Anaïs Portet

Richard Galinier

Damien Lassalle

Alexandre Faille

Benjamin Gourbal

David Duval
email: david.duval@univ-perp.fr

Hemocyte siRNA uptake is increased by 5' cholesterol-TEG addition in Biomphalaria glabrata , snail vector of schistosome

Keywords: Biomphalaria glabrata, hemocyte, RNA interference, Cholesteryl TEG, BgTEP1

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Introduction

The fresh water snail Biomphalaria glabrata is one of the main vectors of the human flatworm parasite, Schistosoma mansoni in the Americas, responsible for Schistosomiasis, the second most widespread human parasitic disease after malaria [START_REF] Batterman | Sustainable control of water-related infectious diseases: a review and proposal for interdisciplinary health-based systems research[END_REF][START_REF] Colley | Human schistosomiasis[END_REF][START_REF] Nelwan | Schistosomiasis: Life Cycle, Diagnosis, and Control[END_REF]). As gastropods are essential for human schistosomiasis transmission, new strategies emphasizing on snail control to reduce schistosomiasis transmission in the field need to be developed. Among these vector control strategies, synthetic or natural chemical agent used as molluscicide [START_REF] Augusto | Effects of the Environment on Developmental Plasticity and Infection Success of Schistosoma Parasites -An Epigenetic Perspective[END_REF][START_REF] Coelho | Critical analysis of molluscicide application in schistosomiasis control programs in Brazil[END_REF][START_REF] Souza | Molluscicide control of snail vectors of schistosomiasis[END_REF][START_REF] Who | Guidelines for laboratory and field testing of molluscicides for control of Schistosomiasis[END_REF] and introduction of snail pathogens [START_REF] Duval | A novel bacterial pathogen of Biomphalaria glabrata: a potential weapon for schistosomiasis control?[END_REF][START_REF] Sandland | Interspecific antagonism and virulence in hosts exposed to two parasite species[END_REF] or predators [START_REF] Gashaw | Assessment of the potential of competitor snails and African catfish (Clarias gariepinus) as biocontrol agents against snail hosts transmitting schistosomiasis[END_REF][START_REF] Sokolow | Reduced transmission of human schistosomiasis after restoration of a native river prawn that preys on the snail intermediate host[END_REF][START_REF] Younes | Biological control of snail hosts transmitting schistosomiasis by the water bug, Sphaerodema urinator[END_REF]) into environment are investigated. Combating disease transmission requires a better understanding of the snail-parasite immunological interaction at the molecular level. In B. glabrata/S. mansoni interaction, a strain dependent compatibility polymorphism occurs [START_REF] Theron | Multi-parasite host susceptibility and multihost parasite infectivity: a new approach of the Biomphalaria glabrata/Schistosoma mansoni compatibility polymorphism[END_REF]. This compatibility gradient extends from totally incompatible interactions (i.e., resistant) to fully compatible interactions (i.e., susceptible). Such compatibility polymorphism arises from several genetic factors [START_REF] Castillo | Biomphalaria glabrata immunity: Post-genome advances[END_REF][START_REF] Coustau | Advances in gastropod immunity from the study of the interaction between the snail Biomphalaria glabrata and its parasites: A review of research progress over the last decade[END_REF][START_REF] Mitta | The Compatibility Between Biomphalaria glabrata Snails and Schistosoma mansoni: An Increasingly Complex Puzzle[END_REF][START_REF] Pila | Schistosomiasis from a Snail's Perspective: Advances in Snail Immunity[END_REF][START_REF] Portet | Integrated multi-omic analyses in Biomphalaria-Schistosoma dialogue reveal the immunobiological significance of FREP-SmPoMuc interaction[END_REF], but can also be influenced by non-genetic factors modulated by environmental cues [START_REF] Augusto | Effects of the Environment on Developmental Plasticity and Infection Success of Schistosoma Parasites -An Epigenetic Perspective[END_REF]) such as temperature [START_REF] Knight | Susceptibility of Snails to Infection with Schistosomes is influenced by Temperature and Expression of Heat Shock Proteins[END_REF], pollution [START_REF] Ibrahim | Energy allocation patterns in Biomphalaria alexandrina snails in response to cadmium exposure and Schistosoma mansoni infection[END_REF] or UV exposure [START_REF] Ruelas | Effects of UVB on interactions between Schistosoma mansoni and Biomphalaria glabrata[END_REF]).

Deciphering molecular mechanisms by which snails and parasites interact appears essential to finding new ways for manipulating snail intermediate hosts [START_REF] Tennessen | Hyperdiverse Gene Cluster in Snail Host Conveys Resistance to Human Schistosome Parasites[END_REF] or for introducing in the field snails selected for their resistance alleles in order to decrease prevalence of human schistosomiasis [START_REF] Coelho | Transmission control of schistosomiasis mansoni by introduction of a resistant strain of Biomphalaria tenagophila in areas where transmission is maintained by this species[END_REF][START_REF] Marques | Reduced susceptibility of a Biomphalaria tenagophila population to Schistosoma mansoni after introducing the resistant Taim/RS strain of B. tenagophila into Herivelton Martins stream[END_REF].

To validate the role of candidate genes that support the biochemical/molecular pathways involved in resistant and susceptible interactions, gene expression knockdown by RNA interference (RNAi) appeared as the widely used approach in invertebrate models [START_REF] Lamacchia | Silencing of genes and alleles by RNAi in Anopheles gambiae[END_REF][START_REF] Li | Advances in the use of the RNA interference technique in Hemiptera[END_REF]Li et al. 2020b;[START_REF] Robalino | Doublestranded RNA and antiviral immunity in marine shrimp: inducible host mechanisms and evidence for the evolution of viral counter-responses[END_REF], and remains the best strategy available for functional validation in Biomphalaria snails, until CRISPR-Cas gene knockout development [START_REF] Famakinde | Treading the Path towards Genetic Control of Snail Resistance to Schistosome Infection[END_REF][START_REF] Coelho | Diminished adherence of Biomphalaria glabrata embryonic cell line to sporocysts of Schistosoma mansoni following programmed knockout of the allograft inflammatory factor[END_REF]. Indeed, there are few examples of CRISPR editing in gastropods to date [START_REF] Abe | The development of CRISPR for a mollusc establishes the formin Lsdia1 as the long-sought gene for snail dextral/sinistral coiling[END_REF][START_REF] Perry | CRISPR/Cas9-mediated genome modification in the mollusc, Crepidula fornicata[END_REF], but their successful approaches pave the way to this technology development in closely related species. The first RNAi on Biomphalaria sp. was conducted to invalidate expression of Fibrinogen Related Protein 2 (FREP2), a lectin protein involved in snail immune response, with double-stranded RNA (dsRNA) and resulted in about 80% reduction of targeted transcript expression without revealing any particular phenotype [START_REF] Jiang | In vivo and in vitro knockdown of FREP2 gene expression in the snail Biomphalaria glabrata using RNA interference[END_REF]. RNAi-mediated knockdown of FREP3 with a pool of siRNA induces a phenotype switch whereby some resistant snails became susceptible to Echinostoma paraensei [START_REF] Hanington | Role for a somatically diversified lectin in resistance of an invertebrate to parasite infection[END_REF] or to S. mansoni [START_REF] Hanington | A somatically diversified defense factor, FREP3, is a determinant of snail resistance to schistosome infection[END_REF]). The same strategy using combinations of siRNA duplexes was previously used to demonstrate the key role of FREPs in Biomphalaria innate immune memory, reducing the expression of the FREP2, 3 and 4 genes by 2-to 8-fold and rendered infected snails more susceptible to parasite [START_REF] Pinaud | A Shift from Cellular to Humoral Responses Contributes to Innate Immune Memory in the Vector Snail Biomphalaria glabrata[END_REF]. The RNAi strategy used also to demonstrate the key role of the cytokine BgMIF (Macrophage Migration Inhibitor Factor) or the growth factor BgGranulin in hemocyte proliferation and activation promoting parasite encapsulation respectively [START_REF] Garcia | Involvement of the cytokine MIF in the snail host immune response to the parasite Schistosoma mansoni[END_REF]Pila et al. 2016a). The siRNA-mediated knockdown of BgTLR (Toll-Like Receptor), a transmembrane protein expressed in some hemocytes showed defective phagocytosis and partially suppressed the resistance phenotype of BS90 snails (Pila et al. 2016b). All the studies described above show an injection into the pericardial cavity of B. glabrata snails of naked interfering RNA molecules [START_REF] Baron | Parental transfer of the antimicrobial protein LBP/BPI protects Biomphalaria glabrata eggs against oomycete infections[END_REF] or incubated with transfection reagent [START_REF] Allan | Schistosome infectivity in the snail, Biomphalaria glabrata, is partially dependent on the expression of Grctm6, a Guadeloupe Resistance Complex protein[END_REF]Pila et al. 2016a). A non-invasive siRNA delivery has been successfully developed by soaking juvenile snails in PEI (polyethylenimine) a cationic polymer [START_REF] Knight | Polyethyleneimine (PEI) mediated siRNA gene silencing in the Schistosoma mansoni snail host, Biomphalaria glabrata[END_REF]. Despite all these experiments, the nature and number of transfected cells in snails remain unknown.

In the present study, we used a siRNA targeting BgTEP1, a thioester-containing protein mainly expressed in hemocytes [START_REF] Portet | BgTEP: An Antiprotease Involved in Innate Immune Sensing in Biomphalaria glabrata[END_REF], the snail immune cells. It has been suggested that BgTEP1 could play an opsonin role, binding S. mansoni sporocyst surface [START_REF] Portet | BgTEP: An Antiprotease Involved in Innate Immune Sensing in Biomphalaria glabrata[END_REF]. It was also demonstrated that BgTEP1 is able to bind an immune complex formed by SmPoMuc (Schistosoma mansoni Polymorphic Mucins) and FREPs (Li et al. 2020a;[START_REF] Mone | A Large Repertoire of Parasite Epitopes Matched by a Large Repertoire of Host Immune Receptors in an Invertebrate Host/Parasite Model[END_REF]).

Herein we focused on siRNA delivery into hemocytes for efficient gene silencing in vivo. To achieve this, we designed a chemical modification on the 5' end of siRNA by conjugation with a Cholesteryl-TEG (Triethylene Glycol). This lipophilic addition has been shown to be beneficial to increase siRNA uptake by HeLa cells [START_REF] Shmushkovich | Functional features defining the efficacy of cholesterol-conjugated, self-deliverable, chemically modified siRNAs[END_REF]. First, modified and unmodified Cy3-labeled siRNA were compared in hemocytes ex vivo collected from snails to monitor siRNA delivery. Then, flow cytometry analysis was conducted to follow delivery efficiency in hemocytes in-vivo after Chol-TEG siRNA injection into living snails. Finally, silencing of BgTEP1 transcript target, using cholesteryl-TEG siRNA was done. The efficiency of BgTEP1 silencing was assessed at both RNA and protein levels by RT-qPCR and western blot.

Then BgTEP1-siRNA treated snails were exposed to miracidia of S. mansoni to monitor any changes in infection phenotype.

Materials and Methods

Biological Materials

B. glabrata originated from Guadeloupe (BgGUA2) and its sympatric strain of S. mansoni (SmGH2) were used for experimental approaches. BgGUA2 was provided from M. Blouin (Oregon State University) in 2013. These snails were collected in 2005 from Dans Fond on the island of Guadeloupe (DFO; N:16°18.500', W:061°30.720'). For infection experiments, each snail was individually exposed for 12 h to 10 miracidia in 5mL of pond water. Breeding conditions and maintenance of parasite cycle have been conducted as previously described [START_REF] Portet | Sympatric versus allopatric evolutionary contexts shape differential immune response in Biomphalaria / Schistosoma interaction[END_REF].

The laboratory and experimenters possessed an official certificate from the French Ministry of National Education, Research, and Technology, CNRS and DRAAF Languedoc Roussillon for experiments on animals, animal housing, and animal breeding (# A66040; decree # 87-848, October 19, 1987;and authorization # 007083).

siRNA uptake and interference.

Small interfering RNA duplexes against BgTEP1 and Green Fluorescent Protein (GFP used as control) were synthetized and modified by Eurogentec Company and purified by standard SePOP desalting. In this study, two siRNA targeting BgTEP1 transcripts mRNA (GenBank accession No. FJ480411) which are 5' GAC-AGA-UUC-UCA-UCA-AAC-A and 5' GAG-UAU-GAU-UUA-CCA-AGA-U and one against the cnidarian GFP (GenBank accession No. EU430082): 5' CAA-GCU-GAC-CCU-GAA-GUU-C were synthetized. The GFP siRNA was designed with and without a Cholesteryl-TEG added in 5' to assess if this modification can increase siRNA cellular uptake. A Cy3 dye was linked to the 3' termini of each RNA molecule for siRNA duplex in order to follow cellular uptake by flow cytometry approach. To investigate the silencing effect on the BgTEP1 mRNA level and on snail susceptibility phenotype to S. mansoni, the different siRNAs (BgTEP and GFP) were designed only with a Cholesteryl-TEG added in 5'end. Two siRNA targeting BgTEP1 transcripts mRNA were thus injected in equimolar quantity in the same snails.

Each duplex siRNA were annealed and shipped dried by the manufacture (Eurogentec). siRNA was suspended in sterile Chernin's balanced salt solution (CBSS). Concentrations of siRNA were adjusted so injected volumes do not exceed 5µl. Each siRNA was injected into the cardiac sinus of B. glabrata snails (7-8 mm in diameter), using a 50 µl Hamilton syringe with a 26s needle (Hamilton) (Baeza [START_REF] Garcia | Involvement of the cytokine MIF in the snail host immune response to the parasite Schistosoma mansoni[END_REF].

siRNA delivery into hemocytes ex vivo.

500 µL of hemolymph were recovered by head-foot retraction from pool of 3 adult snails, transferred to a 1.5 ml microcentrifuge low DNA binding tube and then incubated with 2 µg of Cy3-labeled GFP siRNA with and without Chol-TEG at 24°C after mixed by gentle inversion.

siRNA delivery was monitored from 30 min to 1, 2, 4, 6 and 8 h post-incubation by flow cytometry analysis (see FACS analysis section). For each experimental point, 4 biological replicates were performed. For comparing the percentage of fluorescent cells following the different treatments a Fisher Exact test was used, results were considered significant for P value ≤ 0.05. For comparison of siRNA incorporation over the kinetic after injection, a Kruskall-Wallis with Dunn post-hoc tests were used to test significant differences (P value ≤ 0.05) between experimental conditions.

siRNA delivery on hemocytes in vivo.

2 µg of Cy3-labeled Chol-TEG siRNA targeted GFP (500 ng/µl) were injected in the snail pericardial cavity. Cellular uptake of siRNA was evaluated at 2, 4, 6, 12 and 24 h after injection (n=4 snails for each condition). The hemolymph was recovered as described above. A negative control consisting in analysing the hemocyte fluorescence from uninjected snails was also performed. Then, a similar approach was conducted by varying the amount of siRNA injected to snails (2, 5 and 10 µg). Hemolymph was recovered 2 h after injection from 4 individual snails used as biological replicates. Significant differences in kinetic of siRNA cellular uptake following injection were tested using Kruskall-Wallis followed by Dunn post-hoc test (P value ≤ 0.05). Significant differences between doses of siRNA were tested using a Mann-Whitney U test.

Results were considered significant when P value ≤ 0.05.

Flow cytometry analysis.

After both in vivo and in vitro siRNA delivery, 100 µL of hemolymph were fixed with 100 µL of 4% paraformaldehyde solution in PBS for 5 min. Then, hemocytes were collected after centrifugation at 1,000 rpm, 10 min and re-suspended in PBS snail as previously described [START_REF] Pinaud | A Shift from Cellular to Humoral Responses Contributes to Innate Immune Memory in the Vector Snail Biomphalaria glabrata[END_REF]. Hemocyte preparations were stored at 4°C and analysed one day after storage. The Flow Cytometry was performed using a FACS Canto BD Biosciences (RIO Imaging Platform, Montpellier, France). For each sample, around 10,000 events were counted. The results were analysed and visualised using the FlowJo V 10.0.8 software. To demonstrate internalization of cholesteryl-TEG siRNA into hemocytes, 500 µL of hemolymph from pool of 3 adult snails were plated for 1 hour on polystyrene chamber slides. Then, hemocytes were incubated 2 hours with 2 µg of Cy3-labeled siRNA. Hemocytes were washed twice in PBS and fixed in 4% paraformaldehyde for 5 minutes. After rinsing with PBS, actin filaments were stained with phalloidin conjugated with Alexa 488 (Thermo Fisher) for 15 minutes and the cell nucleus with DAPI (Biotum) for 30 seconds as previously described [START_REF] Portet | BgTEP: An Antiprotease Involved in Innate Immune Sensing in Biomphalaria glabrata[END_REF]). After rinsing, slides were mounted in Dako fluorescent mounting medium (Dako) and examined using a fluorescence confocal laser-scanning microscope (Zeiss LSM 700, Bio-Environment platform).

For presentation, images were imported into ImageJ software.

RNA extraction and Quantitative RT-PCR analysis

Using HPLC syringe, 10 µg of Chol-TEG siRNAs targeting BgTEP1 (quantity ratio 1:1) or GFP were injected in snail pericardial cavity (2µg/µl). Hemolymph was recovered at 1, 2, 3 and 4 days after injection from 4 independent pools of 3 snails. Hemocytes were recovered by centrifugation and hemocyte total RNA was then extracted using the Total RNA Purification Micro Kit (Norgen Biotek) according to the manufacturer's instructions. Reverse transcription was performed from 100 ng of RNA with oligo dT using Maxima H Minus First Strand cDNA Synthesis Kit with dsDNase (Thermo Scientific, Whaltham, Massachussetts, USA) according to manufacturer's instructions. Quantitative PCR (Q-PCR) was performed using NO ROX SYBR® Master Mix blue dTTP (Takyon) and run on LightCycler 480 thermocycler (Roche) according to the manufacturer's instructions. Sequence of primers used for BgTEP1 amplification (forward: 5' CGT-ACT-TAC-CCT-CGC-TC, reverse: 5' ACC-ATT-AGA-TCC-ACT-GGA-AGA-TA) and ribosomal protein S19 (accession number : XM_013211381) (forward: 5' TTC-TGT-TGC-TCG-CCA-C, reverse: 5' CCT-GTA-TTT-GCA-TCC-TGT-T) were designed using LightCycler Probe Design software version 1.0 (Roche Diagnostics). 2 µl of cDNA diluted to 1/20 in ultrapure water was used in a reaction mixture containing 0.1 µM of each primer. The cycling program was as follows: denaturation step at 95°C for 2 min, 40 cycles of amplification (denaturation at 95°C for 10 s, annealing and elongation at 60°C for 20 s), with a final step at 60°C for 5 min. QPCR was ended by a melting curve step from 65 to 97°C with a heating rate of 0.11°C/s and continuous fluorescence measurement. The cycle threshold (Ct) was determined using the second derivative method of the LightCycler 480 Software release 1.5 (Roche). Sequence of PCR amplicon was checked by Sanger sequencing. The relative expression of BgTEP1 was calculated with the ΔΔCt method as the efficiency of both couple of primers presented the same PCR amplification efficiency. Briefly, BgTEP1 expression was normalised to the endogenous control, the ribosomal protein S19, for each condition (ΔCt, CtBgTEP1-CtS19). Then, the relative expression of BgTEP1 was determined by the ΔΔCt method based on this expression of the nonsilencing control group (ΔΔCt, ΔCt (siRNA injected) -ΔCt (untreated snails)). For graphical representation, relative expression data presented are determined as the ratio between relative expression of BgTEP1 with respect to S19 level under BgTEP and GFP interference condition (Pfaffl, 2011;[START_REF] Knight | Polyethyleneimine (PEI) mediated siRNA gene silencing in the Schistosoma mansoni snail host, Biomphalaria glabrata[END_REF]. Kruskall-Wallis with Dunn post-hoc tests were used to test significant differences (P value ≤ 0.05) between experimental conditions.

BgTEP1 protein expression level analysis.

Using the procedure described previously, 10 µg of Chol-TEG BgTEP1 siRNA were injected in 4 replicates of 3 snails for each condition. Cell free hemolymph was collected 1, 2, 3 and 4 days post injection and protein content were determined using 2-D Quant Kit (GE Healthcare). Five microliters (15 µg total protein / µL of hemolymph) of hemolymph was denatured 5 minutes at 99°C in 1X Laemmli buffer plus β-mercaptoethanol, before proteins separation on 7.5% SDSpolyacrylamide gel and transferred onto a 0.2 µm Hybond ECL membrane (GE Healthcare) using a Transblot transfer system (Bio-Rad). After saturation over a period of 3 h at room temperature in TBSTM [1× TBS (500 mM Tris-HCl, 1.5 M NaCl, pH 7.5), 0.05% Tween-20, 5% non-fat milk], the protein blots were incubated overnight at 4°C in TBSTM, with a 1:5,000 dilution of the rat polyclonal anti-BgTEP1-N-ter antibody (Agro-Bio), raised against the recombinant BgTEP1 N-terminal part (amino acid 204 to 521 from BgTEP1 protein sequence (GenBank ID QEQ12617)). The blots were washed three times with TBST, and further incubated with 1:5,000 dilution of the commercial horseradish peroxidase-conjugated rabbit anti-rat IgG (H+L) antibody (CliniSciences #6180-05). Blots were finally washed three times with TBST, and one time with TBS, and then revealed in the presence of an enhanced chemiluminescent substrate (SuperSignal West Pico Plus Chemiluminescent Substrate, Thermo Scientific). Image acquisition was performed using ChemiDoc MP Imaging System (Bio-Rad) for 3 seconds. Blot picture and relative quantitative analysis of bands were performed using Image Lab Software version 4.0.1.

Biomphalysin was used as internal control for protein loading and to exclude a protein degradation. A western blot on the same samples was performed according to the same procedure used for BgTEP1 protein detection. To reveal Biomphalysin in the cell-free hemolymph, a polyclonal antibody raised against this toxin (Agro-Bio) and an HRP-conjugated goat anti-rabbit IgG secondary antibody (ImmunoPure Antibody, Pierce) were diluted at 1:1000 and 1:7000 respectively in TBST.

Effect of BgTEP1 mRNA silencing on S. mansoni infection phenotype.

BgGUA2 snails were injected with 10 µg of Chol-TEG siRNA duplexes specific for BgTEP1 (43 snails) and GFP (34 snails) and individually exposed for 12h to 10 S. mansoni GH2 miracidia in 5 ml of pond water at 3 days after siRNA injection. Then, 16 days after parasite exposure, the snails were fixed in Raillet-Henry solution. The prevalence (P: % of snail infected) and the intensity (I: number of parasites per infected snail) were determined by counting the primary sporocysts present in each snail tissue as described previously [START_REF] Portela | Evidence for specific genotype-dependent immune priming in the lophotrochozoan Biomphalaria glabrata snail[END_REF]. Briefly, the snails were relaxed in water containing an excess of crystalline menthol for 6 hours. The snail shell was removed and the body was fixed in modified Raillet-Henry's solution (930 ml distilled water, 6g sodium chloride, 50ml formol 40%, 20 ml 95 acetic acid). The presence of Sp1 in each snail was numbered by visual inspection and meticulous dissection of the snail tissues. Following Raillet-Henry's fixation the Sp1 were readily observable as opaque white bodies within a yellow snail tissue background. Significant changes in prevalence and intensity were tested by Fisher exact test and Mann-Whitney U test.

Results

Ex vivo siRNA delivery into hemocyte is enhanced by lipid-conjugation.

To assess the delivery of siRNA conjugated to cholesterol in snail hemocytes, naked and modified (Chol-TEG) GFP-siRNA were coupled with the fluorochrome Cy3. Two micrograms of labelled GFP-siRNA were added to 500 µL of freshly collected hemolymph from a pool of adult snails. Monitoring of cell uptake by FACS revealed that siRNA were quickly internalized by hemocytes in both conditions and showed a high number of fluorescent cells after 30 min of exposition (Fig. 1 and Fig. S1). More siRNA were uptaken by cells when cholesterol was conjugated (Fig. 1A andB), 47 % of cells were counted with a cytosolic fluorescence compared to 5% of cells when using unmodified siRNA (Fisher exact test, p= 0.00001, n=4 per group). No significant differences were observed when comparing unmodified siRNA to naïve snails hemocyte auto-fluorescence (Fisher exact test, p= 0.3687, n=4 for unmodified siRNA and n=8 for control)) (Fig. 1C). Cholesterol conjugation enhances significantly the cellular uptake of siRNA. Also, internalization of siRNA did not increase over time in in vitro condition; the number of fluorescent hemocytes remains similar after 30 min or 8 h exposure time for both conditions (GFP-cy3 Kruskal-Wallis test p = 0.145552, df=5, n=24, H=8.200 ; Chol-TEG-GFP-cy3 Kruskal-Wallis test p = 0.643170, df=5, n=24, H=3.369826, n=4 per group) (Fig. 1C). Therefore, Chol-TEG siRNA was used for subsequent experiments.

In vivo siRNA delivery into hemocyte.

To further validate our GFP-siRNA delivery condition in vivo, 2 µg of Chol-TEG-siRNA against GFP mRNA were injected in snail pericardial cavity. Flow cytometry analysis was performed on hemolymph recovered between 2h and 24h post-injection to follow hemocyte uptake efficiency in vivo. Overall, the percentage of internalized Chol-TEG-siRNA is much lower than that obtained in vitro. Indeed, only 1.9 to 3.3 % of hemocytes have incorporated Chol-TEG-siRNA regardless of exposure time (no significant differences over time: Kruskal-Wallis test p = 0.062544, df=4, n=20, H=8.9428) (Fig. 2) compared to around 50% for in-vitro condition after 30 min (Fig. 1C). Therefore, to optimize cellular uptake, increasing amounts of siRNA have been injected into snails and hemocytes were recovered 2 h post-injection. The proportion of fluorescent cells after 2 h post-injection increased with higher Chol-TEG siRNA concentrations (Fig. 3). Hemocytes have internalized significantly more Chol-TEG-siRNA from 11% or 55% after the injection of 5 µg or 10 µg respectively (Mann-Whitney U-test, U= 0 ; z-score = -2.50672 ; P= 0.00604, n=4 per condition) (Fig 3). Consequently, we decided to use a dose of 10 µg of siRNA coupled with Cholesteryl-TEG for further analysis.

Knockdown of BgTEP expression in guadeloupean snails.

Once we have demonstrated that cholesterol conjugation promotes siRNA delivery into hemocytes, its efficiency for BgTEP1 gene silencing was tested. BgTEP1 is a thioestercontaining protein playing the role in innate immunity as complement-like factor secreted in snail hemolymph (Li et al. 2020a;[START_REF] Mone | A Large Repertoire of Parasite Epitopes Matched by a Large Repertoire of Host Immune Receptors in an Invertebrate Host/Parasite Model[END_REF][START_REF] Wu | Proteomic analysis of Biomphalaria glabrata plasma proteins with binding affinity to those expressed by early developing larval Schistosoma mansoni[END_REF]. Furthermore, a previous report showed that BgTEP1 could act as an opsonin by binding to the surface of diverse intruders [START_REF] Portet | BgTEP: An Antiprotease Involved in Innate Immune Sensing in Biomphalaria glabrata[END_REF]. Whole snails were microinjected with 10 µg of Chol-TEG siRNA against BgTEP1 or GFP (control). Transcriptional expression analysis of BgTEP1 was focused on circulating hemocytes, normalised with the S19 housekeeping gene and compared with Chol-TEG siGFP injection. Thus, we found a significant reduction in BgTEP expression of 4-, 8.5-, and 5,5-fold at day 2, 3 and 4, respectively, when compared to day 1 after siRNA injection (Kruskall-Wallis test: P = 0.000054, df=4, n=45, H=24.848) (Fig. 4A). The efficiency of knockdown was also confirmed at the protein level. Indeed, we observed a decrease in plasmatic BgTEP1 protein in hemolymph from nearly 50% at day 1 to 80% at day 2 and 3 and to 90% at 4 days after siRNA injection, while the amount of Biomphalysin used as control for protein loading did not vary significantly (Fig. 4B). Since mRNA level of BgTEP1 was decreased 2 to 4 days after siRNA injection, BgGUA2 snails were exposed to 10 miracidia of S. mansoni GH2 at the third day (GFP and BgTEP1). No differences in prevalence and intensity of infection were observed between siTEP1-(P= 14.7%, I=1, n=34) and siGFP (P=18.6 %, I= 1.12, n=43) -control injected snails at 16 days following infection (Fisher exact test, P = 0.3687).

Discussion

RNA interference (RNAi) or post-transcriptional gene silencing (PTGS) is a biological process highly conserved across animal and plant kingdoms and involved in gene expression or translation inhibition [START_REF] Almeida | RNA silencing and genome regulation[END_REF][START_REF] Fire | Potent and specific genetic interference by double-stranded RNA in Caenorhabditis elegans[END_REF][START_REF] Plasterk | The silence of the genes[END_REF]. The RNAi pathway is triggered by short double-stranded RNAs about 21 to 23 base pairs in length which can target complementary mRNA leading to its silencing [START_REF] Almeida | RNA silencing and genome regulation[END_REF]. The RNAi strategy has made possible the investigation of gene function on phenotypic level via the loss of function even if it is transient. The use of dsRNA remains a molecular tool of choice in functional genomics, especially when the CRISPR technology is not yet established for the studied organism. Several modifications can be grafted on short nucleic acid such as 2' ribose substitutions [START_REF] Alagia | siRNA and RNAi optimization[END_REF][START_REF] Allerson | Fully 2'-modified oligonucleotide duplexes with improved in vitro potency and stability compared to unmodified small interfering RNA[END_REF][START_REF] Malek-Adamian | Effect of Sugar 2',4'-Modifications on Gene Silencing Activity of siRNA Duplexes[END_REF] or chemically-modified internucleotide phosphodiester [START_REF] Alagia | siRNA and RNAi optimization[END_REF][START_REF] Deleavey | Designing chemically modified oligonucleotides for targeted gene silencing[END_REF][START_REF] Kotikam | Amide-Modified RNA: Using Protein Backbone to Modulate Function of Short Interfering RNAs[END_REF] to increase gene-silencing efficiency. In addition, achieving high RNAi efficiency remains a challenge in particular to target genes in different tissues.

Delivery systems for siRNA based on non-viral vectors such as liposomal vesicle or lipid-nucleic conjugation have been developed to remove barriers to the cellular uptake of siRNA linked to its hydrophilic property [START_REF] De Paula | Hydrophobization and bioconjugation for enhanced siRNA delivery and targeting[END_REF][START_REF] Khalil | Optimization of siRNA delivery to target sites: issues and future directions[END_REF]). However, extrapolation of these results or strategies remains difficult in most invertebrates and requires updates on the siRNA administration method (microinjection, soaking, feeding), and the development of delivery systems (viral or non-viral vector) [START_REF] Selkirk | The development of RNA interference (RNAi) in gastrointestinal nematodes[END_REF][START_REF] Whitten | Novel RNAi delivery systems in the control of medical and veterinary pests[END_REF]Zhu & Palli 2020).

In Biomphalaria snail, since the first study reporting the proof of concept for siRNA-mediated gene silencing [START_REF] Jiang | In vivo and in vitro knockdown of FREP2 gene expression in the snail Biomphalaria glabrata using RNA interference[END_REF], only one has been reported comparing the effect of siRNA and long dsRNA soaked juvenile snails on the silencing of the Cathepsin B gene using a cationic polymer vector [START_REF] Knight | Polyethyleneimine (PEI) mediated siRNA gene silencing in the Schistosoma mansoni snail host, Biomphalaria glabrata[END_REF]). In the present study, we initially focused on the optimization of hemocyte siRNA uptake by conjugating with cholesterol as it was known to be a driving force to enhance cell-penetrating nucleic acid sequences (Zheng & Tai 2020). Interestingly, the delivery of Chol-siRNAs into HeLa cells has been shown to be very rapid and saturate in less than one hour [START_REF] Gilleron | Identification of siRNA delivery enhancers by a chemical library screen[END_REF]. After initially reporting that cholesterol conjugation promotes siRNA delivery on hemocytes, we focused on BgTEP1 gene silencing. Indeed, it was shown that this complement factor like protein is largely expressed by snail hemocytes and released in hemolymph [START_REF] Portet | BgTEP: An Antiprotease Involved in Innate Immune Sensing in Biomphalaria glabrata[END_REF]. The several studies of BgTEP1 confer different immune functions to that protein during snail infection. BgTEP1 as described like an antiprotease against different kind of proteinases (Bender & Bayne 1996), more specifically against a cysteine protease from S. mansoni larvae [START_REF] Fryer | Inhibition of cysteine proteinase from Schistosoma mansoni larvae by alpha-macroglobulin from the plasma of Biomphalaria glabrata[END_REF], is also able to bind the surface of different pathogens suggesting a potential opsonin role (Li et al. 2020a;[START_REF] Mone | A Large Repertoire of Parasite Epitopes Matched by a Large Repertoire of Host Immune Receptors in an Invertebrate Host/Parasite Model[END_REF][START_REF] Portet | BgTEP: An Antiprotease Involved in Innate Immune Sensing in Biomphalaria glabrata[END_REF][START_REF] Wu | Proteomic analysis of Biomphalaria glabrata plasma proteins with binding affinity to those expressed by early developing larval Schistosoma mansoni[END_REF]. On the basis of these different studies, we speculate that BgTEP gene silencing could increase snail susceptibility to S. mansoni parasites.

Nevertheless, no differences were observed in the prevalence and intensity of parasite infection between BgTEP1 siRNA and GFP siRNA treated snails despite the BgTEP1 knock-down at both RNA and protein levels. Several hypotheses can be formulated to explain this unexpected result.

The first is functional redundancy between members of the same multigene family. Recently, it was highlighted that BgTEP1 belongs to a multigenic family harboring at least ten other members comprising three C3-like complement factors, one alpha-2-macroglobulin, two macroglobulin complement-related proteins, four insect-like TEP including BgTEP1 and one CD109 molecule [START_REF] Castillo | Biomphalaria glabrata immunity: Post-genome advances[END_REF][START_REF] Duval | A New Assessment of Thioester-Containing Proteins Diversity of the Freshwater Snail Biomphalaria glabrata[END_REF]. In many invertebrate organisms, several genes encoding TEPs have been identified, fifteen from Anopheles gambiae, six from Drosophila melanogaster or nine from the tick Ixodes ricinus genomes, to name a few examples. If an opsonin role for AgTEP1 could be clearly demonstrated using siRNA [START_REF] Levashina | Conserved role of a complement-like protein in phagocytosis revealed by dsRNA knockout in cultured cells of the mosquito, Anopheles gambiae[END_REF], the function of D.

melanogaster TEPs was much more difficult to decipher. Indeed, the importance of TEPs in defense against microbial pathogens has been clearly demonstrated using a quadruple mutant TEP1-4 flies [START_REF] Dostálová | Thioester-containing proteins regulate the Toll pathway and play a role in Drosophila defence against microbial pathogens and parasitoid wasps[END_REF]), but single, double or triple mutant flies failed to modify the susceptibility of the insect to different pathogens infection [START_REF] Bou Aoun | Analysis of thioester-containing proteins during the innate immune response of Drosophila melanogaster[END_REF]). These results suggest that DmTEPs are interchangeable and functionally redundant in pathogen recognition and immune responses. So, we cannot exclude that the function of silenced B. glabrata TEP1 could be compensated by another members of the BgTEP family resulting to mask the effect of BgTEP1 knock-down. Moreover, BgTEP1 is not the only thioester-containing protein to interact with the sporocyst tegument, other members such as BgTEP2 and complement C4-like protein display a capacity to bind parasite membrane proteins [START_REF] Wu | Proteomic analysis of Biomphalaria glabrata plasma proteins with binding affinity to those expressed by early developing larval Schistosoma mansoni[END_REF].

Conclusion

We have significantly improved hemocyte siRNA uptake through covalent conjugation of siRNA Dunn post-hoc further adjusted by the Benjamini-Hochberg FDR were used, p < 0.05) (Fig. 1C).

Figure 2

In vivo hemocyte incorporation of Cholesteryl-TEG siRNA Flow cytometry analysis of siRNA uptake by hemocyte following in vivo injection of 2 μg of Chol-GFP siRNA along a time serie analysis. No significant differences between time points were observed (Kruskall-Wallis test followed by a Dunn post-hoc test further adjusted by the Benjamini-Hochberg FDR method were used).

Figure 3

Quantitative optimization of siRNA injected into snails for an efficient delivery on hemocyte in vivo.

Flow cytometry analysis of siRNA uptake by hemocyte 2 hours post in vivo injection of different doses of Chol-GFP siRNA. The "*" corresponds to significant differences between two different time points (Mann-Whitney U test was used). BgTEP1 was revealed using a Rat anti-BgTEP1 primary antibody. Amount of BgTEP1 at each day post-siRNA injection was calculated expressed in percentage relatively to BgTEP1 amount in non-injected snails (day 0) using quantitative tools from the Image Lab software v4.0.1. As control, we also monitored the expression of Biomphalysin protein, a protein also expressed in B.

glabrata hemolymph, using a rabbit anti-Biomphalysin primary antibody.

Figure S1

Intracellular uptake of siRNA in hemocytes.

After 2 hours Chol-siRNA-cy3 exposure, hemocytes were analyzed by confocal fluorescence microscopy. 500 µL of hemolymph were recovered by head-foot retraction from pool of 3 adult snails and plated for 1 hour on polystyrene chamber slides. Then, hemocytes were incubated 2 hours with 2 µg of Cy3-labeled GFP siRNA conjugated to cholesterol. Alexa-488 phalloidin was used to visualize actin filaments (green) and DAPI for nuclear staining (blue).

  Figure 1 siRNA incorporation with or without lipid-conjugation in hemocytes ex vivo The no siRNA condition is yellow, GFP siRNA is brown and GFP siRNA with Cholesterol-TEG conjugation (Chol-GFP siRNA) is red. A. Fluorescence profile in the three conditions, count corresponds to the cells numbers and the fluorescence scale corresponds to the fluorescence signal uptake value. Negative control or unexposed cells to siRNA (named: no siRNA) was used to determine the levels of auto-fluorescence (limit 10 3 ). B. Profile of hemocytes according to their fluorescent labeled siRNA uptake and their size. The dotted lines indicate to the limit of auto-fluorescence. C. Flow cytometry analysis of siRNA uptake by hemocytes after in vitro injection of 2μg of GFP siRNA (with or without Chol-TEG). The naive point corresponds to cell auto-fluorescence. The "*" indicate significant difference in the % of cells with fluorescent siRNA comparing control (no siRNA), GFP siRNA and Chol-GFP siRNA (Fisher exact test, p < 0.05) (Fig. 1A). Means with different letters are significantly different (Kruskall-Wallis test with

  Figure 4 Knockdown of BgTEP1 expression in guadeloupean snails. A. Relative expression ration of BgTEP1 transcripts in BgTEP siRNA treated snails compared to GFP siRNA treated snails. The relevant mRNA levels were assessed following normalisation with respect to the S19 housekeeping gene in siGFP versus siBgTEP1 injected snails. Means with different letters are significantly different (Kruskall-Wallis test with Dunn post-hoc further adjusted by the Benjamini-Hochberg FDR method, p < 0.05, were used). B. Relative expression of BgTEP1 protein in hemolymph from snails injected with Chol-BgTEP1 siRNA. BgTEP1 protein level was monitored by immunoblotting during 4 days after injection of 10 μg of siRNA in pericardial cavity. Five microliters of hemolymph (15μg/μL total protein) from each time point (Day 0 to Day 4) were run on 7.5% SDS-PAGE and transferred onto Nitrocellulose membrane.

  Figure 1

Acknowledgments

The authors want to thank Cécile Saint-Beat, Cindy Louvet, Nathalia Arancibia and Anne Rognon for all aspects concerning the maintenance of the life cycle of S. mansoni in Biomphalaria. We also thank the Montpellier RIO Imaging platform for their expertise in flow cytometry techniques (Montpellier, France).


Fabienne Femenia
email: fabienne.femenia@inrae.fr

Laure Latruffe

Jean-Paul Chavas

Responsiveness of farm investment to price changes: Evidence from the French crop sector

Keywords: investissement, aversion au risque, prix, volatilité, grandes cultures, France Classification JEL: Q12, D80 investment, risk aversion, prices, volatility, crop farms, France JEL classification: Q12, D80

Les Working Papers SMART-LERECO n'engagent que leurs auteurs. The views expressed in the SMART-LERECO Working Papers are solely those of their authors Ajustements des investissements agricoles aux changements de prix: Le cas des exploitations françaises en grandes cultures Résumé Dans cet article, nous étudions le comportement d'investissement d'agriculteurs français spécialisés en grandes cultures entre 2002 et 2014, en mettant l'accent sur leurs ajustements au prix de l'investissement et aux prix de la production agricole. Nous estimons un modèle économétrique de choix d'investissement agricole tenant compte de l'hétérogénéité des exploitations. Nous permettons aux paramètres de ce modèle de varier entre deux souspériodes: 2002-2007 et 2008-2012, la seconde sous-période étant caractérisée par un niveau et surtout une volatilité du prix des récoltes nettement plus importants. Nos résultats montrent que pour des montants d'investissement importants, les comportements des agriculteurs ont changé après 2007 du fait d'un changement de leurs préférences vis-à-vis du risque. Ceci peut expliquer la relative stabilité de l'investissement agricole sur la période, malgré la forte augmentation des prix des récoltes et de leur volatilité à partir de 2007.

The SMART-LERECO Working Papers are meant to promote discussion by disseminating the research of the SMART-LERECO members in a preliminary form and before their final publication. They may be papers which have been accepted or already presented in a national or international scientific conference, articles which have been submitted to a peer-reviewed academic journal, or chapters of an academic book. While not peer-reviewed, each of them has been read over by one of the scientists of SMART-LERECO and by one of the two editors of the series. However, the views expressed in the SMART-LERECO Working Papers are solely those of their authors.

This work is licensed under a Creative Commons Attribution -Noncommercial -NoDerivatives 4.0 International

Responsiveness of farm investment to price changes:

Evidence from the French crop sector

Introduction

Farm investment in agriculture is crucial to improve farm competitiveness, sustainability and resilience. Investment allows farmers to adapt to changes in economic conditions (e.g. price variations, policy reform, climate change) and to adjust to public regulations (e.g. environmental or animal welfare regulations). Understanding how farmers make their investment decisions and how they adapt their investment behaviour in changing economic conditions, such as price changes, is therefore crucial. Farmers' investment decisions are influenced not only by investment prices (with lower investment prices encouraging investment), but also by output prices (with higher output prices encouraging investment in order to expand production). In his literature review on the modelling of firms' investment decisions, [START_REF] Chirinko | Business fixed investment spending: Modeling strategies, empirical results, and policy implications[END_REF] concludes that firms' investment is more responsive to output quantities than to capital prices. His conclusion is notably based on [START_REF] Morrison | Structural Models of Dynamic Factor Demands with Nonstatic Expectations: An Empirical Assessment of Alternative Expectations Specifications[END_REF] who uses data on the U.S. manufacturing sector between 1947 and 1981 to estimate the elasticities of demand for capital with respect to the prices of capital and different variable inputs. [START_REF] Morrison | Structural Models of Dynamic Factor Demands with Nonstatic Expectations: An Empirical Assessment of Alternative Expectations Specifications[END_REF] results show stronger responses of capital to output quantities than to input prices (including capital price). On that basis, one may expect investment to be essentially driven by output prices, and policies directly targeting investment costs to have only marginal impacts on investment decisions. In the agricultural economics literature dealing with farm investment, no consensus seems to emerge on the relative impacts of investment price and output price on farmers' investment decisions. For instance, [START_REF] Thijssen | Farmers' Investment Behavior: An Empirical Assessment of two Specifications of Expectations[END_REF], considering Dutch farms observed from 1970 to 1982, finds significant responses of investment to both investment and output prices and concludes that investment subsidies are good policy incentives to agricultural investment. On the other hand, the results obtained by [START_REF] Vasavada | Investment in US Agriculture[END_REF] in the case of U.S. agriculture show no response of quasi fixed factors to their own prices and a negative response to the price of output. Oude [START_REF] Oude Lansink | Asymmetric Adjustment of Dynamic Factors at the Firm Level[END_REF] obtain the same puzzling effect of output price on investment in the case of Dutch cash crop farms between 1971 and 1992. More recently, [START_REF] Serra | Investment Rigidity and Policy Measures[END_REF], using data for Kansas farms from 1997 and 2001, find investment to be more sensitive to output prices in periods of a favourable economic context (i.e. increase in capital stocks) and more sensitive to public subsidies in the case of poor economic conditions. These authors do not directly consider the responses of farmers to changes in investment prices, but their results demonstrate a sensitivity of farm investment behaviours to the economic environment. [START_REF] Sckokai | Modelling the Impact of the CAP Single Farm Payment on Farm Investment and Output[END_REF] Against this background, the objective of our article is to contribute to a better understanding of farmers' investment behaviour in a context of changing investment prices and output prices.

We apply an econometric model of investment choices accounting for farm heterogeneity and farmers' risk aversion, to French crop farms specialised in cereals, oilseeds and protein seeds during the recent period 2002-2014. This period is characterised by relatively low and stable crop prices before 2007, and much higher and volatile crop prices since 2007, which makes it suitable for identifying the impact of a change in crop market conditions on farmers' investment decisions.

The remainder of the article is structured as follows. The next section describes the data and methodology we use to estimate the response of farm investment to price changes. The third section presents the results and the fourth section concludes.

Data and methodology

Data

To investigate the responsiveness of farm investment to price changes, we use a sample of farmlevel data extracted from the French Farm Accountancy Data Network (FADN). Given data availability, the analysis covers the period 2002-2014. The FADN database, managed by the French Ministry of Agriculture, contains yearly data for a sample of French commercial farms that are representative of the French farm population in terms of production specialisations and regions. The French FADN database is a rotating panel with a rotation rate of about 10%, making the sample an unbalanced panel dataset. As investment types and levels may depend on production specialisations, we focus here on a specific type of farming, namely farms specialised in the production of cereals, oilseeds and protein seeds.

The investment level (!) we consider is net investment (we do not consider replacement investment) and is computed as an aggregate of machinery and building net investments. We exclude land investment as it is a minor part of farm investment. 1 In what follows, we consider that farms' owned utilised agricultural area (UAA) remains unchanged over the period, which is actually the case in our data where farms' UAA varies by less than 1% on average from one year to the other. As a result, land is also excluded from the fixed capital stock (k) that we consider in the remaining of the paper. As no price of investment (") is available in the FADN database, we use as a proxy the ratio between annual debt repayments and the annual value of fixed capital stock. Given that cereal, oilseeds and protein seeds prices generally follow similar trends over time, we use the price of wheat, which is the most produced cereal in France, as a proxy of the price (p) of our specialized farm output (y). This price is calculated for each farm in each year using FADN data and is expressed in Euros per kilogram of wheat. As in [START_REF] Chavas | Economic Behavior under Uncertainty: A Joint Analysis of Risk Preferences and Technology[END_REF], the variance of output prices (#), which represents the price risk faced by farmers, is defined as a weighted sum of squared deviations of past prices from their expected values. The capital depreciation rate ($)2 is assumed to be 0.05 and the official annual interest rate provided by the European Central Bank is taken as the actualisation rate (%). All values are measured at constant 2002 prices using the corresponding national price indices.

We focus on large investments to avoid heterogeneity issues in investment behaviour. As suggested by [START_REF] Kapelko | Investment Age and Dynamic Productivity Growth in the Spanish Food Processing Industry[END_REF], low levels of investment may be driven in large part by replacement motives and not profit maximization. In contrast, large investments are more likely to be motivated by profit maximisation. For this reason, we select the farms investing the most, i.e. the farms displaying investment levels higher than the sample average. The sample is unbalanced over the period, and we keep those farms that appear at least two consecutive years.

After cleaning the data and eliminating outliers, the total number of observations in our sample during 2002-2014 is 3,822 (approximately 300 farms per year). Figure 1 reports the evolution of the yearly averages of investment level, investment price and output price over our sample period for the farms selected for our study. The annual values are not reported in levels, but as percentage differences compared to the average value for the full period. Three observations can be made. Firstly, investment levels and output price levels are lower up to 2006 than their levels increase from 2007 onwards. Secondly, while the investment price remains relatively stable during the whole period, the output price experiences ups and downs from 2007 onwards. This conforms to the general knowledge that worldwide crop prices (here wheat prices) are higher on average and much more volatile since 2007 (Von [START_REF] Braun | Global Food Price Volatility and Spikes: An Overview of Costs, Causes, and Solutions[END_REF]. Thirdly, from 2007 onwards, farm investment does not follow the same evolution as output price. All these observations suggest that farmers' investment responses to prices may have changed during the whole period. For this reason, we will assess the impact of the change in market conditions on farmers' behaviour, by introducing a 'time period effect' in the key behavioural parameters of our econometric model. On average during the whole period, farms produced an output of 1,057 Euros per ha per year and invested on average 415 Euros per ha each year (the minimum being 181 and the maximum 5,001 Euros). Table 1 clearly shows that farm investments are lower on average during the first sub-period. As observed on Figure 1, the investment price remains remarkably similar over the whole period (0.11 Euro paid for each Euro of capital, on average), while the output price is much higher in the second than in the first sub-period (146 vs. 105 Euros per ton of wheat). The increase in farm investments after 2007 thus seems, at first sight, attributable to an increase in output price levels leading to a higher crop production (1,142 vs. 950 Euros per ha) and thus higher needs in capital. The strong increase in output price volatility, observed on Figure 1 is also confirmed by the figures reported in Table 1. Given the potential negative impacts of market risk on farm investment decisions, this increase in price volatility may have mitigated the increase in investment induced by the output price increase. The econometric estimation of our investment model will allow further investigation of this issue.

About half of the sample farms have an individual (sole proprietorship) legal status, compared to partnerships or companies. About half of the sample farms are located in the wide Parisian basin area (administrative regions "Ile-de-France", "Picardie", "Champagne-Ardennes" and "Centre"), which is the main area for wheat production in France, while 15% of the farms are located in the other main wheat area, namely South Western France (administrative regions "Midi-Pyrénées", "Aquitaine", "Poitou-Charentes"). These two areas, Parisian basin area and South Western France, exhibit specific favourable characteristics for field crop farms, the former being a region with particularly good cropping conditions and large farms, and the latter being largely composed of farms specialized in irrigated corn production. Finally, in the second sub-period, farms are on average operated by younger farmers (with 61% of farmers being older than 50 in the first sub-period vs. 47% in the second sub-period), and who have a higher degree of education (with 67% of farmers having completed secondary education in the first sub-period vs. 74% in the second sub-period). This reflects the generation renewal trend in the French farming population.

Model and estimation strategy

Two types of approaches are generally used in the economic literature to investigate farmers' investment decisions. Primal approaches rely on structural models obtained from the maximisation of future expected profit under technological constraints (e.g., [START_REF] Gardebroek | Capital Adjustment Patterns on Dutch Pig Farms[END_REF] and Gardebroek and Oude Lansink ( 2004)), while in dual approaches, introduced by Epstein (1981), producers' investment decisions are represented by value functions (e.g., Oude

Lansink and Stefanou (1997), [START_REF] Pietola | Investment under Uncertainty and Dynamic Adjustment in the Finnish Pork Industry[END_REF] and [START_REF] Sckokai | Modelling the Impact of the CAP Single Farm Payment on Farm Investment and Output[END_REF]). Models based on dual approaches allow for more flexibility in the representation of producers' choices; however, their estimation necessitates sufficient variations in input prices across the sample, something that we do not have in our data. 3 For that reason, we follow here a primal approach.

We consider the case where, at time *, the +-th farmer produces output ' ,-using variable inputs . ,-and capital & ,-under the production function ' ,-= /0. ,-1 & ,-2. We assume that this production function is strictly increasing and concave in 0.

where $ 9 0:1 52 is the depreciation rate of capital and ! ,-9 ; 3 is investment at time *.

Market prices for 0' -1 . -1 ! -) are respectively 0( -1 < -1 " -2. In addition, when investing, the farm faces adjustment costs denoted by >0! ,-2. The profit of the +-th farmer at time * is ? ,-@ ( -7/0. ,-1 & ,-2 6 < -. ,-6 " -7! ,-6 >0! ,-2. The farmer makes production decisions at the beginning of each period, with output ' ,-= /0. ,-1 & ,-2 obtained at the end of the period.

Because of this production lag, the output price ( -is not known when inputs are chosen and is thus treated as a random variable. We denote the mean of the output price ( -by A ,-= B ,-0( -2

and the variance of

( -by # ,- ) = B ,-[0( -6 A ,-2 ) ],
where B ,-is the expectation operator based on the information available to the +-th farmer at the beginning of period *C7 The +-th farmer seeks to maximise the expected utility B ,-[D , 0? ,-2], where the utility function D , 0E2 represents her/his risk preferences. Assuming that D , 0?2 is a strictly increasing function, we define the certainty equivalent as the sure amount FB ,-satisfying D , 0FB ,-2 = B ,-[D , 0? ,-2] and the risk premium G ,-7as G ,-@ B ,-0? ,-2 6 FB ,- [START_REF] Pratt | Risk Aversion in the Small and in the Large[END_REF]. In this context, G ,-is the implicit cost of risk measuring the farmer's willingness to pay to eliminate risk by replacing the random variable ? ,-by its mean B ,-0? ,-2. G ,-H = : I : J when

K L M N
KO L H = : P : J, corresponding to the +-th farmer being H risk7neutral risk7averse J . Following [START_REF] Pratt | Risk Aversion in the Small and in the Large[END_REF], we can approximate the risk premium as ) , where R , is the Arrow-Pratt coefficient of absolute risk aversion for the +-th farmer. Letting R , = S , T0( ,-7' ,-2, the risk premium can also be approximated as ) , where S , is a coefficient of relative risk aversion for the +-th farmer.

G ,-Q 4 ) 7R , 7' ,- ) 7# -
G ,-Q 4 ) 7S , 77 U NV W NV # -
Treating S , as a constant corresponds to risk preferences exhibiting decreasing absolute risk aversion (as the absolute risk aversion coefficient R , declines with an increase in expected revenue). In this context, for the +-th farmer at time *, the certainty equivalent FB ,-is FB ,-= B ,-X7( -/0. ,-1 & ,-2Y 6 < -. ,-6 " -7! ,-6 >0! ,-2 6 4 ) 7S , 77

U NV W NV # - ) (2)
We assume that the +-th farmer maximises the expected present value of her/his certainty

equivalents Z \ 4 43^_ - FB ,- `N -b4
, where % c : is the interest rate, 5T05 8 %2 is the discount factor, and d , I 5 is the farmer's planning horizon. Note that expectation about the future is still needed: future certainty equivalents are not perfectly known as the farmer learns about the distribution of future prices over time. Subject to the state equation ( 1), the +-th farmer's at time * are represented by the following Bellman's equation

f ,-0( -1 < -1 " -1 # - ) 1 & ,-2 = max g N1V 1h N1V
jB ,-X7( -/0. ,-1 & ,-2Y 6 < -. ,-6 " -! ,-6 >0! ,-2 6 7777777777777777777777777777777777777777777777777777777767 4 ) 7S , 77

U NV W NV # - ) 8 \ 4 43^_ B ,1-of ,1-34 005 6 $27& ,-8 ! ,-2pq (3)
where f ,-0& ,-2 is the value function defined recursively for * = d , 1 d , 6 51 … 1 w1 5, with f ,1`N34 = :.

Under differentiability and assuming interior solutions, the first-order necessary conditions for the optimal choice of 0. ,-1 ! ,-2 in (3) are (5)

with the simplifying notations / ,-= /0. ,-1 & ,-2, > ,-= >0! ,-2 and f ,-= f ,-0& ,-2.

Equation (4) gives the standard optimality condition for inputs, where marginal revenue is equal to marginal cost, the latter including both the input price < -and the marginal cost of risk,

4 ) 7S , Ky NV Kg NV 77 z V L W NV
. As further discussed below, equation ( 5) has a similar interpretation for investment.

Applying the envelope theorem to equation (3) and combining with equation ( 5) yields

\ 4 43^_ {Z \ 4'ƒ 43^_ "'- `N "b-34 B ,- †( ," 7 Ky N ‡ K• N ‡ 7 6 7 4 ) 7S , Ky N ‡ K• N ‡ 77 z ‡ L W N ‡ ˆ€ = " -8 K• NV Kh NV 7 . ( 6
)
The left-hand side in (6) is the present marginal value of capital, adjusted for the marginal cost of risk. And the right-hand side in ( 6) is the marginal cost of investment, including both the investment price " -and the marginal adjustment cost

K• NV Kh NV
. Thus, equation ( 6) states a familiar optimality condition: at the optimum, the present marginal value of capital equals the marginal cost of investment. Note that the marginal risk premium reduces the marginal present value of capital in (6). As such, under risk aversion (where R I :, and hence S , I :), price risk,7# - ) , and risk aversion, S , , have negative effects on investment incentives.

Finally, we assume that farmer's expectations are naïve, that the production technology is

Cobb-Douglas,4 and that adjustment costs are quadratic as assumed by e.g. [START_REF] Weersink | Resources and Territories is composed of the research units in Economics of INRAE Rennes and INRAE Nantes and of the members of L'institut Agro-Agrocampus Ouest's Department of Economics, Management and[END_REF], [START_REF] Thijssen | Farmers' Investment Behavior: An Empirical Assessment of two Specifications of Expectations[END_REF], and [START_REF] Gardebroek | Farm-Specific Adjustment Costs in Dutch Pig Farming[END_REF]. Then, B ,- †( ," 7

Ky N ‡ K• N ‡ ˆ= ( -'4 Ky NV‰K • NV‰~, Ky NV K• NV = Š7 U NV • NV
where Š 9 0:152 is the production elasticity of capital, >0! ,-2 = ‹ 8 OE7! -, 8 ) where Ž I :, and the optimal investment decision rule is

• ) 7! ,-
! ,1-= 6 • • 6 4 • 7" -8 • • 04'ƒ2 043^2 L '5 6 \ 4'ƒ 43^_ `N'- ' \7 U NV‰• NV‰~_ 7( ,1-'4 6 77777777777777777776 4 ) S , • • 7 04'ƒ2 043^2 L '5 6 \ 4'ƒ 43^_ `N'- ' 4 W NV‰~7 \7 U NV‰• NV‰~_ 7# - ) . ( 7
)
We can notice that, for any time * 9 [51 d , ], the term7\ Based on the model of farmers' investment in equation ( 7), we estimate the following econometric model:

! ,1-= • -1,-8 • -1,-" ,1-8 • ˜1,-™fš ,1-8 • |1,-™fG ,1-8 › ,1-, (8)
where ™fš ,1-and ™fG ,1-respectively denote the marginal value of capital and risk expected by the farmer in period t in equation ( 11):

™fš ,1-= 04'ƒ2 043^2 L { U N1V‰• N1V‰~€ ( ,1-'4 and ™fG ,1-= 4 ) 04'ƒ2 043^2 L 4 W NV‰~{ U N1V‰• N1V‰~€ 7# - )
; › ,1-is the random error, and the • are parameters to be estimated.

The elasticity of investment with respect to the (observed) price of investment (oe!" ,-), the elasticity of investment with respect to the (expected) level of output price (oe!( ,-) and the elasticity of investment with respect to its volatility (oe!# ,-) are, respectively,

oe!" ,-= Kh NV K˜h NV ˜hNV h NV = 6 4 • • NV ž NV h NV , (9) oe!( ,-= Kh NV KW NV‰~W NV‰h NV = • Ÿ NV • • NV X N1V 3¢ Ÿ NV |£ N1V Y h NV , ( 10
) oe!# ,-= Kh NV Kz V z V h NV = 6 ¢ Ÿ NV |£ N1V h NV , (11)
where

Ž ¤ ,-= 6 4 ¥ ¦ § NV (12) OE ¨,-= ¥ ¤ ©1NV ¥ ¤ ¦1NV (13) Š Ÿ ,-= 6 ¥ ¤ ª1NV ¥ ¤ ¦1NV (14) S Ÿ ,-= 6 ¥ ¤ «1NV ¥ ¤ ª1NV (15) R ¨,-= 6 4 0W NV 7U NV 2 ¥ ¤ «1NV ¥ ¤ ª1NV . ( 16
)
Ž ¤ ,-and OE ¨,are the estimated parameters of the capital adjustment cost function; Š Ÿ ,-are the parameters of the production function; S Ÿ ,-and R ¨,are respectively the relative and absolute risk aversion coefficients. Their significance is computed through the delta method.

The potential impact of a short planning horizon on farmer's investment decisions (represented by term \ 4'ƒ 43^_ `N'in equation ( 7)), is captured in the econometric model ( 8) by introducing a decomposition of parameters • ˜1,-and • |1,-according to the value taken by a dummy variable, ¬ ¥-®1,-. This variable takes the value of 1 for farmers aged 50 and more, i.e. for farmers close to retirement with a short planning horizon, and 0 otherwise.

As mentioned in data subsection, we also introduce a 'time period effect' in the key behavioural parameters of our econometric model ( 8 8), • -1,-, is thus decomposed as

• -1,-= • -1-X5 8 • -1)--¯¬)--¯1,-Y , ( 17
)
where • -1-represents the response to investment price in the first sub-period and • -1)--¯ the effect, on that response, of moving from the first to the second sub-period.

The dummy variable ¬ )--¯1,-is also introduced in the parameters associated to the marginal value of capital ™fš ,1-and the marginal value of risk ™fG ,1-in order to estimate the impact of the change in time sub-period on the responses of farm investment to the level and volatility of output price. The parameters are thus decomposed in terms of age and sub-period as follows:

• ˜1,-= • ˜1-X5 8 • ˜1¥-® ¬ ¥-®1,-YX5 8 • ˜1)--¯¬)--¯1,-Y (18)
• |1,-= • |1-X5 8 • |1¥-® ¬ ¥-®1,-YX5 8 • |1)--¯¬)--¯1,-Y . ( 19
)
To account for the potential heterogeneity in farm investment levels, the first additive term in equation ( 8), • -1,-, is decomposed as:

• -1,-= • -1-8 a -1°± ² ,1-8 ³ , , (20)
where ² ,1-is a matrix composed of four dummy variable vectors representing farmers' characteristics and used to partly control for the heterogeneity in investment levels among farms. These variables include a variable capturing the education of farmers and taking the value 1 for farmers having completed secondary education and 0 otherwise; a variable showing the legal status of the farm and taking the value 1 for individual farms and 0 for partnership farms and companies; and two regional variables, the first one taking the value 1 for farms located in the large Parisian basin area and 0 otherwise, and the second one taking the value 1 for farms located in the South Western France and 0 otherwise. To control for the unobserved heterogeneity in investment levels, we also introduce an individual random effect ³ , , assumed to be independent from the error of the model › ,1-. Some unobserved factors that may have an impact on investment levels, like farmers' personal skills or extension access, may also influence farms' productivity. To deal with this potential correlation between the random term ³ , and the exogenous variables in model ( 8), which would lead to biased estimates, we apply the [START_REF] Hausman | Panel Data and Unobservable Individual Effects[END_REF] instrumental variable approach.

Results

Table 2 reports the regression results of the estimation of the investment model in equation ( 8), accounting for the decompositions of parameters presented in equations ( 17)-( 20). We can first notice that the model fits the data relatively well, with a pseudo-R 2 of 0.63 and most parameters significantly estimated and of expected signs for the main variables of interest. The price of investment negatively affects farm investment per hectare (through parameter • -1-), similarly across both sub-periods (non significant parameter • -1)--¯) . The value of the marginal capital productivity positively affects farm investment per hectare in both sub-periods, but more so in the first sub-period (through parameter • ˜1-) than in the second sub-period (through

• ˜1-8 • ˜1)-4¯) .
There is however no significant age effect, implying that the influence of productivity on investment is similar for younger and older farmers. As regard the marginal cost of risk, the effect on farm investment per hectare is negative, with a slight reinforcement in the second subperiod (parameter • |1)-4¯) and for farmers aged 50 or above (parameter • |1¥-® ). Regarding the variables accounting for farmers' heterogeneity, farmers operating individual farms and having attained secondary education at least, invest more per hectare, while farmers operating farms in South Western France invest less per hectare than the other farmers. The estimated model parameters reported in Table 2, as well as the variance-covariance matrix of estimates (not reported), enable us to calculate the value and the significance of the structural parameters that underlie the investment decision in equation ( 7), namely the parameters of the capital adjustment costs and production functions, as well as the relative and absolute risk aversion coefficients. Table 3 shows the values and significance of these structural parameters.

As expected, the Ž parameter is positive implying that the capital adjustment cost function is Similarly, the parameter, which corresponds to the elasticity of production with respect to capital, takes values between 0 and 1, implying that the production function is concave. The relative and absolute risk aversion coefficients are positive in the first sub-period and not significantly different from zero in the second sub-period. What is noticeable is that the change in these risk aversion coefficients between both sub-periods is significant, while the changes in the adjustment cost function and production technology parameters between both sub-periods are not significant. It thus appears that farmers' investment behaviours have changed between both sub-periods and that this change can be attributed to a modification of their risk preferences: from relatively highly risk averse in the first sub-period with a risk ) 27of about 170 Euros per hectare, which represents 18% of their production value, they become risk neutral in the second sub-period. It is also interesting to notice here that even if the increase in crop farm revenue between both sub-periods can partly explain the decrease in farmers' absolute risk aversion coefficient (R) under our DARA assumption, the fact that their relative risk coefficient (S) also significantly decreases suggests that this change in risk preferences is due to other (unobserved) factors. Such factors may relate to the change in socio-demographics characteristics of farmers across sub-periods. As the sample selected is unbalanced, some farms in the first sub-period are not observed in the second period, and reciprocally. Descriptive statistics show that farmers observed in the second subperiod are significantly younger and more educated (see Table 1). While this simply reflects the general trend on farms in France, it may contribute to the decrease in farmers' risk aversion across sub-periods. 5

premium (G ,-Q 4 ) 7S , 77 U NV W NV # -
5 thank an anonymous Reviewer for pointing this out. The elasticities, computed along equations ( 9)-( 11) with the parameters of Table 3 for each observation, are reported in Table 4 as averages for the sample. Both price levels elasticities, that is to say with respect to the price of investment and with respect to the price of output, are significant in both sub-periods considered and have the expected sign. Investment decreases with the price of investment and increases with the price of output. In absolute values, both elasticities are on average the same. This reveals that farmers are equally responsive to changes in the expected output price and in the investment price. There is no significant change in price elasticities on average across sub-periods. The elasticity with respect to price volatility is negative in the first sub-period, suggesting a negative impact of market risk on investment. It is positive, but not significant, in the second sub-period, and the change between both subperiods is not significant as well. Given the significant change in farmers' risk preferences, it can, at first sight, seem counterintuitive that the elasticity of investment with respect to output price volatility, which depends on risk aversion, does not significantly vary between the two sub-periods. This result has in fact to be considered in regards to the strong increase in output price volatility from 2007: it is because farmers' preferences toward risk change, that the elasticity of investment with respect to output price volatility does not significantly vary over time. In order to further investigate the implications of the change in farmers' investment behaviour between the two sub-periods, we use the estimated investment model to simulate the evolution of farm investments between 2002 and 2014. Figure 2

Conclusion

We investigated the investment response of French crop farmers to changes in prices (investment price; and output price, both in levels and volatility) during the period 2002-2014.

Focusing on large investors among farms specialised in cereals, oilseeds and protein seeds from the French FADN database, we estimated an econometric model of farm investment accounting for risk aversion and using a Hausman-Taylor estimation framework enabling to control for farmer's heterogeneity.

Our estimation results reveal a change in farm investment behaviour over time for large investments. More precisely, we find farmers to be risk averse in the first sub-period of our data, namely between 2002 and 2007, and risk neutral in the second sub-period (2008)(2009)(2010)(2011)(2012)(2013)(2014)).

Yet, this second sub-period is characterised by a higher level of price volatility on crop markets, compared to the first sub-period. As shown by our simulation results, without change in farmers' risk preference between both sub-periods, this increase in price volatility would have induced a significant decrease in farm investments. The results we find for the first sub-period corroborate those of [START_REF] Sckokai | Modelling the Impact of the CAP Single Farm Payment on Farm Investment and Output[END_REF] who find price uncertainty to have a significant The small change in farmers' investment behaviour may be explained by the fact that farmers may have adapted their behaviour to the new context of uncertainty on crop markets. Also, the increase in crop prices, and hence in crop farm income, observed after 2007 may have led farmers to invest for other motives than increasing their production factors, given the tax exemption policy applicable to farm investments in France during the period studied here. The result that farmers become risk neutral in the second sub-period characterised by a higher level of price volatility on crop markets, may be counterintuitive. Although one explanation may lie in the fact that the second sub-period is also characterised by higher output price, further research in behavioural economics is necessary to understand farmers' changes in risk attitudes.

There are several other avenues for future research on farm investment decisions. First, the assumption of naïve expectations constrains the model to a static one. Modelling other types of expectations includes more complexity in the model but may also make it more flexible. In addition, the changes in economic conditions on crop markets might have generated a change in expectation schemes that appears as a change in risk preferences in our model. As shown by [START_REF] Manski | Measuring Expectations[END_REF], the two elements are indeed difficult to distinguish. When data are available on a longer period and enable the use of time series data, one could estimate the investment model developed here under the assumption of quasi-rational expectations [START_REF] Nerlove | Analysis of Economic Time Series: A synthesis[END_REF]. In this scheme, farmers form their expectations on a series of past observations. In this context, it would be interesting to test whether farmers' expectations become quasi-rational in the period with high output price volatility. A second development may be to consider the case of low investments. In this article we present findings that are specific to farmers implementing large (expansionary) investments, and cannot be generalised to all levels of investments, as farmers' economic behaviour may be different for low (replacement) investments. One interesting issue is that low investment may actually be driven by other factors than those related to the level and uncertainty on market prices that appear to have a significant impact on large investments.

These types of investment may thus have evolved differently, and for other reasons between the two sub-periods. Investigating this issue would require a specific modelling of adjustment costs as in [START_REF] Gardebroek | Capital Adjustment Patterns on Dutch Pig Farms[END_REF], or a threshold regression method with various regimes allowing to characterize different types of investment as in [START_REF] Serra | Investment Rigidity and Policy Measures[END_REF].

  Working Paper SMART -LERECO N°21-02 Les Working Papers SMART-LERECO ont pour vocation de diffuser les recherches conduites au sein de l'UMR SMART-LERECO dans une forme préliminaire permettant la discussion et avant publication définitive. Selon les cas, il s'agit de travaux qui ont été acceptés ou ont déjà fait l'objet d'une présentation lors d'une conférence scientifique nationale ou internationale, qui ont été soumis pour publication dans une revue académique à comité de lecture, ou encore qui constituent un chapitre d'ouvrage académique. Bien que non revus par les pairs, chaque working paper a fait l'objet d'une relecture interne par un des scientifiques de l'UMR SMART-LERECO et par l'un des éditeurs de la série. Les Working Papers SMART-LERECO n'engagent cependant que leurs auteurs.

  also find the response of farm investment to depend on the economic context and notably on the volatility of agricultural markets. Their estimations have been conducted on data ranging from 1994 to 2003, a context of relatively stable agricultural prices, and thus low price uncertainty, compared to what has been observed since 2007. One important question is whether these changes in economic context have had an impact on farmers' investment behaviour.

Figure 1 :

 1 Figure 1: Evolutions of the sample's yearly averages of investment level, investment price and output price over the 2002-2014 period, in comparison with the period average

  It follows that a short planning horizon has a negative effect on the marginal present value of capital and thus on investment incentives. Notably, farmers close to retirement are less encouraged to invest.

  ) in order to assess the impact of the change in market conditions on farmers' behaviour. Two sub-periods are considered in our estimations:2002- 2007 and 2008-2014. Although changes in economic conditions start to be visible in 2007 (Figure1), we make our second-sub-period start in 2008 as farmers have naïve expectations: their 2008 behaviour is thus based on conditions prevailing in 2007. A dummy variable, ¬ )--¯1,-, taking the value 1 for observations belonging to the second sub-period(2008)(2009)(2010)(2011)(2012)(2013)(2014) of our sample and 0 for observations belonging to the first sub-period(2002)(2003)(2004)(2005)(2006)(2007), is thus used to estimate the impact of the change in time period on the parameters of interest in our model representing the responses of farm investment to economic incentives. The parameter associated to the investment price in equation (

  reports the investment levels actually observed over the full period (light line) and the investment levels simulated with two versions of our model, based on observed market conditions (investment price, output price, output price volatility) and farmers' characteristics (age, region, education and status). In the first set of simulations (plain dark line), we use the full version of the model, accounting for the estimated changes in the parameters between the sub-periods, in the second set of simulations (dotted dark line), we use an alternative version of the model with no changes in the parameters, i.e. with the estimated second period effects (• ¤ -1)--¯, • ¤ ˜1)--¯ and • ¤ |1)--¯) set to zero. The second set of simulations thus corresponds to a counterfactual situation where farmers' investment behaviour, and especially farmers' risk preferences, do not change over time. We can first notice, by comparing the light and dark plain lines on Figure 2, that the investment levels simulated with the full version of the model are very close to the observed levels, which demonstrates a good predictive performance of our model. The simulation results of the model without change in behaviour are, of course, identical to those of the full model in the first sub-period, but show a strong decrease in farm investments in the second sub-period. This decrease can be attributed to the increase in output price volatility that would have discouraged risk averse farmers to invest, despite the increase in output price level.

Figure 2 :

 2 Figure 2: Observed and simulated investment levels over the period 2002-2014

  negative impact on farm investment over the period1994-2003. However, these results lead the authors to conclude that an increase in output price volatility due to a removal of intervention price would decrease farm investment. Our article sheds a new light on that issue by showing that, for various reasons such as the socio-demographic evolution of farms, farmers' risk change in behaviours preferences have in fact been different in the recently observed context of uncertainty on crop markets, leading to a relative stability of farm investment across both sub-periods.

Table 1 : Descriptive statistics of the sample used

 1

	Whole period	2002-2007	2008-2014
	Mean	S. D.	Mean	S. D.	Mean	S. D.

Source: The authors based on French FADN data.

Table 1

 1

provides descriptive statistics of our variables of interest for the whole 2002-2014 period and for the two sub-periods. During the whole period the farms in our sample operated on average 160 hectares (ha) of UAA and used 1,638 Euros of capital per ha. The respective figures for the two sub-periods are very similar, indicating that, although it is not a balanced sample throughout the full period, structural characteristics are similar for the sub-sample of 2002-2007 and the sub-sample of 2008-2014.

  ,-1 & ,-2. Capital evolves over time

	according to the following state equation
	& ,1-34 = 05 6 $27& ,-8 ! ,-

Table 2 : Estimated parameters of the investment model (8)

 2

	Variable	Estimated parameter	Standard error
	Constant term (• -1-) Dummy variables	357.41***	26.06
	Individual legal status (• -1°4 ) Parisian basin area (• -1°) ) South Western France (• -1°´) Secondary education (• -1°µ ) Price of investment	94.75*** -8.55 -36.19* 30.82**	15.00 14.39 19.78 14.94
	First period (• -1-) Second period effect (• -1)--¯) Value of marginal capital productivity	-499.88*** 0.42	105.73 0.33
	First period (• ˜1-) Second period effect (• ˜1)--¯) Age effect (• ˜1¥-® ) Market risk (output price volatility)	0.77** -0.45* -0.48	0.31 0.25 0.30
	First period (• |1-) Second period effect (• |1)--¯) Age effect (• |1¥-® ) Wald Chi-square statistic	-112.74*** -1.06*** -1.08*** 163.82***	43.86 0.06 0.34
	Pseudo-R 2	0.63
	Number of observations	3,822

Note: Significance levels: * 10%, ** 5%, *** 1% Source: The authors based on French FADN data.

Table 3 : Values and significance of the investment decision parameters

 3 , Ž •, Š • , S • and R ¶ are the average values, over i and t of the estimated parameters.

					Significance of the difference
	Parameters for		2002-2007	2008-2014	between both sub-periods
	Capital adjustment cost function parameter Capital adjustment cost function parameter Production technology parameter Relative risk aversion coefficient Absolute risk aversion coefficient	OE ¶ Ž • Š • S • R ¶	-0.84*** (0.017) 0.002*** (0.0004) 0.001*** (0.0004) 72.08* (41.89) (0.05) 0.08*	-0.59*** (0.07) 0.001*** (0.0002) 0.0007*** (0.0001) -4.90 (8.99) (0.008) -0.004	(prob>Chi2) 0.18 0.17 0.31 0.07* 0.07*
	Notes: Standard deviations of estimates are in parentheses. Significance levels: * 10%, ** 5%, *** 1%. The parameters OE ¶ Source: The authors based on French FADN data.

Table 4 : Average elasticities of investment computed for each observation and significance

 4

				Significance of the difference
		2002-2007	2008-2014	between both sub-periods
				(prob>Chi2)
	With respect to investment	-0.14***	-0.19***	0.12
	price (oe!" ,-) With respect to output price	(0.03) 0.14***	(0.02) 0.17***	0.64
	level (oe!( ,-) With respect to output price	(0.06) -0.025*	(0.06) 0.020	0.24
	volatility (oe!# ,-)	(0.018)	(0.034)
	Notes: Standard deviations of estimates are in parentheses. Significance levels: * 10%, ** 5%, *** 1%.
	Source: The authors based on French FADN data.

While our sample data show investments in building and machinery in 80 out 100 cases, investments in land only occur in 10 out of 100 cases.

Different values have been tested but estimation results are unchanged.

Contrary to cereal prices, which exhibit strong variations over our sample period, with coefficient of variation around 13 for output price indices using 2005=100 as a base year, the agricultural input price index remains almost stable over the same period, with a coefficient of variation around 0.7 using the same base year.

A translog production function was also tested in the empirical application but did not appear to fit the data since the estimated cross-term coefficients were not significant.

to these confidential data has been made possible within a secure environment offered by CASD -Centre d'accès sécurisé aux données (Ref. 10.34724/