized as follows: the theoretical framework relative to the links between monetary disturbances and macroeconomic performance is proposed in section 2 ; section 3 presents the original procedure; section 4 reports our results. Section 5 concludes.

In ‡ation, ouput growth, nominal and real uncertainty: A uni…ed framework

The foregoing analysis of the paper is based on the following theoretical framework:

y t y p t + z t + " t (1)
y p t = + y p t 1 + 2 (2)
z t = ' (L) (i t E t 1 t ) + (L) z t + 2 + g t (3)
t = k m + (L) t + (L) z t + " t " t t 1 N 0; 2 t (4) = r + (5)
i t = + [E t t+k ] + z [E t z t+l ] + M m M T LR t m (6)
i t = i t 1 + (1 ) i t + t ( 7
)
m t p t = k y y t k i i t + w t (8)
where: y t is the actual value of real GDP; z t is the output gap; Eq. ( 4) is a « two-pillar » Phillips curve [START_REF] Gerlach | Interest Rate Setting by the ECB: Words and Deeds[END_REF]. It is a standard Eq. ( 6) and Eq. ( 7) represent the central bank's behaviour. Eq. ( 6) indicates that the desired value of the nominal interest rate for the current period (i t ) is determined by monetary authorities according to an Ireland's rule [START_REF] Ireland | Money's role in the monetary business cycle[END_REF]. Like an in ‡ation target, this rule calls for the Central bank to adjust the short-term nominal interest rate in reaction to deviations of expected in ‡ation and output from their steady-state levels to assure monetary stability in the short-run to medium term. However, this rule also calls for the Central bank to adjust the short-term interest rate to deviations of actual money growth from its medium-term to long run reference value corresponding to the steady state level of nominal money demand. In the case where the interest rate is determined according to the Friedman's k-percent money supply rule.

y
Eq. ( 8) is a Friedman-Meltzer type speci…cation of the demand for money [START_REF] Nelson | News-Magazine Monetarism[END_REF] where it depends negatively on the return rate on its substitutesequities, bonds, physical capital -and positively on the interest rate on monetary assets.

The model encapsulates the proposal we are interested in here. According to Eq. ( 2) and Eq. ( 3), in ‡ation uncertainty, due mainly to monetary disturbances, impacts negatively on economic growth as represented by potential output growth and output gap.

Empirical analysis

According to the theoretical model, the test of the Friedman's and Mishkin's hypotheses is based on the comparison between in ‡ation rate, in ‡ation variability (nominal uncertainty), output variability (real uncertainty), output gap and potential output growth. In order to get the convenient series, we implement an original method based on the CF …lter to get output components and the TGARCH model to extract nominal uncertainty.

Decompostion of GDP using the CF …lter

The decomposition of GDP in a cyclical, a non-cyclical component and an error term in order to test the Friedman's hypothesis can be apprehensive about …lters as:

y t y p t + z t + " t
where y p t is the potential output growth, z t the output gap and " t the real shock. In what follows, we implement the CF …lter to output data, according to its robustness. We proceed as follows. First, we seasonally adjust ouput series using Census X12 and we isolate the trend cycle component, Ct, that measures variation due to the long-term trend, the business cycle, and other long-term cyclical factors.

Then, using the CF …lter, we isolate the business cycle from the potential output.

where the considered frequency domain lies between 18 months (1.5 years) to 96 months (8 years). At this stage, output is decomposed as the sum of the cyclical series including the business cycle. Real shocks (considered hereafter as real uncertainty) are obtained by substracting the trend cycle component from the seasonally adjusted output series.

Extraction of nominal uncertainty

After having decomposed output, we use a TGARCH(p,q) model for extracting nominal uncertainty. The model assumes that the persistence in the dynamics comes from the conditional second moment of the series. Although the GARCH(p,q) conditional variance model is widely used, there are other alternatives to represent the conditional variance of the in ‡ation rate. In the standard GARCH(p,q) model, positive and negative residuals have a symmetric impact on the conditional variance. However it seems relevant to incorporate a threshold element and introduces a Threshold-GARCH (p,q) model, hereafter, TGARCH, that allows for negative residuals to have a di¤erent impact on the conditional variance than do positive residuals [START_REF] Glosten | On the relation between the expected value and the volatility of the nominal excess return on stocks[END_REF]):

t = 0 + 1 (L) t + 2 (L) z t + " t " t t 1 N 0; 2 ;t 2 ;t = ! + (L) " 2 t + " 2 t 1 I t 1 + (L) 2 ;t (L) = p X i=1 i L i ; (L) = q X i=1 i L i ; 1 (L) = r X i=1 1i L i ; 2 (L) = r X i=1 2i L i I t 1 = 8 > < > :
1; if " t 1 < 0 0; otherwise where t is the in ‡ation rate; z t is the output gap component on potential output, " t error term; t 1 , available information set in period t-1; L stands for the lag operator, 2 ;t , the conditional variance of in ‡ation which depends linearly on past squared-error terms, past variances and on the negative shocks of 0 ; 1 ; 2; ! > 0; i ; i 0 are parameters to be estimated.

I t 1 = 1 if " t

Data and results

The empirical work is based on monthly data of Consumer Price Index (headline CPI), Consumer Price Index less food and energy (core CPI) and the Industrial Price Index (IPI) obtained from the OECD database for US, Japan, UK, Canada, France and Germany. These series are respectively used as proxies of general price level and output. Our analysis covers the period 1957M2-2007M12.

We proceed in several steps.

First, using the methodology presented in section 3, we decompose IPI series in a cyclical, a non-cyclical component and an error term (See …gures in annex).

Second, we test for unit roots. ADF tests (with 4 lags) indicate that we can reject the null hypothesis for all considered series at 1% level (Table 1).

[Table 1 here] Third, we extract the variability of (headline) in ‡ation (i.e. nominal uncertainty) using TGARCH models (Table 2). The relevant variables are determined by a stepwise analysis based on a Schwarz criterion where the maximum number of lags for in ‡ation and real output growth is equal to 12.

Results show that headline in ‡ation and real output growth are signi…cantly and positively linked in US, UK and Germany. For the other countries, our results highlight that real output growth is not a signi…cant determinant of in ‡ation. The conditional variance equation of in ‡ation rate (in ‡ation uncertainty) shows that asymetries are signi…cant for US, Japan, UK and Germany but not for Canada and France. Moreover, each variance is de…ned and stable as the sum of coe¢ cients is positive and inferior to 1.

[Table 2 here]

In order to implement Granger causality tests of the Friedman's hypothesis, we build a VAR model between in ‡ation, nominal uncertainty, real uncertainty (as de…ned in section 3) and output gap or potential output growth. The optimal number of lags is determined by a Schwarz criterion.

With regards to the short run where output gap is included to the VAR system (table 3), Granger causality tests o¤er three main results. First, they indicate a causality between in ‡ation and uncertainty of in ‡ation US, Japan, UK, Canada and France but not in Germany. According to the VAR coe¢ cients this link is positive, which coincides to a part of the Mishkin's hypothesis: the higher the in ‡ation, the higher the nominal uncertainty. Second, our results bring to the fore that output gap positively Granger causes in ‡ation in all considered OECD countries, France excepted. Third, evidence is mixed regarding the link between nominal uncertainty and output gap: even if the sign is negative in all cases, as suggested by the Mishkin's hypothesis, Granger causality is only signi…cant for US, Japan and France 1 .

[Table 3 here]

The test of the Friedman's hypothesis o¤ers mixed results (table 4). As in the short run, in ‡ation positively Granger causes nominal uncertainty, Germany excepted. However, the link between nominal and real variables is not signi…cant in most countries: in ‡ation negatively Granger causes potential output growth only for the US.

Table 4 also highlights that potential output growth negatively Granger causes real uncertainty in all considered countries.

[Table 4 here]

This last result may be explained by the fact that headline in ‡ation is not the best measure of long run in ‡ation and thus cannot have any impact on potential 1 As the series of nominal uncertainty is built from estimated coe¢ cients, we test the robustness of these results with bootstrap techniques. Results are quite robust (and available on request). output growth [START_REF] Mishkin | Headline versus core in ‡ation in the conduct of monetary policy, speech delivered at the Business Cycles[END_REF]. Hence, we proceed to a similar analysis (i.e., VAR and Granger analysis) with core in ‡ation, based on the CPI less food and energy (tables 5 and6).

In the short run, our results show that core in ‡ation gives quite similar results as those obtained with headline in ‡ation (table 5). Core in ‡ation positively Granger causes nominal uncertainty in all countries, Canada and Germany excepted. Results are less clear about the link between core in ‡ation and output gap: if output gap positively Granger causes core in ‡ation US, Japan and Germany, core in ‡ation has no impact on output gap for any country. This result may be explained by the fact that core in ‡ation only modi…es output growth in the medium-long run.

[Table 5 here]

In the long run, however, the link between nominal variables and potential output growth is signi…cant only for UK and Germany (table 6). For UK, results are quite surprising as core in ‡ation positively Granger causes potential output growth. Note however that nominal uncertainty negatively Granger causes potential output growth. Hence, core in ‡ation, measured as CPI less food and energy prices movements does not appear to be a better indicator of long run price movements, Germany and UK excepted.

[Table 6 here]

Concluding remarks

This paper provides several …ndings. First, the Friedman's and Mishkin's hypotheses are formulated within an uni…ed theoretical framework. Second, we suggest to decompose output growth in potential output growth, output gap and a residual in order to disinguish between the short run Mishkin's statement and the mediumlong run Friedman's hypothesis. Third, we implement TGARCH methods in order to extract nominal uncertainty. Then, we both test the Mishkin and Friedman's proposals with Granger causality tests on headline and core in ‡ation, nominal uncertainty, real uncertainty, output gap and potential output growth.

Our results show that both headline and core in ‡ation are positively linked with nominal uncertainty. Headline in ‡ation negatively Granger causes output gap in US, Japan, UK Canada and Germany but has no impact on potential output growth, US excepted. Compared to headline in ‡ation, core in ‡ation, measured as CPI less food and energy prices movements, is better for taking into account fundamental drivers of the in ‡ation process only in UK and Germany. This result may be explained by the fact that our measure of core in ‡ation is a basic measure that is not necessarily the most accurate: a prolongation to this paper would be to implement our method by considering …ner measures of core in ‡ation.

  backward-looking Phillips curve, but with the intercept (k m ) depending on the medium term /long run (MTLR) component of money supply growth relative to the MTLR component of real money demand growth. (L) and (L) stand for lag operators.

  More precisely, econometric techniques o¤er the possibility of extracting cycles that move in given frequency bands (cf.[START_REF] Hodrick | Postwar Business U.S. Cycles: An Empirical Investigation[END_REF][START_REF] Baxter | Measuring business cycles: Approximate bandpass …lters for economic time series[END_REF][START_REF] Christiano | The band pass …lter[END_REF]. Broadly, these methods can be estimated in the frequency domain by minimizing the conditional expected mean-squared error:M in : E (y t b y t ) 2 jz ; z (z 1 ; :::; z T ) b y tis the linear projection of onto every element in the data set, z t is the component allowed to pass through the …lter.Through these common characteristics, each …lter-that are the Hodrick-Prescott …lter (1997) (Hereafter the HP …lter), the Baxter-King …lter (1999) (hereafter the BK …lter)) and the CF …lter-presents singular features. Contrary to the HP …lter, the BK and CF …lters can be implemented as well for business cycles (between 1.5 years to 8 years) than for higher frequencies (short run shocks) and lower frequencies (the long run or potential output). Compared to the BK …lter, the CF …lter uses all observations of a series while the BK …lter does not (Cf. Shelley and Wallace, 2005).

  1 < 0 and 0 otherwise. If the asymmetry parameter is negative then negative in ‡ationary shocks result in the reduction of in ‡ation uncertainty.

We include variables in the mean equation by implementing a stepwise process based on a Schwarz criterion. More precisely, the method begins with no added regressors. We select the variable that would lead to the lowest Schwarz value of the TGARCH model were it added to the regression. If the Schwarz value is lower than the Schwarz value of selected regression, the variable is added. The selection goes on by selecting the variable that gives the lowest Schwarz value of the regression, given the inclusion of the …rst variable. The procedure stops when the Schwarz value of regressions with not yet included variables is greater than the Schwarz value of the selected regression. The maximum number of lags for each variable is 12.

Table 1 ADF unit root tests

 1

	Variables	US	Japan	UK	Canada	France	Germany
	Real uncertainty	-12.65***	-12.17***	-12.79***	-12.15***	-16.23***	-11.93***
	Output gap	-4.14***	-4.56***	-4.25***	-4.48***	-4.55***	-5.00***
	Potential output growth	-6.95***	-3.53***	-7.32***	-6.19***	-7.14***	-5.69***
	Inflation	-5.58***	-6.83***	-6.01***	-5.48***	-4.21***	-9.14***
	Core inflation	-4.49***	-5.17***	-5.57***	-4.72***	-4.12***	-8.43***
	Nominal uncertainty	-5.73***	-3.23**	-2.88**	-7.66***	-8.81***	-8.39***
	Note: ***, **,

* respectively indicates rejection of the null at 1%, 5% and 10% significance levels. ADF unit root tests are implemented with 4 lags.

Table ( s)

 (

Table 2 T-GARCH(1,1) models

 2

		US	Japan	UK	Canada	France	Germany
	Mean equation (dependent variable : Headline inflation)
	Inflation
	t-1	0.28***		0.09***		0.29***	0.16***
	t-2				0.12**
	t-3				0.13***	0.18***
	t-4				0.17***
	t-6		0.12***	0.15***		0.21**
	t-7	0.16***
	t-9				0.12**
	t-10						0.13**
	t-11	0.15***
	t-12	0.22***	0.55***	0.66***	0.27***	0.25***	0.5***
	Output growth
	t-2	0.05***
	t-5			0.04*
	t-7			0.04***
	t-12						0.02***
	₀	3.79E-04***	4.68E-04***	3.42E-04***	7.02E-04***	2.46E-04***	4.66E-04***
	Variance Equation ( , )
		7.46E-07***	5.18E-07*	2.06E-07	8.79E-07*	2.76E-06**	1.30E-06**
	̂	0.28***	0.09***	0.14***	0.07**	0.16	0.06*
	̂	-0.2**	-0.13***	-0.17***	-0.06	-0.1	0.18*
		0.71***	0.94***	0.93***	0.89***	0.4*	0.69***
	Note: ***, **, *

respectively indicates rejection of the null at 1%, 5% and 10% significance levels.

Table 3 Granger-causality tests between headline inflation, nominal uncertainty, real uncertainty and output gap

 3

	US	Headline inflation	Nominal uncertainty	Output gap	Real uncertainty
	Headline inflation		115.13***(+)	1.89(+)	13.6**(-)
	Nominal uncertainty	8.91(+)		12.79***(-)	2.71(-)
	Output gap	18.09***(+)	6.12(+)		8.43(+)
	Real uncertainty	4.88(+)	3.98(+)	2.86(+)
	Japan	Headline inflation	Nominal uncertainty	Output gap	Real uncertainty
	Headline inflation		393.82***(+)	4.75(+)	7.97*(+)
	Nominal uncertainty	80.9***(+)		12.05***(-)	4.28(-)
	Output gap	35.64***(+)	10.25**(+)		4.37(+)
	Real uncertainty	1.87(-)	7.82*(+)	2.87(-)
	UK	Headline inflation	Nominal uncertainty	Output gap	Real uncertainty
	Headline inflation		344.08***(+)	1.14(+)	7.29(+)
	Nominal uncertainty	32.3***(+)		6.79(-)	2.42(-)
	Output gap	15.35***(+)	7.48(+)		8.19(+)
	Real uncertainty	7.1(+)	7.07(-)	11.2**(+)
	Canada	Headline inflation	Nominal uncertainty	Output gap	Real uncertainty
	Headline inflation		218.64***(+)	1.1(+)	3.09(-)
	Nominal uncertainty	15.29***(-)		5.75(-)	2.11(-)
	Output gap	9.18*(+)	4.44(+)		6.28(-)
	Real uncertainty	1.07(+)	3.28(-)	4.72(+)
	France	Headline inflation	Nominal uncertainty	Output gap	Real uncertainty
	Headline inflation		117.34***(+)	1.28(-)	3.91(-)
	Nominal uncertainty	6.88(-)		15.84***(-)	3.39(+)
	Output gap	5.31(+)	7.08(+)		7.31(+)
	Real uncertainty	8.87(+)	1.54(-)	20.65***(+)
	Germany	Headline inflation	Nominal uncertainty	Output gap	Real uncertainty
	Headline inflation		4.55(+)	2.23(+)	4.05(+)
	Nominal uncertainty	17.67***(+)		0.29(-)	2.51(-)
	Output gap	8.08*(+)	9.12*(+)		2.3(-)
	Real uncertainty	4.09(-)	3.88(+)	6.69(+)

Notes: A (+) (resp. (-))

indicates that the sum of the lagged coefficients of the causing variable is positive when (+) or negative when (-). ***, **, * respectively indicates rejection of the null at 1%, 5% and 10% significance levels. Numbers are the Chi-squared.

Table 5 Granger-causality tests between core inflation, nominal uncertainty, real uncertainty and output gap

 5

	US	Core inflation	Nominal uncertainty	Output gap	Real uncertainty
	Core inflation		27.38***(+)	2.78(+)	12.19*(-)
	Nominal uncertainty	30.23***(+)		13.97**(-)	28.81***(-)
	Output gap	19.19***(+)	11.76*(+)		10.13(-)
	Real uncertainty	6.05(+)	2.6(+)	4.64(+)
	Japan	Core inflation	Nominal uncertainty	Output gap	Real uncertainty
	Core inflation		154.62***(+)	0.46(+)	2.28(+)
	Nominal uncertainty	64.64***(+)		4.21(-)	1.16(+)
	Output gap	28.88***(+)	21.52***(+)		1.9(+)
	Real uncertainty	2.24(+)	3.4(-)	1.89(-)
	UK	Core inflation	Nominal uncertainty	Output gap	Real uncertainty
	Core inflation		214.51***(+)	6.45(-)	9.27(+)
	Nominal uncertainty	15.77**(+)		10.35(-)	3.44(-)
	Output gap	9.98(+)	7.82(+)		10.13(+)
	Real uncertainty	15.28**(+)	9.63(-)	17.91***(+)
	Canada	Core inflation	Nominal uncertainty	Output gap	Real uncertainty
	Core inflation		33.65***(-)	3.03(-)	3.58(-)
	Nominal uncertainty	6.86(+)		3.57(-)	6.15(-)
	Output gap	3.98(+)	3.49(+)		5.94(-)
	Real uncertainty	1.06(+)	1.24(-)	4.57(+)
	France	Core inflation	Nominal uncertainty	Output gap	Real uncertainty
	Core inflation		113.02***(+)	3.44(-)	6.93(-)
	Nominal uncertainty	11.94**(+)		9.62*(-)	8.36(-)
	Output gap	3.43(+)	8.2(+)		6.77(+)
	Real uncertainty	13.76**(+)	2.62(-)	22.1***(-)
	Germany	Core inflation	Nominal uncertainty	Output gap	Real uncertainty
	Core inflation		3.44(-)	2.93(-)	4.97(+)
	Nominal uncertainty	7.54(+)		1.05(-)	0.87(-)
	Output gap	10.03*(+)	2.61(+)		2.07(-)
	Real uncertainty	2.49(-)	3.67(+)	7.49(+)

Notes: A (+) (resp. (-))

indicates that the sum of the lagged coefficients of the causing variable is positive when (+) or negative when (-). ***, **, * respectively indicates rejection of the null at 1%, 5% and 10% significance levels.

Annex: Decomposition of potential output, cyclical output and residual output using the Christiano and Fitzgerald's filter