«Farmer Impatience and Grain Storage for the Hunger Season»

Transcription

1 «Farmer Impatience and Grain Storage for te Hunger Season» Tristan LE COTTY Eodie MAITRE D HOTEL Rapaë SOUBEYRAN Juie SUBERVIE DR n

2 Farmer Impatience and Grain Storage for te Hunger Season T. Le Cotty E. Maître d Hôte R. Soubeyran J. Subervie Abstract In African countries, food security greaty depends on farmers propensity to store grain unti te ean season. Using origina data coected from 1,500 farmers in Burkina Faso in 2013, we sow tat individua risk and time preferences pay a centra roe in grain storage decisions. We use a sampe seection mode as we as a structura estimation approac and find tat bot ead to very simiar resuts. Specificay, we find tat a one-standard-deviation increase in te discount rate (resp. risk aversion) resuts in a arge decrease (resp. increase) in grain storage of about 45% (resp. 25%). We simuate a grain price stabiisation poicy and sow tat af of farmers in our sampe woud benefit from suc a poicy. Key Words: Storage, Food Security, Time Discounting, Risk Aversion, Price Stabiisation Poicy. JEL: D13, D14, D91, O12. CIRAD, UMR 8568 CIRED, F Montpeier - France. CIRAD, UMR 1110 MOISA, F Montpeier - France. INRA, UMR 1135 LAMETA, F Montpeier - France. INRA, UMR 1135 LAMETA, F Montpeier - France. Corresponding autor. Emai: subervie@supagro.inra.fr UMR LAMETA, Campus INRA-SupAgro, 2 pace Pierre Viaa, Montpeier Cedex 1, France. Pone: + 33(0) Fax: + 33(0) Tis researc woud not ave been possibe witout te fu cooperation of te Confédération Paysanne du Faso (CPF). Funding for tis researc was provided by te EU wit counterpart funding from AGRINATURA for te Farm Risk Management for Africa (FARMAF) project. We are particuary gratefu to Saima Bouayad Aga, Syvain Cabé-Ferret, Matieu Couttenier, Aain Carpentier, Aex Goin, Antoine Lebois and Aain Trannoy. We received vauabe feedback from seminar at AMSE-GREQAM, CREM, LAMETA, and SMART-LERECO. We tank Jean-Marc Roussee for is researc assistantsip. 1

3 1 Introduction In African countries, many grain farmers suffer from starvation during te ean season wen te vaue of teir product reaces a peak. 1 Tis occurs because farmers eiter consume or se teir entire arvest wen te price of grain is owest. Given tat grain storage can be used to increase food security, wy don t farmers store some of teir arvest unti te ean season? Te most common reason wy farmers are tougt not to take advantage of seasona price fuctuations troug storage is tat tey face temporary iquidity constraints tat force tem to convert teir grain into cas, even toug tey know tat tey may need to buy back more grain ater at a iger price (Stepens and Barrett, 2011; Van Campenout, Lecoutere, and D Exee, 2015). Anoter expanation is tat risk aversion and impatience imit storage. 2 At first gance, te roe of impatience in te African context is not obvious : given te typicay arge increase in grain prices between te arvest and te ean season, 3 tis second expanation woud od ony if farmers were extremey impatient. Tis paper igigts te roe of impatience in driving African farmers agricutura beaviour. We use origina data from Burkina Faso to study tis issue empiricay. Taking into account te fact tat farmers wo coose to se grain in te arvest season may be iquidity constrained, we provide evidence tat eterogeneity in storage beaviour is argey expained by individua risk attitudes and time preferences. To do so, we deveop a styized on-farm storage mode tat expicity takes into account te ouseod preference for risk, time, and grain reative to oter goods. Parameterized to our data, te mode predicts tat stored quantities decrease wit impatience and increase wit risk aversion. In order to test tese predictions and quantify tese effects, we use origina data on agricutura decisions tat we ave coected from 1,500 farmers wo were aso asked ypotetica questions about risk aversion and time discounting. Risk and time preferences ave ong been recognized by teoretica modes of storage as an important factor in te storage decision-making process (Newbery, 1989; Deaton and Laroque, 1992). However, te extent to wic tey pay a roe in storage decisions is ess understood from an empirica perspective. Identifying te effects of individua preferences on agricutura decisions is a difficut task for at east two reasons. First, eiciting risk and time preferences requires impementing artefactua fied experiments (in te terminoogy of Harrison and List (2004)), wic is more difficut tan running decarative surveys, for practica reasons. We buit our risk aversion experiments foowing Hot and Laury (2002) and our time preference experiments foowing Harrison, Lau, and Wiiams (2002). However, we ad to adapt te content of te experiments in order to offer ypotetica payoffs tat made sense to te respondents. We ten foow te same approac as Andersen, Harrison, Lau, and Rutstrom (2008) in order to infer te risk aversion coefficients and te discount rates impied by te raw responses. In our sampe, most of te farmers appear risk averse at eves tat are comparabe to tose obtained by Harrison, Humprey, and Verscoor (2010), wo used simiar experiments in India, Etiopia, and Uganda. Our estimates of te time preference parameter fa we above previous estimates of discount rates tat ave been eicited for seected segments of popuations in more 1 In West-African countries, te price of grains suc as miet, maize, and sorgum typicay decines during te arvest season, refecting an increased suppy of grain from ongoing arvests, and increases tereafter wit te onset of te ean season. 2 A tird expanation concerns imits to storage tecnoogy. In our context, tis is ess of an issue as farmers ave access to traditiona storage metods at ow costs. 3 For exampe, during te season, in rura markets in Burkina Faso were our study takes pace, we observe tat maize prices increased by 40 % between te arvest season and te ean season (Figure 1). 2

4 deveoped countries. 4 Tese resuts are consistent wit ow farmers ive in Burkina Faso and wit recent papers from te fied experiment iterature sowing tat peope iving in weatier areas are not ony ess risk averse but aso more patient. Second, we generay cannot coect a of te information on ouseod beaviour tat we need to make causa inference using simpe econometric modes. Wie it is possibe to coect data on grain quantities tat are sod over a season, it is muc more difficut to coect data on grain quantities tat are purcased because tese transactions are muc smaer in magnitude and more numerous in quantity. Tis generates missing data probems. In tis paper, we first address tis issue by estimating a sampe seection mode. Tis approac yieds resuts tat are consistent wit teoretica predictions. Our estimated effects are statisticay significant and robust to various measures of time and risk preferences. Despite te fact tat farmers appear to ave yperboic time preferences, we do not find evidence tat tis feature significanty affects storage decisions. Because te vaidity of te excusion restriction in a seection mode cannot be tested, we ten turn to a more structura approac. Using tis approac, we obtain resuts tat are very simiar in size. We find tat a one-standard-deviation increase in te discount rate (resp. risk aversion) appears to resut in a arge decrease (resp. increase) in storage of about 45% (resp. 25%). We moreover find tat quantities of grain sod, as predicted by te mode, fa cose to te quantities actuay sod by te farmers in te sampe over te period under study. Tis suggests tat our mode performs quite we in reproducing te observed data. We furter use te teoretica mode to simuate a pubic poicy aiming to smoot inter-seasona price variabiity. 5. We use te teoretica resuts derived from our on-farm storage mode to simuate a grain price stabiisation poicy, and we quantify farmers wiingness to accept not impementing it. We sow tat af of farmers wo se grain woud benefit from suc a poicy. We moreover sow tat te amount of cas tat woud compensate te median farmer for not impementing te poicy is about 1,200 CFA francs. Tis vaue does not exceed per capita storage costs associated wit te poicy. Tis paper presents one of te first fied evidence tat directy inks eicited individua preferences to observed agricutura decisions. Oter recent studies address simiar topics, but tey do not focus on grain storage decisions, use experimenta metods to eicit individua preferences, nor provide a teoretica framework tat coud be used to simuate pubic poicies. Asraf, Karan, and Yin (2006), Bauer, Cytiova, and Morduc (2012), and Dupas and Robinson (2013) impement randomized controed trias to sow tat present-bias preferences measured using a survey instrument may expain individuas coices of adopting savings or credit innovations in te Piippines, India, and Kenya respectivey. Tey construct time-inconsistency dummies from ypotetica time discounting questions tat are ten used in a probit mode to anayse te decision to take up innovative products. A of tese autors conjecture from teir resuts tat time-inconsistency may be an important constraint 4 Harrison, Lau, and Wiiams (2002) eicit individua discount rates from a nationay representative sampe of 268 Danis peope. Aso using a sampe of 253 Danis peope, Andersen, Harrison, Lau, and Rutstrom (2008) jointy eicits bot discount rates and risk aversion coefficients, an approac tat provided ower estimates of discount rates compared to previous studies. Focusing on deveoping countries, Harrison, Humprey, and Verscoor (2010) use data coected from risky coice experiments in Etiopia, India, and Uganda. Tanaka, Camerer, and Nguyen (2010) coect data from a sampe of 160 Vietnamese viagers. Bauer, Cytiova, and Morduc (2012) coect data from a sampe of 570 women in rura India. 5 In countries wit a arge number of poor iving witout safety nets, food price spikes often force governments to impement food price stabiisation poicies in te form of direct interventions ike pubic stocks (Abbott, 2010; Word Bank, 2012; Jayne, 2012; Goue, 2014) Based on data coected from 81 countries, for exampe, Demeke, Pangrazio, and Maetz (2009) sow tat 35 countries reeased pubic stocks at subsidised prices during te food crisis. 3

5 for savings activity, weter at ome or in a microcredit sef-ep group. Liu (2013) conducted a fied experiment to eicit te risk preferences of Cinese farmers. Se sows tat risk aversion may affect farmers decisions regarding te adoption of geneticay modified cotton. In summary, existing empirica studies tat ink individua preferences wit observed agricutura decisions remain very scarce. To our knowedge, tere is no existing empirica evidence to suggest tat impatience drives important agricutura decisions suc as storage. Te present paper tus contributes to a better understanding of te decision mecanisms tat drive deveopment. Tis paper proceeds as foows. Section 2 describes te teoretica mode inking individua preferences to storage decisions. Section 3 describes te sampe, te experimenta design for eiciting individua risk aversion coefficients, discount rates and yperboic discounting parameters, and te survey data. Section 4 provides expected resuts using secondary data. Section 5 dispays te resuts of te causa reationsip between storage decision and risk and time preferences wen using a sampe seection mode. Section 6 provides te resuts from te structura estimation of te teoretica mode. Section 7 provides te resuts of a counterfactua experiment wic simuates a grain price stabiisation poicy. Section 8 concudes. 2 Teoretica Framework 2.1 An On-farm Storage Mode We construct a two-period agricutura ouseod mode tat aows for goods consumption smooting between te two periods. Te first period refers to te arvest season (subscript ) wie te second period refers to te ean season (subscript ). Consider a ouseod wose utiity depends on te consumption of two goods a quantity of grain, tat we denote c g, and a quantity of a generic good tat is bougt on te market, meat for exampe, wic we denote c m. Te ouseod arvests a quantity of grain (H) and generates some cas income from oter agricutura and non-agricutura activities (B). Te ouseod can purcase and se, at te market price, a quantity of grain denoted q g. Te price of te generic good is assumed to be constant and is normaized to one, 6 wie grain price increases from te arvest season (p) to te ean season (p). 7 Between te two seasons, te ouseod as te opportunity to save in te form of grain storage (s). 8 Te generic good cannot be stored and is consumed immediatey after purcase. 9 Te ouseod purcases te generic good using te cas income derived from te sae of grain 6 Tis assumption is not crucia. Assuming tat te price of te generic good varies from p m in te arvest season to p m does not affect our resuts quaitativey. In Proposition 1, Proposition 2, and Coroary 1 tat foow, θ is repaced by θ = ( ( ) ) 1 (1 r ) (1 + δ) p m p/pm (1+σ)r σ p. Coroary 2 and Proposition 3 are not modified. Te forma statement in Proposition 4 becomes: q g r ( < 0 pp m /ppm ) 1 1+σ 1 < δ, wic impies tat te condition is more easiy met ony if te price of te generic good increases between te two seasons. 7 For simpicity, we assume tat, in te arvest season, te ouseod knows wit certainty te price of grain in te ean season. In Appendix B, we sow ow our resuts can be extended to a situation in wic, at te arvest season, te ouseod is uncertain about te exact eve of te price of grain of te ean season. 8 It is commony reported tat grain may spoi due to pests or moisture. Adding a constant spoiing rate of grain is equivaent to considering a ower price ratio, p/p. 9 We may consider tat farmers aso store money and te generic good. However, in our context, grain storage is more profitabe tan eiter money or generic good storage because p/p > 1. Since tere is no uncertainty in our mode, it is optima to store neiter money nor te generic good. See Appendix B for an extension of te mode incuding price uncertainty. 4

6 as we as from oter activities, wit b and b denoting cas spending during te arvest season and during te ean season, respectivey, and b + b B (Equation 2). Te ouseod is moreover assumed to be credit constrained. As a resut, te ouseod can borrow neiter grain nor money so tat s, b, and b must be non-negative (Equation 3). At te arvest season, te stored quantity s, pus te sod quantity q g, pus te consumed quantity c g equas te arvested quantity H (Equation 4). Te vaue of te generic good purcased must equa te vaue of grain saes pq g pus cas spending b (Equation 5). At te ean season, te ouseod aocates te quantity of stored grain s between consumption c g and saes q g (Equation 6). Again, te vaue of te purcased generic good must equa te vaue of grain saes pq g pus cas spending b (Equation 7). Te ouseod makes consumption, storage, and marketing decisions eac season to maximize discounted utiity. Te ouseod s fu optimization probem during te year can be expressed as foows: 10 Maximize U = 1 s.t. 1 r ( (c ) g )σ 1 r c m δ 1 1 r ( (c g ) ) σ 1 r c m, (1) b + b B (cas constraint), (2) s 0, b 0, b 0 (non negativity), (3) c g + q g + s = H (arvest season grain baance), (4) c m = pqg + b (arvest season budget constraint), (5) c g + q g = s (ean season grain baance), (6) c m = pq g + b (ean season budget constraint). (7) Utiity is assumed to be time separabe wit a constant reative risk aversion parameter. Preferences are fuy described by tree parameters: σ 0, wic determines te reative sare of grain and of te generic good witin te tota expenditure; r, wic measures reative risk aversion wit respect to te consumption of te generic good; and δ, wic is te discount rate. Reative risk aversion wit respect to grain consumption is equa to σ(r 1) + 1. We assume tat r > σ/(1 + σ), so tat te utiity function U is concave Optima Consumption, Saes and Storage Decision In tis section, we sove te ouseod s utiity maximization probem focusing on optima eves of consumption and storage. Proofs are reegated to Appendix A. Proposition 1 [Consumption and Storage]: At te arvest season, te optima eves of generic good 10 See Park (2006) for a simiar per-period utiity function for consumption of grain and a generic good bougt on te market. 11 We may reax te assumption tat U is concave (i.e. r > σ/(1+σ)) and instead assume tat U is quasi-concave. We must ten sove te ouseod maximization probem for r < σ/(1 + σ). In tis case, te optima consumption eves provided ( 1 r by Proposition 1 remain uncanged. However, te optima storage eve becomes s = 0 if δ > p/p) 1, s = H + B/p if δ < ( p/p) 1 r 1, and s [ 0, H + B/p ] if δ = ( p/p) 1 r 1. 5

7 consumption c m and of grain consumption c g are suc tat c g ) ) c m = p (H 1 + Bp 1 + σ s and c (H g = σ + Bp 1 + σ s. At te ean season, te optima eves of generic good consumption c m are suc tat c m = p 1 were te optima quantity of stored grain, s, is ( ( ) ) 1 (1 r ) (1+σ)r σ were θ = (1 + δ) p/p. 1 + σ s and c g ( ) s = 1 H + B, 1 + θ p = σ 1 + σ s, Te optima amount of cas spending in eac season is suc tat and of grain consumption b = B and b = 0. Te ouseod spends a its cas income B during te arvest season because it is aways more profitabe to store grain tan to store money, since te grain price increases between seasons. Te quantity H + B p can be seen as an effective quantity of grain, part of wic, 1 1+θ, is stored during te arvest season and ten consumed in te ean season in te form of grain consumption, grain saes, and generic good purcases. Te sare 1 1+θ depends, in a non trivia way, on te discount rate δ, te reative risk aversion parameter r, and te grain preference parameter σ. 12 Moreover, it increases wit te price ratio, given r > σ/(1 + σ). Note tat te form cosen for te utiity function in Equation (1) impies tat te optima consumption of eac good is stricty positive. It aso impies tat te sare of expenditures spent on grain, σ/(1 + σ), and te sare of expenditures spent on te generic good, 1/(1 + σ), are constant and sum to one. 13 Te form of te utiity function aso enabes us to expicity specify te reative risk aversion parameter, discount rate, and consumption sares. 2.3 Cas Income and Saes In order to appy our data to te mode, we must now sift our focus from te quantity of stored grain to te quantity of grain sod during te arvest season. In tis section, we tus determine te optima eve of grain sod during te arvest season, and we sow tat tere is a teoretica equivaence between studying te effect of time and risk preferences on saes and studying te effect of time and risk preferences on storage. 12 An increase in te grain preference ( parameter σ increases grain storage ony if te ouseod is sufficienty impatient ) (r 1) and risk averse, i.e. (1 + δ) (r 1) 2 p/p 1. Te underying intuition is tat an increase in σ increases ouseod risk aversion wit respect to grain consumption ony if r 1. Assume, for instance, tat r 1. Tus, an increase in σ increases risk aversion wit respect to grain, and, if te ouseod is sufficienty impatient (preferring to consume reativey arge quantities during te arvest season), it increases grain storage in order to smoot its consumption. Te opposite ods for r Te easticities of consumption wit respect to H + B p s are constant and sum to one, as we. 6

8 Proposition 2 [Saes]: At te arvest season, optima grain saes are suc tat and, in te ean season, tey are suc tat ) q (H g = 1 + Bp 1 + σ s B p, q g = σ s. From te arvest season budget constraint (Equation 5), we ave q g + B p = cm p, wic indicates tat te cas income generated from grain saes and cas income B are used togeter to purcase te generic good c m.14 Because a B is spent during te arvest season for generic good purcases (b = B), te ouseod tat woud ike to purcase additiona generic goods to reac te optima eve c m Coroary 1: must se grain. Tere is tus a reationsip between B and q g, wic we make expicit in Coroary 1 [Saes and Cas]: Grain saes (resp. grain purcases) decrease (resp. increase) wit cas income B in te arvest season: q g ( B = σ θ 1 + θ ) < 0, and, ouseods aving a sma cas income B wi se rater tan purcase grain: q g 0 p θ 1 + σ(1 + θ) H B. Te intuition beind Coroary 1 is tat ouseods wit sma cas income B must se grain during te arvest season if tey woud ike to purcase some of te generic good during te arvest season. Tis resut is at te eart of te identification strategy in te empirica anaysis tat foows. We now turn to te equivaence between q g and s wen examining te comparative static effects of some preference parameter x: Coroary 2 [Equivaence]: Preference parameter x {r, δ} affects post-arvest saes and storage suc tat: q g x = 1 s 1 + σ x. Coroary 2 states tat te margina effect of an increase in te preference x (eiter risk aversion or time preference parameters) on storage is proportiona to te margina effect of an increase in te preference x on post-arvest saes. Coroary 2 impies tat, provided we are abe to empiricay estimate te impact of preferences on post-arvest saes, we are abe to derive te impact of preferences on storage eves as we. Coroary 2 aso impies tat te size of te margina effect of a preference parameter is aways arger for storage tan for post-arvest saes: q g x < s x, x {r,δ}. (8) 14 If q g 0, Equation (5) means tat te cas income B is used to buy te generic good and aso some grain. 7

9 2.4 Comparative Static Effects of Preferences In tis section we determine te comparative static effects of time and risk preferences tat wi ten be estimated in te empirica anaysis. Proposition 3: [Discounting] An increase in te discount rate, δ, aways increases post-arvest saes: 15 q g δ > 0. Te formua is given by: q g δ = θ 1 (1 + θ) σ 1 H + B/p > 0. (9) 1 + δ (1 + σ)r σ Using Coroary 2, one can aso concude tat an increase in te discount rate decreases grain storage, and using Proposition 1, tat it increases te ouseod s consumption of bot grain and te generic good in te arvest season (c g and cm ) and decreases te ouseod s consumption of bot grain and te generic good in te ean season (c g and c m ). 16 Proposition 4: [Risk Aversion] Post-arvest saes decrease wit risk aversion if and ony if te ouseod is sufficienty impatient: q g r ( ) 1 1+σ < 0 p/p 1 < δ. Proposition 4 states tat te effect of a cange in te reative risk aversion wit respect to te quantity of grain sod depends on te eve of te discount rate. 17 Te formua is given by: q g r = 1 θ H + B/p ( 1 + σ (1 + θ) 2 (r σ + r σ) 2 n ) (1 + δ) 1+σ p/p. (10) ( ) 1 1+σ Te intuition of Proposition 4 is as foows. If p/p 1 < δ, i.e. if te ouseod strongy discounts future utiity and/or te price ratio is sma enoug, it tends to consume arge quantities of grain and te generic good during te arvest season. However, te more it is risk averse wit respect to te generic good, te ess grain te ouseod ses in te arvest season because it seeks to smoot its consumption of te two goods between te two periods. In order to consume te two goods in te ean season, it must store grain in te arvest season. As a resut, grain saes in te arvest season decrease wit risk aversion. Conversey, if te ouseod does not strongy discount future utiity ( ) 1 1+σ and/or te price ratio is ig enoug, i.e. p/p 1 δ, it tends to store arge quantities of grain. However, te more te ouseod is risk averse wit respect to te generic good, te ess it stores 15 Tis is true for r > σ/(1 + σ). If r < σ/(1 + σ), post-arvest saes do not depend on impatience, q g δ = We assume tat tere is no ink between te amount of cas B and te discount rate δ. Aternativey, one coud assume tat B is negativey correated to δ, tat is B B(δ) wit B (δ) < 0. Defining saes q g as a function of δ and B(δ), condition (9) woud ten write: d q g dδ = q g δ + q g B B (δ) > q g δ > 0, wic means tat te effect of impatience on saes woud actuay be stronger. 17 Tis is true for r > σ/(1+σ). If r < σ/(1+σ), saes at te time of arvest season do not depend on risk aversion, q g = 0. r 8

10 grain in te arvest season, again because it seeks to smoot its consumption. In order to consume more of te generic good in te arvest season, it must se more grain. For tis reason, grain saes increase wit risk aversion in tat case. 18 In summary, tis styized mode igigts te fact tat impatience is ikey to decrease storage among a farmers and tat risk aversion is ikey to increase storage among impatient farmers and decrease storage among patient farmers. 2.5 Grain Price Stabiisation Poicy and Wefare In tis section, we provide a framework for studying a price stabiisation poicy aiming to smoot fuctuations in domestic grain prices over te two seasons. We ten derive te expression determining a farmer s wiingness to accept suc a poicy, wic is equa to te amount of cas income tat woud exacty compensate im if te poicy were not impemented. We consider a scenario in wic te government cooses te grain quantity G to be bougt at te arvest season and sod at te ean season, 19 suc tat te equiibrium market price p is te same over bot seasons (p = p = p ). 20 In order to determine G and p, we first write te aggregate suppy and demand functions, assuming as before tat ouseods consume sef-produced grain. 21 We ten define te market cearing conditions. On te suppy side, we derive from te two-period ouseod mode te aggregate suppy of grain at te arvest season as we as te aggregate suppy of grain at te ean season. Bot suppies depend on te price of grain at te arvest season and te price of grain at te ean season. Formay, etting N denote te set of farmers wo se grain at te arvest season (q g > 0), te aggregate suppy of grain at te arvest season, S (p, p), is given by: S (p, p) = N q g, (11) were q g is te quantity of grain sod by te farmer at te arvest season defined by Proposition 2 in Section 2.3. Simiary, etting N denote te set of farmers wo se grain at te ean season (q g te aggregate suppy of grain at te ean season, S (p, p), is given by: > 0), S (p, p) = q g, (12) N were q g is te quantity of grain sod by te farmer at te ean season (as before, see Proposition 2 in Section 2.3). For te sake of simpicity, we assume tat te demand function, D(p), wic is a decreasing func- 18 We assume tat tere is no ink between te amount of cas B and te risk aversion parameter r. Aternativey, one coud assume tat B is negativey correated to r, tat is B B(r ) wit B (r ) < 0. Defining saes q as a function of δ and B(r ), condition (10) woud ten write: d q g = q g + q g dr r B B (r ) > q g, r wic means tat te effect of risk aversion on saes woud actuay be weaker (given tat, if te ouseod is sufficienty impatient, te rigt and side is negative, see Proposition 4). 19 We assume tat a avaiabe maize is ocay produced. According to te Burkina Faso Annua Agricutura Survey, Burkina Faso produces sufficient quantities of maize to satisfy nationa demand. 20 We assume tat te government does not discount time between te two seasons. 21 In tis, we differ from te standard modes proposed by Newbery (1989) wo considers a two-period mode, or more recenty by Goue (2013), wo considers a rationa expectation infinite orizon mode. 9

11 tion of te price, is identica in bot seasons. We are ten abe to define (G,p ) wic soves te two market cearing conditions: D(p ) +G = S (p, p ) (13) D(p ) = S (p, p ) +G (14) Condition (13) is te market cearing condition at te arvest season: te demand pus te quantity bougt by te government must equa te quantity suppied by te farmers. Condition (14) is te market cearing condition at te ean season: te demand must equa te quantity suppied by te farmers pus te quantity suppied by te government. Soving (13)-(14) yieds an expression of G and of p. We ten compute teir vaue from our data. Foowing tis, we study te wefare effect of te price stabiisation poicy. To do so, we define ( te amount ) of cas tat exacty compensates te farmer for not impementing tis poicy. Let V p, p,σ,b be te indirect utiity of te farmer, i.e. te eve of utiity e derives from te optima eves of consumption, storage, cas spending, and saes (Section 2.1). Te farmer s wiingness to accept (WTA) is caracterized by: V ( ) p, p,σ,b + WTA = V ( p, p,σ,b ), (15) Te expression of WTA derived from equaity (15) sows tat, provided we are abe to estimate te vaue of B, of σ and of p, we are aso abe to quantify te impact of suc a poicy on farmers wefare. Tis is precisey te purpose of te empirica anaysis we propose in te foowing sections. 3 Data In order to test te predictions of te teoretica mode and quantify te effects of time and risk preferences on storage beavior, we use origina data on agricutura decisions, coected from 1,500 farmers in two regions of Burkina Faso, wo were aso asked ypotetica questions designed to eicit time discounting and risk aversion preferences. 3.1 Samping Te survey design generated a representative sampe of ouseods in two administrative districts of Burkina Faso, te Tuy and Mououn provinces. Tose provinces are ocated in te western region of te country, wic is te main maize production area. Data were coected in cooperation wit te Confédération Paysanne du Faso (CPF), a nation-wide organization of farmers. A tota of 73 viages were randomy seected from te CPF ist (Figure 2). In tese viages, an average number of 20 ouseods were seected troug te use of a door-to-door strategy wit te aim of gatering a random sampe of ouseods. Wit te ep of te Burkinabe Agricuture Ministry, twenty investigators and two supervisors were recruited for te data coection. A tota of 1,549 ouseods were surveyed in February Surveys were conducted in te Dioua anguage. Te investigators interviewed te ouseod ead, defined as te person responsibe for farming decisions. 22 Te participants com- 22 We remain agnostic concerning te way in wic te individua preferences and beiefs are aggregated witin eac famiy. 10

12 peted a face-to-face interview and participated in a fied experiment. 3.2 Survey Data Te decarative survey is a reca survey about wat appened between January 2012 and February It is comprised of nine distinct sections: (i) te socio-economic caracteristics of te ouseod and of te ouseod s ead; (ii) te ouseod s economic assets; (iii) te type and amount of crop production; (iv) crop saes; (v) fertiizer expenses: (vi) te type and amount of non agricutura activities undertaken by te ouseod members; (vii) te ouseod s socia expenses; (viii) te type and te amount of te ouseod s oans and (ix) te ouseod s food expenses. Tabe 1 reports mean vaues for various farmer caracteristics. On average, surveyed ouseods ave 13 members, 7 of wom work in farming activities. In amost a cases (98%), te ouseod is eaded by a man of an average age of 43 years, wo as received a forma education in 40% of cases, ives a 40-minute wak from te cosest market, 23 and is very often (in 85% of cases) a member of a producer organization, weter CPF or some oter producer organization. In te Tuy and Mououn provinces, te main crops are cotton, maize, sorgum, miet, and sesame. Maize is te most marketed grain. Most ouseods of te sampe (73%) arvested maize during October or November, wie te rest arvested in December One tird of te sampe sod maize during During te arvest season, i.e. between October 2012 and January 2013, 25% of ouseods made one maize sae, and 13% of ouseods made two. Te quantity sod by tose wo made a singe sae over te arvest season is one ton on average. Tis represents about 25% of te tota maize arvest. Since te data were coected in February 2013, we do not observe te quantity of maize sod during te ean season of te studied crop year but we do observe te quantity of maize sod during te ean season of te previous crop year. Tabe 2 summarizes information on maize saes at te arvest season, i.e. between October 2012 and January 2013 (q ), and te quantity of maize sod at te previous ean season, i.e. between February 2012 and September 2012 (q ). It appears tat 67% of te ouseods did not se maize over te arvest season. Moreover, 52% of ouseods did not se maize during te previous ean season eiter, wic suggests tat tey usuay prefer to consume maize rater tan to se it. Unfortunatey, data are missing on maize purcases Eiciting Risk and Time Preferences In order to eicit ouseods time and risk preferences, we use an artefactua fied experiment, to use te terminoogy of Harrison and List (2004). As wit te survey, te experiments were conducted in te Dioua anguage Risk Aversion Data Our experiments were buit on te risk aversion experiments of Hot and Laury (2002). We used a mutipe price ist design to measure individua risk preferences. We ran two experiments offering successivey ow and ig payoffs. In eac experiment, eac participant was presented a coice between 23 We cacuated te distance between eac viage and its associated assemby market using te Argis Software. We assumed te speed of veices traveing on paved roads to be equa to 40 km per our and te speed on non-paved roads to be equa to 10 km per our. 24 In practice, it is amost impossibe to coect reiabe data from ouseods wo are asked to reca a crop purcases since te beginning of te year. In contrast, it is muc easier to coect data on saes, wic are generay few over te period. 11

13 two otteries of risky and safe options, and tis coice was repeated nine times wit different pairs of otteries, as iustrated in Tabe 3. Farmers were asked to coose eiter ottery A or ottery B. For exampe, te first row of Tabe 3 indicates tat ottery A offers a 10% probabiity of receiving 1,000 CFA and a 90% probabiity of receiving 800 CFA, wie ottery B offers a 10% probabiity of a 1,925 CFA payoff and a 90% probabiity of 50 CFA payoff. Low payoffs were cosen because tey were in ine wit te ranges of reative risk aversion parameters in previous experiments by Hot and Laury (2002) and Andersen, Harrison, Lau, and Rutstrom (2008), and because tey amount to approximatey one day s wort of income for a non-skied worker in Burkina Faso (around 1,000 CFA a day, i.e. about 2 USD a day in 2012), wic seemed credibe to respondents. In te second experiment, farmers were asked to coose between otteries wit ten times iger payoffs (10,000 CFA, or around 20 USD, corresponding to te average price of a 100-kg-bag of cerea at te arvest season). In practice, otteries A and B were materiaized by two bags of 10 marbes of different coours: green for 1000 CFA, bue for 800 CFA, back for 1925 CFA and transparent for 50 CFA. Te composition of te bags was reveaed to te farmers, but tey coud not see inside te bag. As indicated in te ast coumn of Tabe 3, risk neutra individuas (r = 0) are expected to switc from ottery A to ottery B at row 5, risk oving individuas (r < 0) are expected to switc to ottery B before row 5, and risk averse individuas (r > 0) are expected to switc to ottery B after row 5. In order to make our resuts comparabe to previous studies, we assume a constant reative risk aversion (CRRA) utiity function, wic enabes to compute te intervas provided in te ast coumn of Tabe We ten foow te same approac as Andersen, Harrison, Lau, and Rutstrom (2008) to infer te risk aversion coefficients and te discount rates impied by te raw responses. We aow risk aversion to be a inear function of te observed ouseods caracteristics. We consider six caracteristics tat we assume to be unambiguousy exogenous in driving risk preferences: gender, age, education, viage, and province. Eicited individua r coefficients are predicted vaues in te mode, wic we estimate using an interva regression, a generaization of censored regression for data were eac observation is measured using an interva scae. Figure 3 and Figure 4 dispay te distribution of te eicited risk aversion coefficients predicted from te ow-payoff experiment and te ig-payoff experiment, respectivey. Resuts from bot experiments sow tat a minority of farmers exibit risk oving or risk neutra beaviour. Most farmers are risk averse, wit an average of r = 0.69 in te ow-payoff experiment and r = 0.63 in te igpayoff experiment (Tabe 4). Tese average vaues are comparabe to tose obtained by Harrison, Humprey, and Verscoor (2010) wo used simiar experiments in India, Etiopia, and Uganda. 25 Te CRRA utiity function as te foowing form: U (x) = x 1 r /(1 r ), were x is te ottery prize and r is te parameter to be estimated and denotes te constant reative risk aversion of te individua. Expected utiity is te probabiity weigted utiity of eac outcome in eac row. An individua is indifferent between ottery A, wit associated probabiity p of winning a and probabiity 1 p of winning b, and ottery B, wit probabiity p of winning c and probabiity 1 p of winning d, if and ony if te two expected utiity eves are equa: p.u (a) + (1 p).u (b) = p.u (c) + (1 p).u (d), or, p. a1 r b1 r + (1 p). 1 r 1 r wic can be soved numericay in terms of r. c1 r d 1 r = p. + (1 p). 1 r 1 r 12

14 3.3.2 Discount Rate Data We buit our time preference experiment on Harrison, Lau, and Wiiams (2002) and on Coer and Wiiams (1999), wo coected experimenta data in Denmark and in te U.S., respectivey. However, we ad to adapt te content in order to offer ypotetica pay-offs tat made sense to te respondents. To do so, we ran pre-tests of te experiment wit a subset of farmers. Finay, we conducted two experiments tat differed in te time deays offered to respondents. In te first experiment, farmers were invited to coose between receiving a given amount in one day s time (option A) or receiving a arger amount in five-days time (option B), and tis coice was repeated nine times, wit increasing payoffs as option B. Tabe 5 dispays te experiment aiming to eicit te four-day-deay discount rate. In te second experiment, farmers were invited to coose between receiving a given amount in one mont s time (option A) or receiving a arger amount in two-monts time (option B), and tis coice was repeated eigt times, wit increasing payoffs as option B. Tabe 6 dispays te experiment aiming to eicit te one-mont-deay discount rate. Again, in order to make our resuts comparabe to oter studies, we assume tat farmers ave additivey time separabe preferences wit a per-period CRRA utiity function. 26 We take te sampe mean of te eicited risk aversion coefficient (r = 0.69) to cacuate te interva bounds. Ten, as we did for te risk aversion coefficient r, we aow δ to be a inear function of exogenous covariates (gender, age, education, viage, and province). Te eicited individua δ coefficients are predicted vaues of a inear mode, wic we estimate using an interva regression. Resuts are dispayed in Tabe 4. Tey sow tat farmers are very impatient in te far future, wit an average vaue of 24 percent per mont. Interestingy, tey are even more impatient in te near future, wit an average vaue of 10 percent for every four days. Recent work as addressed an important issue in muc of te iterature on discount rate eicitation, sowing tat a more appropriate specification of discount-rate modes soud incude a curvature correction for non-inearity in te utiity function in order to account for te infuence of risk aversion on time preferences (Laury, McInnes, and Todd Swartout, 2012). We tus foow te approac proposed by Andersen, Harrison, Lau, and Rutstrom (2008), wo appy maximum ikeiood estimation to jointy estimate risk and time preferences. 27 By tis approac, individuas appear to discount te future even more tan in previous estimates (Tabe 7). Our estimates of te time preference parameter fa we above previous estimates of discount rates tat ave been eicited for seected segments of popuations in deveoped countries, wic range between one and tree percent per mont 26 Te form of te utiity function is: U (x) = x 1 r /(1 r ), were x is te ottery prize and r denotes te constant reative risk aversion of te individua. An agent is indifferent between receiving payment M t at time t or payment M t+1 at time t + 1 if and ony if: U (w + M t ) U (w) = U (w) δ 1 + δ U (w + M t+1) were w is is background consumption and δ accounts for te discount rate. Using te CRRA per period utiity and assuming no background consumption (w = 0), we write: Mt 1 r 1 r = 1 M t+1 1 r 1 + δ 1 r, from wic we can expicity sove for δ as a function of risk aversion r : [ ] Mt+1 1 r δ = 1 M t 27 Te ess computationay expensive way of running te maximum ikeiood estimations is to use a exponentia discount factor, i.e. exp( δ) instead of 1 1+δ. 13

15 (Harrison, Lau, and Wiiams, 2002). Our estimates aso suggest tat te farmers in our sampe ave iger discount rates tan rura viagers wo participated in te experiments conducted by Tanaka, Camerer, and Nguyen (2010) in Vietnam and Bauer, Cytiova, and Morduc (2012) in India. Atogeter, tese resuts suggest tat Burkinabe farmers are more impatient on average tan Vietnamese and Indian farmers, and tat Vietnamese and Indian farmers are more impatient tan a nationay representative sampe of Danis peope. Tis ranking makes sense since tose wit te east amount of weat are expected to ave te igest eves of impatience. Indeed, a very ig discount rate caracterizes ife among farmers in Burkina Faso: ife expectancy is reativey sort, and te ikeiood of osing one s savings due to diseases and agricutura socks can be quite ig Evidence for Hyperboic Time Preferences In order to render tem comparabe, we converted te four-day discount rate to te equivaent discount rate for a one-mont-deay. Te resuts sow tat te four-day discount rate differs consideraby from te one-mont discount rate in a way tat suggests yperboic preferences. We run a test of te equaity of te distributions and a test of equaity of te means, and te nu ypotesis is indeed rejected in bot cases. Impatience in te near future is in fact iger tan impatience in te far future for amost 90% of respondents, as iustrated in Figure 5. Tis resut is in ine wit recent iterature tat sows te existence of yperboic discounting from experimenta data (Noor, 2009; Rode, 2010). We take tis into account in our estimates by introducing a yperboic parameter α in te utiity function (Preec, 2004). 29 Unfortunatey, our data do not aow us to estimate an individua yperboic parameter α i for eac ouseod. 30 However, we are abe to jointy estimate individua discount rates as we as a common vaue for te yperboic parameter tat equas α = 0.46 (sd = 0.025). Tis metod yieds estimates of te individua discount rates tat do not differ muc from tose we previousy obtained (see te ast row in Tabe 7). We retain tese estimates for robustness cecks. Finay, we are abe to cacuate individua yperboic parameters from individua discount rates tat are estimated separatey. 31 Tis variabe wi be used to test weter yperboic preferences pay a significant roe in storage decisions. 28 Our estimates of te discount rate differ consideraby from tose provided by Liebenem and Waibe (2014), wo conducted simiar experiments wit 211 ouseods in Mai and Burkina Faso in 2007 and Tey report discount rates cose to zero, meaning tat ouseods are extremey patient. Tis is a surprising resut considering tat poor farmers are usuay expected to ave ig eves of impatience. However, it is wort mentioning tat tis resut may be due to te fact tat te autors study a reward tat is deivered immediatey (rater tan deayed), wic is not common practice for tis type of experiment due to peope s extreme preferences for immediate rewards. 29 To do so, we introduce te α parameter in te utiity function wen appying te maximum ikeiood approac to jointy estimate risk and time preferences. We use te genera yperboic specification proposed by Preec (2004), werein te discount factor is defined as exp( δ i t α ), and t is te time deay. Te α parameter caracterizes te decreasing impatience of te decision maker, wic is a smooter way to capture te notion of passion for te present in quasi-yperboic specifications (Andersen, Harrison, Lau, and Rutstrom, 2008). Te δ i parameter caracterizes time preference in te usua sense. 30 Even wen using data from te four experiments, te maximum ikeiood procedure does not converge. 31 To do so, we foow Preec (2004), considering te foowing equaity: ( ) expδ near 4 αi i = expδ far 30 i (1) α i were δ near (resp. δ far ) refers to te vaue of te four-day deay discount rate (resp. one-mont deay discount rate), wic i i can be soved in term of α i. 14

16 4 Expected Sign of te Effect of Preferences on Saes At tis stage, we aready ave te necessary information tat wi aow us to determine te sign of te effects under study. Tis is possibe tanks to Proposition 3 and Proposition 4. We use te sampe means of r and δ (Tabe 4) aong wit secondary data on p and p. We moreover estimate a σ parameter from our experimenta data, assuming tat ouseods are omogeneous wit respect to tis parameter. To do so, we introduce te σ parameter in te utiity function wen appying te maximum ikeiood approac to jointy estimate risk and time preferences. 32 From tis procedure, we obtain a common parameter tat equas 1.32 (sd = 0.318), wic is very cose to te vaue tat can be derived from te Burkina Faso Annua Agricutura Survey (EPA 2010/2011) run by te Ministry of Agricuture. 33 In order to make predictions regarding te effect of impatience on te quantity of grain sod during te arvest season, we first ceck our assumption tat r > σ/(1 + σ). Te average vaue for is around 0.56, wic is ower tan te sampe mean of r. Terefore, according to Proposition 3, we expect tat te effect of impatience on te quantity of grain sod at te arvest season is positive. In order to make predictions regarding te effect of risk aversion on te quantity of grain sod ( ) 1 1+σ during te arvest season, we must compare te tresod p/p to te ouseod discount factor ( 1 T 1+δ) were T is te time interva between te arvest and te ean season (Proposition 4). To do so, we use data from te Burkina Faso Market Information System, te SONAGESS, wic gaters and disseminates data on grain prices in severa oca markets trougout te country. Using data over te period from te regions of Tuy and Mououn, we observe tat maize prices increase by an average of 44% between te arvest season and te ean season. Te average annua price ratio is ten p/p = 100/144, were p refers to te arvest period and p refers to te ean period. Using ( ) 1 1+σ te estimated vaue of σ, we tus ave p/p = ( ) Next, assuming a tree-mont interva between te arvest season and te ean season ( T = 3), we ave ( ) 1 T ( 1+δ = ) 0.52 or ( ) 0.09, depending on te time deay considered in te experiment. Tese vaues are unambiguousy beow te 0.84 tresod. Using Proposition 4, we tus concude tat te expected effect of risk aversion on te quantity of grain sod at te arvest season is negative. 34 In wat foows, we provide two approaces tat enabe us to quantify tese effects. 32 More precisey, we consider U (x) to be an indirect utiity function defined as foows. Assume tat ouseods use ottery gain x to buy and consume grain (at price p) and te generic good, maximizing teir utiity function u(c g,c m ) = ( 1 (c g )σ 1 r c m) 1 r. Te indirect utiity function is written: U (x) = A 1 r x (1 r )(1+σ) (1 r ), were A = ( σ ) ( ) σ 1 1+σ 1+σ. Note tat we were unabe to estimate individua vaues for σ because even wen using te four experiments, te maximum ikeiood procedure did not converge. 33 In our mode, sef-consumption is given by (c g + c g )/H = 1+σ σ, provided B is negigibe. Using te average sefconsumption eve of 55% provided by Annua Agricutura Survey, one finds σ = Tis is a te more true wen storage costs are ig. In contrast, tis prediction woud be reversed if, for instance, one assumed tat te price of maize doubes between te arvest season and te ean season and ouseod sef-consumption fas beow 40%. In tis case, we woud ave (p/p) 1 1+σ σ 1+σ 15

17 5 Effects of Preferences on Storage: A Sampe Seection Mode 5.1 Identification Strategy In tis section, we present te econometric mode used to estimate te effects of preferences on te quantity of grain sod post-arvest (and on storage), and we address te seection issue tat arises due to a missing data probem Equation to be Estimated From Proposition 2, we derive te equation to be estimated: q g = θ 1 + θ σ ( H + B p ) B p (16) ( ( ) ) 1 (1 r ) (1+σ)r σ were θ = (1 + δ) p/p We ten use a inear approximation of q g in order to write te regression equation tat wi be estimated: q g β 0 + β 1 r + β 2 δ + β 3 H + β 4 σ + β 5 B (17) Our estimates wi enabe us to vaidate te comparative static resuts regarding te effects of r and of δ on te quantity of maize sod at te arvest season. Te objective of our anaysis ere is to recover consistent and unbiased estimates of te unknown coefficients β 1 and β 2 using our data. Our data consist of two measures of te variabe r and two measures of te variabe δ (te eicited parameters tat we infer from te experiments), a measure of q g, te quantity of maize sod post-arvest, as we as a measure of H, te arvested quantity of maize in We do not directy observe cas income B. However, severa variabes in our dataset may provide some measurement of te cas avaiabe to te farmer (e.g. te arvested quantities of sorgum, miet, rice, groundnut and cotton, te tota number of catte and poutry). A oter potentia sources of cas suc as non-agricutura income, as we as te reative preference for grain σ, remain unobserved. We tus specify te regression mode as foows: q i = µ 0 + β 1 r i + β 2 δ i + β 3 H i + X i β 6 + ɛ i, (18) were q i is te quantity of maize sod by ouseod i during te arvest period. Tis ouseod as risk and time preferences r i and δ i respectivey, and arvests a quantity H i of maize. Proxy variabes for cas avaiabiity (B i ) are stored in vector X i, and ɛ i is an error term Seection Probem Appying ordinary east squares (OLS) to te regression equation (18) for te sampe of avaiabe data woud yied biased estimates of te βs. Indeed, a seection probem arises in te fact tat te sampe consists uniquey of ouseods wo se maize (since we observe q i ony wen q i > 0), and tat tese ouseods may differ in important unmeasured ways from tose tat do not (Heckman, 1979). For exampe, some ouseods may beong to te sampe of seers not because tey are impatient but because tey need cas (i.e. tey ave a sma cas income B), and tis caracteristic is unobservabe to us. Te probem is tat, weter or not time preference is correated wit cas income in te overa 16

18 popuation, tese two variabes are correated in te seected sampe. By using te OLS estimation metod, one woud tus underestimate te effect of δ on q. We terefore turn to a sampe seection mode to describe our estimation probem: q i = { γ0 + γ 1 r i + γ 2 δ i + γ 3 H i + γ 4 X i + η i if Ṽ i > 0 if Ṽ i 0 (19) were ouseod i ses maize ony if Ṽ i is positive. Te seection equation for participating in te market in order to se maize can be written as: Ṽ i = λ 0 + λ 1 r i + λ 2 δ i + λ 3 H i + Z i λ 4 + X i λ 5 + ɛ i (20) were Ṽ i represents te ouseod s utiity to se maize. Z i incudes expanatory variabes tat do not appear in te outcome equation. ɛ i is assumed to be jointy normay distributed wit η i. We do not observe Ṽ i, but we do observe a dicotomous variabe V i tat equas one if te farmer ses maize (Ṽ i > 0) and zero oterwise. Tere are two approaces to estimating te sampe seection mode under te bivariate normaity assumption: te two-step procedure used by Heckman (1979), and Maximum Likeiood Estimation (MLE). In tis paper we use bot. Te Heckman estimator consists of estimating te seection equation troug te use of te usua Probit mode in order to generate an estimate of te inverse Mis ratio. Tis procedure requires severa instruments, wic are stored in Z i. We use two variabes as instruments. Te first, wic we denote po, is a dummy variabe tat equas one if te ouseod ead is member of a producer organization (PO) and zero oterwise. We argue tat participation in a PO is very ikey to determine participation in te market as a seer. Tere are indeed arge fixed costs required in order to reac distant markets, e.g. te purcase or renta of a truck, wic woud be very difficut for an individua producer to afford. For tis reason, farmers often organize in groups in order to sare te cost burden associated wit tese types of expenses. In our data, te odds of a PO member being a seer are 0.56, wic is 3.5 times iger tan te odds of non-members. On te contrary, it is reasonabe to assume tat PO membersip does not determine te quantity of grain sod itsef because variabe costs (te price for an additiona bag of maize) are ow compared to fixed costs. Our second instrument, wic we denote q ean, is a dummy variabe tat equas one if te ouseod sod some maize during te previous ean season. Houseods wo were abe to se some maize over te previous season are ikey to be abe to bear te fixed costs of reacing te market. Consequenty, aving sod maize during te previous season soud be correated wit te probabiity of participating in te market as a seer in te current season. 35 In our data, te odds of a previous seer being a seer over te arvest season are indeed 3.2 times iger tan te odds for a farmer wo did not se any maize over te previous ean season. Te empirica mode aso incudes te foowing contro variabes stored in X : te arvested quantities of sorgum, miet, rice, groundnut, and cotton, te tota number of catte and poutry, te size of te famiy, and te distance from te viage to te market in minutes (Tabe 8) However, te quantity of grain sod over te previous ean season is very unikey to be correated wit te quantity sod over te arvest season because te vast majority of ouseods are not abe to save maize from one arvest to anoter. 36 Since we incude viage dummy variabes in te mode used to estimate te risk and time preference parameters, we 17

19 5.2 Resuts Main resuts are presented in Tabe 9. Coumn (1) dispays te resuts tat we obtain wen appying te Heckman two-step (H2S) consistent estimator to our data, wie coumns (2) to (5) dispay te resuts we obtain wen appying te MLE. Comparing coumn (1) and coumn (2), we observe tat bot estimators provide very simiar resuts. In te case of MLE, we report standard errors tat are custered at te viage eve. Since te predicted vaues for preferences are generated from a prior regression, we aso use bootstrap tecniques to obtain standard errors tat expicity take into account te presence of generated regressors (Pagan, 1984). 37 Te ikeiood-ratio test (χ 2 ) provided at te bottom of Tabe 9 justifies te use of te Heckman seection mode wit our data. 38 In accordance wit tese resuts, oter tests reject te independence of te two equations (19) and (20), as we, so we reject te ypotesis tat te inverse yperboic tangent of ρ equas zero 39 (tis estimate is reported as atanρ in te bottom of te tabe), as we as te ypotesis tat λ = 0, were λ = πρ (tis estimate is reported in te bottom of te tabe). Overa, te resuts appear very stabe. Risk aversion affects te quantity of maize sod during te arvest season at standard eves of significance, wit te expected negative sign. Tis resut ods watever te measure used (ig or ow payoffs experiments). Te resuts moreover indicate tat a one-standard-deviation increase in reative risk aversion decreases te quantity of maize sod by about 140 kg (taking te smaest estimated impact), wic corresponds to a 10% decrease from te mean maize arvest. Tis impact is even arger wit respect to storage, as it is mutipied by (1 + σ) (see Coroary 2 in Section 2.3). As a resut, a 10% decrease in saes corresponds to a 24% increase in storage. Estimates of te impact of time preference are even more precise (most times we can reject te nu at te 1% significance eve). Examining te impact of impatience in te far future, tese resuts indicate tat a one-standard-deviation increase in impatience increases te quantity of maize sod by about 260 kg (coumns 1 to 3 in Tabe 9). Tis effect is simiar in size wit respect to impatience in te near future (coumns 4 and 5 in Tabe 9). Note tat tis effect is not ony precisey estimated but aso arge in magnitude, as it corresponds to a 20% increase in saes from te mean vaue, and a 44% decrease in storage. For instance, a jump from te 25t percentie to te 75t percentie in te discount rate is estimated to correspond to a 12% increase in post-arvest saes and a 28% decrease in storage. Resuts are robust to various measures of time and risk preferences. Tabe 10 dispays te resuts obtained wen we use jointy estimated measures of time and risk parameters (coumns 1 and 2) as we as tose obtained from measures tat incude a yperboic preference parameter tat is common to a farmers (coumn 3 and 4). Again, impatience appears to affect te quantity of maize sod during te arvest season at standard eves of significance, wit te expected positive sign. Te impact of risk aversion as te expected negative sign, but does not appear to be significant. We moreover test cannot incude dummy variabes for viages in te sampe seection mode because tis woud generate a muti-coinearity probem. In order to contro for viage specificities, we tus incude in te empirica mode a variabe tat measures te time to reac te market from te viage. 37 Resuts are dispayed in Appendix C. 38 Te reported ikeiood-ratio test is an equivaent test for ρ = 0, were ρ is te correation between η i and ɛ i, and is computationay te comparison of te joint ikeiood of an independent probit mode for te seection equation (20) and an OLS regression mode on te observed q i data against te Heckman mode ikeiood. 39 Te reported test for atanρ = 0 is equivaent to te test for ρ = 0. 18

20 te impact of te constructed variabe α i, wic measures some yperboic preference for present consumption, but we fai to detect any significant impact on saes (Tabe 11). Turning to te seection equation, we observe tat bot instrumenta variabes pay a significant roe in participation as a seer. We moreover observe te seection effect discussed in Section 5.1.2: wie one woud expect seers to be more impatient tan non-seers, resuts instead indicate tat tey are more patient on average. Tis may be due to te possibiity tat a arge number of patient ouseods were forced to se over te arvest season because of an immediate need for cas. Oter expanatory variabes 40 indicate tat maize seers in te arvest season are aso rice seers, wie farmers wo do not participate in te market as maize seers tend to be arge producers of sorgum and miet. Interestingy, te variabe tat measures te time to reac te market (time) significanty determines te probabiity of participating in te market as a seer, atoug it does not determine te quantity of grain sod in te outcome equation. Tis suggests tat te transactions costs incurred to reac te market in order to se maize are fixed costs rater tan variabe costs. In order to compete te discussion concerning te sampe seection issue, we aso provide te resuts we obtain wen appying te ordinary east square estimator to te sampe of maize seers (Tabe 12). As expected, te effects from tis anaysis are smaer compared to tose we obtain using te Heckman seection mode. Tese resuts indicate tat a one standard deviation increase in te discount rate transates into an increase in te quantity of maize sod at te arvest season of ony 7 to 9%, wie te same increase is two times greater wen generated by te Heckman seection procedure. Tese resuts ceary sow tat taking into account te seection issue reated to unobserved cas needs is of crucia importance for our estimates. 6 Structura Estimate of te Effects of Preferences Because te vaidity of te excusion restrictions in a seection mode cannot be tested, we return to te teoretica mode wit te aim of structuray estimating te impact of risk and time preferences. Wie we must sti dea wit te missing data issue, it is possibe to sove tis probem witout making any assumptions about te seection process tat sorts farmers into te group of seers. Specificay, we address tis issue by estimating te vaue of te unobserved cas avaiabiity (B) for te subset of seers. To do so, we use Proposition 2, wic describes te reationsip between q g and B (and a oter observabe parameters). Because tis reationsip is inear in B p, we are abe to obtain an estimator of B p directy by appying te OLS estimator to te foowing regression equation: q g i = x 0i + B p x 1i + υ i (21) ( ) were x 0i = θi ( ( ) ( 1 1+θ i 1+σ) H, x1i = θi ( ( ) 1 1+θ i 1+σ) ) (1 ri ) 1 (1+σ)r i σ 1 and were θi = (1 + δ i ) p/p. We obtain an estimate of te (omogeneous) parameter B tat fas cose to 60,000 CFA if computed from measures of impatience in te far future, and around 30,000 CFA if computed from measures of impatience in te near future. 40 For te sake of readabiity, te coefficients associated wit contros are not sown in te tabes. Resuts are avaiabe upon request. 19

21 Having estimated a vaue for B/p (and te estimated common parameter σ), we are abe to compute te individua margina impact of impatience (δ i ) on saes (q g ) using Equation (9), were we i introduce subscript i to denote ouseod specific variabes (see Section 2.4): q g i θ i 1 = δ i (1 + θ i ) σ as we as te margina impacts of risk aversion using Equation (10): q g i = 1 r i 1 + σ were θ i is defined as in Equation (21). θ i H i + B/p (1 + θ i ) 2 1 H i + B/p 1 + δ i (1 + σ)r i σ, (22) (r i σ + r σ) 2 n ( ) (1 + δ i ) 1+σ p/p, (23) Tabe 13 compares te resuts we obtain from tis structura approac wit tose we obtain from te inear approximation approac (i.e. te sampe seection mode). Te average margina impacts are actuay very cose. Using te measure of impatience derived from te one-mont-deay experiment, a one-standard-deviation increase in impatience resuts in an increase in te quantity of grain sod by about 350 kg in te structura estimation, and by about 260 kg in te inear approximation mode. Resuts are comparabe wen considering te measure of impatience derived from te four-day-deay experiment: a one-standard-deviation increase in impatience resuts in an increase in te quantity of grain sod by about 280 kg in te structura mode versus 220 kg in te inearized mode. Tis corresponds to an increase in saes (from te mean vaue) tat ranges from 19% to 21% wen reying on estimates from te inearized mode, and from 16% to 26% wen reying on structura estimates. Tis transates to even arger impacts on storage: a one-standard-deviation increase in impatience resuts in a decrease tat ranges from 44% to 47% wen we use te inearized mode, and from 37% to 60% wen we use te structura mode. Simiar comments can be made about te impact of risk aversion: bot approaces yied average estimates tat are simiar in size, abeit muc ess precise (Tabe 14). A one-standard-deviation increase in risk aversion resuts in a decrease in saes (from te mean vaue) tat ranges from 10% to 14% wen we use te inearized mode, and from 10% to 50% wen we use te structura mode. Tis transates to an increase in storage tat ranges from 24% to 33% using te inearized mode, and from 23% to 113% using te structura mode. Overa, our resuts are robust to te two approaces. We are tus confident tat te teoretica framework, parameterized to our data, can be used to simuate pubic poicies. 7 Price Stabiisation Poicy In tis section, we use te teoretica resuts from Section 2.5 to simuate a grain price stabiisation poicy, and we quantify farmers wiingness to accept (WTA) not impementing tis poicy. Te WTA can be understood as te individua cas transfer tat soud be provided by te government to make a farmer from te group of seers indifferent between receiving tis cas transfer and benefiting from te impementation of te price stabiisation poicy. 20

22 7.1 A Counterfactua Simuation Experiment In order to cacuate te vaues of p and G tat define te counterfactua price stabiisation poicy, we begin by computing te tota quantity of grain sod during bot seasons. Again using secondary data on grain prices made avaiabe by SONAGESS (see Section 4), we repace p = 100 CFA francs per kg and p = 144 CFA francs per kg in Equation (16) tat describes te reationsip between q g, p, p, te previousy estimated common parameters B and σ, and a oter individuas parameters observabe in our data (H, δ, r ). Te same computations are performed for q g. By aggregating te vaues of q g and q g for a farmers in te sampe, we obtain 684 tons of maize for te arvest season and 604 tons of maize for te ean season. It is wort noting tat tese quantities, wic are predicted by te mode, are very cose to te aggregated quantities of maize tat were actuay sod by te farmers in te sampe. In our data, te aggregated quantity sod by farmers during te arvest season is 666 tons of maize. 41 Figure 6, wic compares te actua and predicted quantities sod, suggests tat our mode performs quite we in reproducing te observed data. Assuming tat te demand function is inear, D(p) = ap + d, we are ten abe to recover te two parameters of te demand function: its sope a < 0 and its maximum d > 0. We find a 1,829 and d 866,989. Soving for te market cearing conditions (see conditions 13 and 14 in Section 2.5), we find tat p fas around 120 CFA francs per kg. Tis corresponds to a price easticity of grain demand around Te corresponding quantity G fas cose to 107 tons of maize. 42 Repacing p by its vaue in te expression of te optima grain saes at te arvest season q g (see Proposition 2), we are abe to compute te grain saes for eac farmer under te scenario were te price of grain is 120 CFA francs per kg trougout te year. Figure 7 compares te predicted quantities sod witout poicy wit tose tat te mode predicts under te price stabiisation poicy scenario. Te cart iustrates tat a price grain poicy woud transate into iger saes by farmers post-arvest (about 70 tons more in a, i.e. a 10% increase). 7.2 Farmer Wiingness to Accept Repacing p by its vaue in te expression of WTA derived from equaity (15), we ten compute te WTA for eac farmer. Te distribution of individua WTAs is dispayed on Figure 8. Haf of farmers ave a positive wiingness to accept, wic indicates tat tey woud benefit from te maize price stabiisation poicy. For tese farmers, te WTA exceeds 1,200 CFA. For one quarter of te farmers, te WTA even exceeds 15,000 CFA, wic corresponds to one 100kg bag of maize. Te fact tat a price stabiisation poicy woud be beneficia to af of te farmers in our sampe is mainy driven by te price increase in te arvest season (+20%). Interestingy, tis transates to iger consumption of te generic good (+20%) in te arvest season for te median farmer. Grain consumption does not increase muc (+1.5%). In te ean season, bot consumption eves are ower (a 30% decrease in grain consumption and a 42% decrease in generic good consumption). Finay, we examine te cost-effectiveness of te price stabiisation poicy under study. Assuming tat te costs of storing grain incurred by te Government represent around 9% of te market vaue 41 We do not observe saes tat occur between February 2013 and September However, we observe saes tat occur between February 2012 and September 2012, wic refers to te previous ean season. Te aggregated quantity sod over tis period is 546 tons. 42 Using conditions (13) and (14), we ave G = 1 ( ) ( 2 S S and p = a 1 12 ( ) ) S + S d. 21

23 of te quantity G tat is stored unti te ean season, 43 we estimate tese costs to amount to about 2,300 CFA francs per farmer. Because te median WTA does not exceed 1,200 CFA francs, we concude tat te price stabiisation poicy woud not be cost-effective for te median seer in our sampe Concusion Onfarm grain storage is an important consumption smooting asset in deveoping countries, and storage decisions can vary significanty across ouseods from a given region. Most studies sow tat many farmers wo are expected to store grain often coose to se teir grain instead because tey need cas. We ave gone furter by examining te roe of individua preferences in storage decisions. Taking into account te fact tat most farmers wo coose to se grain in te arvest season are iquidity constrained, we ave provided evidence tat impatience and risk aversion aso significanty affect te quantity of grain sod in te arvest period. We report arge effects of risk and time preferences on storage beaviours. A one-standard-deviation increase in impatience resuts in a arge decrease in storage of about 45%, and a one-standard-deviation increase in risk aversion resuts in a arge increase in storage, about 25%. Te estimated effects are statisticay significant and robust to various measures of time and risk preferences. We moreover sowed tat our teoretica mode performs quite we in reproducing te observed data. We terefore utiized it to simuate a grain price stabiisation poicy. We sowed tat af of farmers among seers woud benefit from suc a poicy and tat tis resut is mainy driven by te increase in te price of grain during te arvest season. Finay, we sowed tat te amount of cas tat woud compensate te median farmer for not impementing te grain price stabiisation poicy is about 1,200 CFA francs. Tis vaue does not exceed te per capita storage costs associated wit te poicy. References ABBOTT, P. (2010): Stabiisation poicies in deveoping countries after te food crisis, Discussion paper, OCDE, Goba Forum on Agricuture November 2010 Poicies for Agricutura Deveopment, Poverty Reduction and Food Security OECD Headquarters, Paris. ANDERSEN, S., G. W. HARRISON, M. I. LAU, AND E. E. RUTSTROM (2008): Eiciting Risk and Time Preferences, Econometrica, 76(3), ASHRAF, N., D. KARLAN, AND W. YIN (2006): Tying Odysseus to te Mast: Evidence from a Commitment Savings Product in te Piippines, Te Quartery Journa of Economics, 121(2), AYEL, G., R. BEAUJEU, R. BLEIN, J. COSTE, F. GÉRARD, S. KONATÉ, H. LETURQUE, P. RAYÉ, AND G. SIAM (2013): Les stocks aimentaires et a réguation de a voatiité des marcés en Afrique. Agence française de déveoppement. 43 Tis figure is based on estimates provided by Aye, Beaujeu, Bein, Coste, Gérard, Konaté, Leturque, Rayé, and Siam (2013). 44 Te price stabiisation poicy woud be cost-effective for 47% of farmers. 22

24 BAUER, M., J. CHYTILOVA, AND J. MORDUCH (2012): Beaviora Foundations of Microcredit: Experimenta and Survey Evidence from Rura India, American Economic Review, 102(2), COLLER, M., AND M. WILLIAMS (1999): Eiciting Individua Discount Rates, Experimenta Economics, 2(2), DEATON, A., AND G. LAROQUE (1992): On te Beaviour of Commodity Prices, Review of Economic Studies, 59(1), DEMEKE, M., G. PANGRAZIO, AND M. MAETZ (2009): Country Responses to te Food Security Crisis: Nature and Preiminary Impications of te Poicies Pursued, Discussion paper, Initiative on Soaring Food Prices, FAO. DUPAS, P., AND J. ROBINSON (2013): Wy Don t te Poor Save More? Evidence from Heat Savings Experiments, American Economic Review, 103(4), GOUEL, C. (2013): Optima food price stabiisation poicy, European Economic Review, 57(C), (2014): Food Price Voatiity and Domestic Stabiization Poicies in Deveoping Countries, in Te Economics of Food Price Voatiity, ed. by J.-P. Cavas, D. Hummes, and B. Wrigt, Capter 7, pp Cicago: University of Cicago Press. HARRISON, G., S. HUMPHREY, AND A. VERSCHOOR (2010): Coice under Uncertainty: Evidence from Etiopia, India and Uganda, Economic Journa, 120(543), HARRISON, G. W., M. I. LAU, AND M. B. WILLIAMS (2002): Estimating Individua Discount Rates in Denmark: A Fied Experiment, American Economic Review, 92(5), HARRISON, G. W., AND J. A. LIST (2004): Fied Experiments, Journa of Economic Literature, 42(4), HECKMAN, J. J. (1979): Sampe Seection Bias as a Specification Error, Econometrica, 47(1), HOLT, C. A., AND S. K. LAURY (2002): Risk Aversion and Incentive Effects, American Economic Review, 92(5), JAYNE, T. (2012): Managing food price instabiity in East and Soutern Africa, Goba Food Security, 1(2), LAURY, S., M. MCINNES, AND J. TODD SWARTHOUT (2012): Avoiding te curves: Direct eicitation of time preferences, Journa of Risk and Uncertainty, 44(3), LIEBENEHM, S., AND H. WAIBEL (2014): Simutaneous Estimation of Risk and Time Preferences among Sma-scae Catte Farmers in West Africa, American Journa of Agricutura Economics. LIU, E. M. (2013): Time to Cange Wat to Sow: Risk Preferences and Tecnoogy Adoption Decisions of Cotton Farmers in Cina, Te Review of Economics and Statistics, 95(4), NEWBERY, D. M. (1989): Te Teory of Food Price Stabiisation, Economic Journa, 398(99),

25 NOOR, J. (2009): Hyperboic discounting and te standard mode: Eiciting discount functions, Journa of Economic Teory, 144(5), PAGAN, A. (1984): Econometric Issues in te Anaysis of Regressions wit Generated Regressors, Internationa Economic Review, 25(1), pp PARK, A. (2006): Risk and Houseod Grain Management in Deveoping Countries, Economic Journa, 116(514), PRELEC, D. (2004): Decreasing Impatience: A Criterion for Non-stationary Time Preference and "Hyperboic" Discounting, Scandinavian Journa of Economics, 106(3), ROHDE, K. (2010): Te yperboic factor: A measure of time inconsistency, Journa of Risk and Uncertainty, 41(2), STEPHENS, E. C., AND C. B. BARRETT (2011): Incompete Credit Markets and Commodity Marketing Beaviour, Journa of Agricutura Economics, 62(1), TANAKA, T., C. F. CAMERER, AND Q. NGUYEN (2010): Risk and Time Preferences: Linking Experimenta and Houseod Survey Data from Vietnam, American Economic Review, 100(1), VAN CAMPENHOUT, B., E. LECOUTERE, AND B. D EXELLE (2015): Inter-Tempora and Spatia Price Dispersion Patterns and te We-Being of Maize Producers in Soutern Tanzania, Journa of African Economies, 24(2), WORLD BANK (2012): Using Pubic Food Grain Stocks to Enance Food Security, Word Bank Oter Operationa Studies 11878, Te Word Bank. 24

26 Tabes and Figures Tabe 1: Sampe Caracteristics Caracteristics Unit Obs. Mean Std. Dev. Min Max Famiy size number Labor force number Sex man= Age years Education yes= Producer organization yes= Catte (none) yes= Catte (more tan 10) yes= Catte (ess tan 10) yes= Pow number Poutry number Distance to market minutes Cutivated areas Cotton a Maize a Sorgum a Miet a Sesam a Groundnut a Rice a Production eves Cotton ton Maize ton Sorgum ton Miet ton Sesam ton Groundnut ton Rice ton Maize marketing Saes (post-arv) yes= Saes (ean) yes= Quantity sod (post-arv) kg Quantity sod (ean) kg Note: Tis tabe sows summary statistics for a set of variabes. yes=1 means tat te variabe is a dummy. 25

27 Tabe 2: Maize Saes over te Two Seasons current current q = 0 q > 0 tota previous q = previous q > tota Note: Previous q refers to maize saes tat occur between February 2012 and September Current q refers to maize saes tat occur between October 2012 and January Tabe 3: Te Paired Lottery-coice Decisions wit Low Payoffs ottery A ottery B p gain a 1 p gain b p gain c 1 p gain d range of r Note: Last coumn was not sown to respondents. Tabe 4: Eicited Risk Aversion and Discount Rate Variabe Mean 1 st Quartie Median 3 rd Quartie r (ow payoffs) r (ig payoffs) δ far (1 mont) δ near (4 days) Note: Te first row (r (ow payoffs)) and te second row (r (ig payoffs)) dispay summary statistics for te risk aversion parameters tat were eicited from te ow-payoff experiment and te ig-payoff experiment, respectivey. Te tird row (δ far ) and te fourt row (δ near ) dispay summary statistics for te discount rates tat were eicited from te 1-mont-deay experiment and te 4-day-deay experiment, respectivey. Tis was done given a constant reative risk aversion utiity function were te risk aversion parameter was set to te sampe mean (ow payoffs), r =

28 Tabe 5: Woud you prefer to get A in one day or B in five days? A B range of δ Note: Coumn range of δ indicates te associated interva for monty δ for a respondent wo switces from A to B. Tabe 6: Woud you prefer to get A in one mont or B in two monts? A B range of δ Note: Coumn range of δ indicates te associated interva for monty δ for a respondent wo switces from A to B. 27

29 Tabe 7: Eicited Discount Factors Discount factor Obs. Mean 1 st Quartie Median 3 rd Quartie Separate estimate Joint estimate Joint estimate (α) Note: Tis tabe sows summary statistics for discount factors (not discount rates) in order to make te vaues directy comparabe. Te first row (Separate estimate) dispays summary statistics for te discount factor tat was eicited from te 1-mont-deay experiment, in wic risk aversion is set to te sampe mean, r = Te second row (Joint estimate) dispays summary statistics for te discount factor tat was eicited jointy wit te risk aversion parameter, from te four experiments. Tis discount factor is assumed to be of te exponentia form, tat is exp( δ i t), were t is te time deay and δ i is a monty vaue. Te ast row (Joint estimate (α)) dispays summary statistics for te discount factor tat was eicited jointy wit te risk aversion parameter and a common yperboic parameter α. Tis discount factor is assumed to be of te form exp( δ i t α ), were were t is te time deay and α captures yperboic preferences. Tis tabe reports summary statistics for positive discount factors ony. Tabe 8: Description of Variabes Labe Unit Description risk aversion (r ) none risk aversion coefficient discount rate (δ) none discount rate yperboic parameter (α) none constructed from expδ near i maize arvest (H) tons maize arvest ( 4 30 ) αi = expδ far(1) α i i catte>= 10 dummy equas one if te farmer as more tan 10 oxen (none is te reference) catte< 10 dummy equas one if te farmer as ess tan 10 oxen (none is te reference) poutry number number of cickens, turkeys, ducks, and geese famiy number number of members in te ouseod sorgo arvest tons quantity of sorgo arvested in 2012 miet arvest tons quantity of miet arvested in 2012 gnut arvest tons quantity of groundnut arvested in 2012 rice arvest tons quantity of rice arvested in 2012 cotton arvest tons quantity of cotton arvested in 2012 time minutes time to reac te market po dummy equas one if te farmer is member of a producer organization q ean dummy equas one if te farmer sod maize during previous ean season 28

30 Tabe 9: Te Effect of Preferences on Saes (1) (2) (3) (4) (5) Dep. Var. is Saes (q ) H2S MLE MLE MLE MLE risk aversion * * * discount rate *** ** ** ** ** H maize *** *** *** *** *** Dep. Var. is V risk aversion 0.30 *** 0.29 *** 0.25 *** 0.35 *** 0.28 *** discount rate *** ** ** *** *** H maize 0.04 *** 0.06 ** 0.06 ** 0.06 ** 0.06 ** po 0.55 *** 0.46 *** 0.46 *** 0.45 ** 0.45 ** q ean 0.32 *** λ *** *** *** *** *** atanρ ** ** ** ** χ ** 5.53 ** 5.81 ** 5.58 ** Number of obs Censored obs Uncensored obs Payoffs ow ow ig ow ig Time deay 1 mont 1 mont 1 mont 4 days 4 days Note: Tis tabe reports estimation resuts for te sampe seection mode. Te top of te tabe reports te estimates of te outcome equation, were te dependent variabe is te quantity of maize sod during arvest season. Te bottom of te tabe reports te estimates of te seection equation. Bot equations aso incude as contros te arvested quantities of sorgum, miet, rice, groundnut, and cotton, te tota number of catte and of poutry, te famiy size and time to trave to te market. Coumn (1) reports Heckman-Two-Step estimates, coumns (2) to (5) report Maximum Likeiood estimates. λ, atanρ, and χ 2 are statistics of tree tests of te nu ypotesis ρ = 0, were ρ is te correation between te error terms of te two equations. Standard errors custered at viage eve are in itaics. Tree asterisks *** (resp. **, *, ) denote rejection of te nu ypotesis at te 1% (resp. 5%, 10%, 15%) significance eve. Te variabes risk aversion and discount rate are individua parameters tat were estimated separatey from te experiments, as expained in Section and in Section Te row Payoffs indicates weter te ow-payoff experiment or te ig-payoff experiment was used to eicit te risk aversion parameter incuded in te mode. Te row Time deay indicates weter te 4-day-deay experiment or te 1-mont-deay experiment to eicit te discount rate incuded in te mode. 29

31 Tabe 10: Te Effect of Preferences on Saes - joint estimates of preferences (1) (2) (3) (4) Dep. Var. is Saes (q ) H2S MLE H2S MLE risk aversion discount rate *** ** *** ** H maize *** *** *** 0.11 *** Dep. Var. is V risk aversion discount rate *** *** *** *** H maize 0.04 *** 0.06 ** 0.04 *** 0.06 ** po 0.56 *** 0.47 *** 0.56 *** 0.47 *** q ean 0.32 *** *** λ *** *** *** *** atanρ ** ** χ ** 5.45 ** Number of obs Censored obs Uncensored obs Hyperboic no no yes yes Note: Tis tabe reports estimation resuts for te sampe seection mode, were individua preferences are jointy eicited. Te top of te tabe reports te estimates of te outcome equation, were te dependent variabe is te quantity of maize sod during arvest season. Te bottom of te tabe reports te estimates of te seection equation. Bot equations aso incude as contros te arvested quantities of sorgum, miet, rice, groundnut, and cotton, te tota number of catte and of poutry, te famiy size and time to trave to te market. Coumns (1) and (3) report Heckman-Two-Step estimates, coumns (2) to (4) report Maximum Likeiood estimates. λ, atanρ, and χ 2 are statistics of tree tests of te nu ypotesis ρ = 0, were ρ is te correation between te error terms of te two equations. Standard errors custered at viage eve are in itaics. Tree asterisks *** (resp. **, *, ) denote rejection of te nu ypotesis at te 1% (resp. 5%, 10%, 15%) significance eve. Te variabes risk aversion and discount rate are individua parameters tat were jointy estimated from te experiments, as expained in Section Te eicited discount rates are a monty vaues. Te row Hyperboic indicates weter te joint eicitation of risk and time preferences incudes te commom yperboic discounting parameter (à a (Preec, 2004)). 30

32 Tabe 11: Te Effect of Preferences on Saes - Specification incuding yperboic parameter α Dep. Var. is Saes (q ) H2S MLE MLE MLE MLE risk aversion -475,63 *** -412,36 ** -300,68 * -384,73 ** -260,25 * 176,09 191,04 155,13 182,71 138,68 discount rate 1633,67 *** 1425,37 *** 1548,99 ** 4248,00 *** 4536,10 *** 476,77 537,45 604, , ,75 yperboic α 214,93 182,66 181,93 357,81 * 368,34 * 201,92 153,19 156,27 198,41 201,30 H maize 94,72 *** 116,37 *** 115,27 *** 116,48 *** 114,99 *** 19,75 29,38 29,57 29,51 29,76 Dep. Var. is V risk aversion 0,38 *** 0,38 *** 0,33 *** 0,36 *** 0,30 *** 0,07 0,12 0,10 0,12 0,10 discount rate -1,07 *** -1,00 ** -1,14 ** -3,31 ** -3,57 *** 0,19 0,46 0,47 1,29 1,29 yperboic α 0,04 0,04 0,04-0,12-0,14 0,11 0,12 0,12 0,14 0,14 H maize 0,05 *** 0,08 *** 0,08 *** 0,08 *** 0,08 *** 0,01 0,03 0,03 0,03 0,03 op 0,45 *** 0,34 * 0,34 * 0,33 * 0,32 * 0,13 0,18 0,18 0,18 0,18 q ean 0,29 *** 0,13 0,14 0,14 0,15 0,09 0,14 0,24 0,14 0,14 λ -1576,86 *** -1330,93 *** -1341,33 *** -1340, ,37 *** 493,24 597,75 618,55 604,85 626,81 atanρ -1,01 ** -1,02 ** -1,02-1,03 ** 0,45 0,47 0,46 0,48 χ 2 4,96 ** 4,65 ** 4,91 ** 4,61 ** Number of obs Censored obs Uncensored obs Payoffs ow ow ig ow ig Time deay 1 mont 1 mont 1 mont 4 days 4 days Note: Tis tabe reports estimation resuts for te sampe seection mode, incuding te individua yperboic discounting parameter α. Te top of te tabe reports te estimates of te outcome equation, were te dependent variabe is te quantity of maize sod during arvest season. Te bottom of te tabe reports te estimates of te seection equation. Bot equations aso incude as contros te arvested quantities of sorgum, miet, rice, groundnut, and cotton, te tota number of catte and of poutry, te famiy size and time to trave to te market. Coumn (1) reports Heckman-Two-Step estimates, coumns (2) to (5) report Maximum Likeiood estimates. λ, atanρ, and χ 2 are statistics of tree tests of te nu ypotesis ρ = 0, were ρ is te correation between te error terms of te two equations. Standard errors custered at viage eve are in itaics. Tree asterisks *** (resp. **, *, ) denote rejection of te nu ypotesis at te 1% (resp. 5%, 10%, 15%) significance eve. Te variabes risk aversion and discount rate are individua parameters tat were estimated separatey from te experiments, as expained in Section and in Section Te row Payoffs indicates weter te ow-payoff experiment or te ig-payoff experiment was used to eicit te risk aversion parameter incuded in te mode. Te row Time deay indicates weter te 4-day-deay experiment or te 1-mont-deay experiment to eicit te discount rate incuded in te mode. 31

33 Tabe 12: OLS Estimates of te Effect of Preferences on Saes (1) (2) (3) (4) Dep. Var. is Saes (q ) OLS OLS OLS OLS risk aversion discount rate * * H maize *** *** *** *** Number of obs Payoffs ow ig ig ow Time deay 1 mont 1 mont 4 days 4 days Note: Tis tabe reports OLS estimation resuts for a regression of te grain saes on risk and time preferences. Contros incude te arvested quantities of sorgum, miet, rice, groundnut, and cotton, te tota number of catte and of poutry, te famiy size and time to trave to te market. Standard errors custered at viage eve are in itaics. Tree asterisks *** (resp. **, *, ) denote rejection of te nu ypotesis at te 1% (resp. 5%, 10%, 15%) significance eve. Te variabes risk aversion and discount rate are individua parameters tat were estimated separatey from te experiments, as expained in Section and in Section Te row Payoffs indicates weter te ow-payoff experiment or te ig-payoff experiment was used to eicit te risk aversion parameter incuded in te mode. Te row Time deay indicates weter te 4-day-deay experiment or te 1-mont-deay experiment was used to eicit te discount rate incuded in te mode. 32

34 Tabe 13: Structura Estimates of te Effect of Impatience on Saes and on Storage Margina Effect on Saes +1 SD on Saes (kg) +1 SD on Saes (%) Effect on Storage (%) (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) risk aversion discount rate Linear Structura B/p Linear Structura Linear Structura Linear Structura ow payoffs 1 mont 1126 ** 1546 *** 687 *** +258 kg +354 kg +19% +26% -44% -60% ig payoffs 1 mont 1153 ** 1537 *** 591 *** +264 kg +352 kg +19% +26% -45% -60% ow payoffs 4 days 2739 ** 2286 *** 299 *** +285 kg +238 kg +21% +17% -48% -40% ig payoffs 4 days 2656 ** 2071 *** 364 *** +276 kg +215 kg +20% +16% -47% -37% Note: Tis tabe compares estimation resuts for te sampe seection mode and te structura approac. Tree asterisks *** (resp. **, *, ) denote rejection of te nu ypotesis at te 1% (resp. 5%, 10%, 15%) significance eve. For te structura estimates, standard errors are computed using a bootstrap procedure. Coumn (1) indicates weter te ow-payoff experiment or te ig-payoff experiment was used to eicit te risk aversion parameter. Coumn (2) indicates weter te four-day-deay experiment or te onemont-deay experiment was used to eicit te discount rate. Coumn (3) reports te average effect of an increase in te discount rate on saes wen using te sampe seection mode. Coumn (4) reports te average effect of an increase in te discount rate on saes computed from equation (22). Coumn (5) reports te estimates of te cas amount B/p (in kg of maize). Coumns (6) and (7) report additiona saes of maize (in kg) induced by a one-standard-error increase in te discount rate wen using te sampe seection mode and te structura mode, respectivey. Coumns (8) and (9) report te same resuts expressed as a percentage of average saes. Coumns (10) and (11) report additiona stored quantities of maize (in percentage of average stored quantities) induced by a one-standard-error increase in te discount rate wen using te sampe seection mode and te structura mode, respectivey. 33

35 Tabe 14: Structura Estimates of te Effect of Risk Aversion on Saes and on Storage Margina effect of risk aversion +1 SD on Saes (kg) +1 SD on Saes (%) +1 SD on Storage (%) risk aversion discount rate Linear Structura B/p Linear Structura Linear Structura Linear Structura (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) ow payoffs 1 mont *** 687 *** -158 kg -662 kg -12% -49% +27% +113% ig payoffs 1 mont *** 591 *** -139 kg -419 kg -10% -31% +24% +71% ow payoffs 4 days -318 * *** -194 kg -271 kg -14% -20% +33% +46% ig payoffs 4 days -232 * -190 ns 364 *** -165 kg -135 kg -12% -10% +28% +23% Note: Tis tabe compares estimation resuts for te sampe seection mode and te structura approac. Tree asterisks *** (resp. **, *, ) denote rejection of te nu ypotesis at te 1% (resp. 5%, 10%, 15%) significance eve. For te structura estimates, standard errors are computed using a bootstrap procedure. Coumn (1) indicates weter te owpayoff experiment or te ig-payoff experiment was used to eicit te risk aversion parameter. Coumn (2) indicates weter te four-day-deay experiment or te one-mont-deay experiment was used to eicit te discount rate. Coumn (3) reports te average effect of an increase in te risk aversion parameter on saes wen using te sampe seection mode. Coumn (4) reports te average effect of an increase in te risk aversion parameter on saes computed from equation (22). Coumn (5) reports te estimates of te cas amount B/p (in kg of maize). Coumns (6) and (7) report additiona saes of maize (in kg) induced by a one-standard-error increase in te risk aversion parameter wen using te sampe seection mode and te structura mode, respectivey. Coumns (8) and (9) report te same resuts expressed as a percentage of average saes. Coumns (10) and (11) report additiona stored quantities of maize (in percentage of average stored quantities) induced by a one-standard-error increase in te risk aversion parameter wen using te sampe seection mode and te structura mode, respectivey. 34

36 Figure 1: Woesae price of cereas in Mououn (nomina price in CFA/kg) Source: SONAGESS. 35

37 Figure 2: Location of surveyed farmers 36

38 Figure 3: Eicited risk aversion coefficients (ow payoffs) Density Linear prediction Figure 4: Eicited risk aversion coefficients (ig payoffs) Density Linear prediction 37

39 Figure 5: Comparison of eicited discount rates (δ) 1-mont discount rate Density days discount rate monty discount rate Graps by sampe Figure 6: Distribution of grain saes (predicted versus actua vaues) 38

40 Figure 7: Distribution of predicted saes (in kg) Figure 8: Distribution of Wiingness To Accept (in CFA francs) 39

41 Appendix A: Proofs Proof of Proposition 1 and 2: Notice tat te cas constraint is necessariy saturated, i.e. b + b = B. Using tis condition and conditions (5) and (7) and substituting c m, cm and b, te optimization probem (1) can be soved by considering te foowing simpified optimization probem (we wi ceck tat te ignored non negativity constraint ods): Maximize} U = 1 1 r { c g,q g,c g,q g ( (c g ) ( )) σ pq g 1 r + b δ 1 r ( (c g ) σ ( g ) ) 1 r pq + B b, (24) suc tat: c g + q g + c g + q g = H, (25) and, b B. (26) Let te Lagrange mutipiers associated wit te constraints (25) and (26) be λ and µ. Te Lagrangian is given by L = U + λ [ H c g q g c g q g ] + µ(b b ), (27) suc tat λ 0, µ 0, λ [ H c g q g c g q g ] 0 and µ(b b ) 0. Te first order conditions incude: and (25). L c g L q g L c g L q g L = σ ( c g = p ( c g = = σ 1 + δ 1 b = ( c g 1 + δ p ( c g ) σ(1 r ) 1 ( pq g + b ) 1 r λ = 0, (28) ) σ(1 r ) ( pq g + b ) r λ = 0, (29) ( g ) σ(1 r ) 1 ( g ) 1 r c pq + B b λ = 0, (30) ) σ(1 r ) ( pq g ) ( ) σ(1 r ) pq g r + b 1 + B b ) r λ = 0, (31) 1 + δ ( g ) σ(1 r ) ( g ) r c pq + B b µ = 0 (32) Let us first sow tat µ > 0. Suppose te contrary, i.e µ = 0. Ten, (32) becomes Combining (29) and (31), we obtain ( g ) σ(1 r ) ( c c g = 1 g pq + B b 1 + δ pq g + b ( g ) σ(1 r ) c c g = p p δ ( g pq + B b pq g + b ) r. ) r. We ten must ave p = p, wic is a contradiction. We ten ave µ > 0 and b = B. 40

42 Combining (28), (29), (30), and (31), we find, ( ) σ q g + B = c g p (33) σq g q g = c g (34) ( ) = 1 q g θ + B, (35) p ( ( ) ) 1 (1 r ) (1+σ)r σ were θ = (1 + δ) p/p. Using (25), we obtain ( ) q g = 1 θ H + B B 1 + σ 1 + θ p p, (36) and ten, we ave c g c g q g = = = ( ) σ θ H + B, 1 + σ 1 + θ p ( ) (37) σ 1 H + B, 1 + σ 1 + θ p ( ) (38) σ 1 + θ H + B p, (39) and, using (5) and (7), we aso ave and, ( ) c m = p 1 θ H + B, (40) 1 + σ 1 + θ p ( ) c m = p 1 1 H + B. (41) 1 + σ 1 + θ p Te Lagrange mutipiers are suc tat ( ( ) 1 r λ = (σ) σ(1 r ) 1 p 1 + σ θ 1 + θ ( H + B p )) σ(1 r ) r > 0, and, µ = ( p ) ( ( r σ σ(1 r ) 1 1 H + B 1 + δ 1 + σ 1 + θ p )) σ(1 r ) r ( ) p p 1 > 0. Proof of Coroary 2: Saes at te arvest season are non negative if and ony if 1 θ 1+σ 1+θ θ 1+σ 1+θ p 1 1 H B, 41

43 or, θ p 1 + σ(1 + θ) H B. Proof of Proposition 3: Te derivative of q g q g ( ) δ = θ 1 (1 + θ) 2 H + B 1 + σ p wit respect to δ is given by: δ (1 + σ)r σ (42) It is positive as ong as r > σ 1+σ. Proof of Proposition 4: Te derivative of q g q g r = σ wit respect to r is given by s ( H + B p s ) ( H + B p )(r σ + r σ) 2 n ( ) (1 + δ) 1+σ p/p, (43) wic is negative ony if or, ( ) (1 + δ) 1+σ p/p 1, (44) ( ) 1 1+σ p/p 1 < δ. (45) Appendix B: Mode wit price risk Assume tat te situation is te same as te one described in Section 2 except tat, at te arvest season, te ouseod does not know te (future) price of grain at te ean season. Instead, we assume tat, at te time of arvest, te anticipated price of grain at te ean season is p, and it is a random variabe wit mean p > p, were p is te (known) price of grain at te arvest season. Te uncertainty regarding te price of grain at te ean season is resoved before te ouseod makes its seing and consumption decisions at te ean season. Tus, te timing is as foows: at te arvest season, te ouseod arvests a quantity of grain (H) and generates some cas income from oter agricutura or non-agricutura activities (B). Te ouseod can purcase and se, at te market price, a quantity of grain denoted v g. Te price of te generic good is assumed to be constant and is normaized to one. At tis point in time, te ouseod knows te price of grain at te arvest season, p, but not te price of grain at te arvest season, p. Te ouseod ten makes its consumption and storage decisions. At te ean season, te ouseod earns te reaized price of grain and consequenty aocates te quantity of stored grain s between consumption c g and saes q g. We use te foowing assumption regarding te ean season price uncertainty (E denotes te expectation operator): Assumption (R): E( ( p ) 1 r ( ) r ) pe( p ) > 0. In order to get some intuition as regards tis assumption, assume tat te price risk is additive, tat is p = p + ε, 42

44 were ε is a random variabe wit mean 0 and variance σ 2 ε. Te assumption becomes E(( p + ε ) 1 r ) pe( ( p + ε ) r ) > 0. Using a second order Tayor approximation, tis inequaity can be rewritten as ( ) [ ] foows: 1 σε 2 p p 2 p p r 2 p+p p r + p p p > 0. A sufficient condition for tis inequaity to od is tat σ ε < ( ) p p 8 p. In oter words, if te variance of te price of grain at te ean season is sufficienty p+p ow (wic encompasses te case deveoped in te body of te paper, tat is σ ε = 0), Assumption (R) ods. Notice tat, at te arvest season, te ouseod makes its consumption decisions, c g and cm, its seing decision, q g, its cas spending decision,b, and its storage decision, s, anticipating tat it wi be abe to make its consumption and sae decisions at te ean season knowing te true ean season price of grain. We ten sove te probem backward: we first consider te ean season and caracterize te optima consumption and sae decisions, c g, cm and q g, taking te price of grain, p, te stored quantity of grain, s, and te stored amount of non agricutura income, b, as given. We ten consider te arvest season and caracterize te consumption, saes, grain storage and non agricutura income spending eves, c g, cm, q g, wic maximize te ouseod arvest season expected discounted utiity. Let us first anayze its optima decision probem at te ean season. Lean season: At te ean season, te programme of te ouseod is te foowing: suc tat M ax { c g,cm,q g,b } U = 1 1 r ( (c g ) ) σ 1 r c m, (46) c m = pq g + b, (47) c g + q g = s, (48) and, q g U Te soution of tis maximization probem is b = B b, c g ( s σ p b = 1 1+σ ). Let U b B b. (49) ( = σ 1+σ s + b p ), c m = 1 ( ) 1+σ ps + b and be te optima vaue of te utiity of te ouseod at te ean season, wit ( s,b, p ) ( ) = 1 1 r A ( ps+b b) 1+σ 1 r ( p) σ We now anayze te decision at te arvest season. were A = (σ) σ(1 r ) ( 1 1+σ) (1+σ)(1 r ). Harvest season: At te arvest season, te programme of te ouseod is te foowing: M ax { c g,cm,q g,b,s } EU = 1 1 r ( (c g ) ) σ 1 r c m δ EU ( s,b, p ), (50) suc tat and, and, b B,, (51) c m = pqg + b, (52) c g + q g + s = H. (53) 43

45 Let us substitute c m wit pqg +b and denote λ 1 and λ 2 te Lagrange mutipiers associated wit te constraints (51) and (53), respectivey. Te Lagragian of te optimization probem can be written as foows: L = 1 1 r ( (c g ) ( )) σ pq g 1 r + b 1 + Te first order conditions incude: L c g (( ) 1+σ ) 1 r 1 ps + B b 1 + δ 1 r A.E ( ) σ p = σ ( c g +λ 1 (B b )+λ 2 ( H c g q g s) (54) ) σ(1 r ) 1 ( pq g + b ) 1 r λ2 = 0, (55) L q g = p ( c g ) σ(1 r ) ( pq g + b ) r λ2 = 0, (56) L b = ( c g [( ) ) ( ) (1+σ)(1 r ) 1 ] σ(1 r ) pq g r + b 1 + σ ps + B b 1 + δ A.E ( ) σ(1 r ) λ 1 = 0, (57) p [ L s = 1 + σ ( ) (1+σ)(1 r ) 1 ] ps + B b 1 + δ A.E p ( ) σ(1 r ) λ 2 = 0, (58) p ( g λ 1 (B b ) = 0;λ 2 H c q g s) ;λ 1 0,λ 2 0,B b 0; H c g q g s = 0. (59) Combining (56), (57) and (58), we ave [ pλ 1 = 1 + σ ( ) (1+σ)(1 r ) 1 ] ps + B b 1 + δ A.E p ( ) σ(1 r ) p p 1 + σ 1 + δ A.E [( ps + B b ) (1+σ)(1 r ) 1 Assume tat λ 1 > 0, ten b = B and condition (60) becomes: ( p ) σ(1 r ) ]. (60) pλ 1 = 1 + σ ( [ ( 1 + δ A (s)(1+σ)(1 r ) 1 ) ] 1 r E p pe [( p ) r ]), (61) wic is stricty positive, according to Assumption (R). Tus, conditions (55), (56) and (58) become: σ ( c g ) σ(1 r ) 1 ( pq g + B ) 1 r = λ2, (62) and, p ( c g ) σ(1 r ) ( pq g + B ) r = λ2, (63) and, Using (59), after some computations, we obtain: 1 + σ [ ( 1 + δ A (s)(1+σ)(1 r ) 1 ) ] 1 r E p = λ 2. (64) q g = θ ( ) θ H + B B 1 + σ p p, (65) 44

46 were θ = ( (1 + δ) ( [ ]) E ( p) 1 r 1 ) 1 ( ) (1 r ) p (1+σ)r σ. Notice tat te expression of q g is te same as in te case witout price risk except te term ( [ ( ) ]) 1 r 1 ( ) (1 r ) E p wic repaces p in te case witout risk. Te optima storage eve is: and te optima consumption eves are: ( ) s = θ H + B, (66) p c g = θ ( ) σ 1 + θ H + B, (67) 1 + σ p c m = p θ ( ) θ H + B, (68) 1 + σ p ( ) c g = 1 σ 1 + θ H + B, (69) 1 + σ p ( ) c m = p θ H + B. (70) 1 + σ p Te optima eves of storage and consumption differ from te eves we obtained wen tere is no price risk in two ways. First, θ is repaced by θ, wic affect a te optima eves. Second, te consumption of te generic good at te ean season depends on te reaized price of grain (notice tat te consumption of grain is not affected by te reaization of te price). We can ten sow te foowing resut: σ Proposition 5: Te foowing caims od if and ony if 1+σ r 1. Price risk affects consumption, saes and storage as foows : (i) it increases te consumption of grain and of te generic good at te arvest season; (ii) it decreases te consumption of grain and te expected consumption of te generic good at te ean season; (iii) it decreases grain storage and saes at te ean season; (iv) it increases grain saes at te arvest season. Proof of Proposition 5: Te expected consumption of generic good at te ean season is E ( c m ) = ( ) [ p 1 1 ( 1+ θ 1+σ H + B ) ] 1 r p. To prove te resuts of te proposition, it is sufficient to notice tat E p ( [ ]) 1 r ( ) 1 r E p = p if and ony if 0 σ 1+σ r 1, because x (x)1 r is concave wen σ 1+σ r 1 and convex oterwise. Hence, θ σ θ if and ony if 1+σ r 1. Now, et us discuss ow te price risk affects te comparative static resuts provided in te body of te paper. Coroary 1 is quaitativey unaffected: saes at te arvest are sti decreasing wit te cas income, q g ( ) B = 1 1 θ 1+σ < 0, and ouseods aving a sma cas income B are sti tose 1+ θ wo wi se rater tan buy grain at te arvest season: q g 0 p tresod is arger wen tere is a price risk. θ 1+σ ( 1+ θ Coroary 2 and Proposition 3 remain uncanged. Proposition 4 becomes: ) H B. However, te Proposition 4 : Saes at te arvest season decrease wit risk aversion if and ony if te ouseod is 45

47 sufficienty impatient: q g r [ ( ) ] 1 r E p < 0 ( ) 1 1+σ p [ ( exp ( ) (1 r ) ( ) ] r σ ) E p n p [ 1 + σ ( ) ] 1 < δ. (1 r ) E p Proof of Proposition 4 : It is sufficient to study te sign of θ r, wic is suc tat θ r = (1 + σ) θ ((1 + σ)r σ) 2 [ ] wic is negative ony if E ( p) 1 r ( p ) 1 1+σ exp ) n(1 + δ) 1 1+σ (p n + ( r σ 1+σ [ ( ) ] (1 r ) + ne p [ ) E ( p) (1 r ) n( p) ] [ ] E ( p) (1 r ) ( [ (r ) E σ ( p) (1 r ) n( p) ] ) [ 1+σ ] 1 < δ. E ( p) (1 r ), (71) Hence, te main insigt of Proposition 4 is not affected by te introduction of te price risk. However, te tresod above wic impatience is sufficienty arge now depends on te risk aversion parameter. 46

48 Appendix C: Te Effect of Preferences on Saes - Bootstrapped Standard Errors (1) (2) (3) (4) (5) Dep. Var. is Saes (q ) H2S MLE MLE MLE MLE risk aversion -255,24-258,39-196,04-317,98 ** -231,61 202,55 172,13 141,06 173,10 143,10 discount rate 1163,60 ** 1125,83 ** 1153,40 ** 2739,43 ** 2655,81 ** 594,75 482,97 502, , ,76 H maize 92,46 ** 110,90 *** 110,00 *** 110,39 *** 108,67 *** 38,71 32,13 32,03 31,51 31,58 Dep. Var. is V risk aversion 0,30 ** 0,29 ** 0,25 ** 0,35 *** 0,28 ** 0,13 0,13 0,12 0,13 0,13 discount rate -0,86 ** -0,82 * -0,86 ** -2,48 *** -2,44 *** 0,43 0,43 0,43 0,90 0,92 H maize 0,04 ** 0,06 ** 0,06 ** 0,06 ** 0,06 ** 0,02 0,02 0,03 0,02 0,02 op 0,55 *** 0,46 *** 0,46 *** 0,45 ** 0,45 ** 0,17 0,17 0,17 0,18 0,18 q ean 0,32 ** 0,18 0,19 0,19 0,19 0,13 0,13 0,12 0,13 0,13 λ -1272,83 * -1252,02 *** -1248,32 *** -1258,35 ** -1259,97 *** 728,19 485,02 486,08 483,30 485,42 atanρ -0,91 *** -0,90 ** -0,91 *** -0,91 *** 0,35 0,36 0,35 0,36 χ 2 24,82 *** 24,12 *** 25,48 *** 24,80 *** Number of obs Censored obs Uncensored obs Payoffs ow ow ig ow ig Time deay 1 mont 1 mont 1 mont 4 days 4 days Note: Tis tabe reports estimation resuts for te sampe seection mode. Te top of te tabe reports te estimates of te outcome equation, were te dependent variabe is te quantity of maize sod during arvest season. Te bottom of te tabe reports te estimates of te seection equation. Bot equations aso incude as contros te arvested quantities of sorgum, miet, rice, groundnut, and cotton, te tota number of catte and of poutry, te famiy size and time to trave to te market. Coumn (1) reports Heckman-Two-Step estimates, coumns (2) to (5) report Maximum Likeiood estimates. λ, atanρ, and χ 2 are statistics of tree tests of te nu ypotesis ρ = 0, were ρ is te correation between te error terms of te two equations. Standard errors custered at viage eve are in itaics. Tree asterisks *** (resp. **, *, ) denote rejection of te nu ypotesis at te 1% (resp. 5%, 10%, 15%) significance eve. Te variabes risk aversion and discount rate are individua parameters tat were estimated separatey from te experiments, as expained in Section and in Section Te row Payoffs indicates weter te ow-payoff experiment or te ig-payoff experiment was used to eicit te risk aversion parameter incuded in te mode. Te row Time deay indicates weter te 4-day-deay experiment or te 1-mont-deay experiment to eicit te discount rate incuded in te mode. 47

49 Documents de Recerce parus en 2014 DR n : DR n : DR n : Sopie CLOT, Fano ANDRIAMAHEFAZAFY, Gies GROLLEAU, Lisette IBANEZ, Piippe MÉRAL «Payments for Ecosystem Services: Can we ki two birds wit one stone? Insigts from a Natura Fied Experiment in Madagascar» Sopie CLOT, Gies GROLLEAU, Lisette IBANEZ «Mora sef-icensing and socia diemmas: An experimenta anaysis from a taking game in Madagascar» Racida HENNANI, Mice TERRAZA «La crise des dettes souveraines : contagions ou interdépendances des principaux indices de a zone euro?» DR n : DR n : DR n : DR n : DR n : DR n : Karizze Anne PUZON, Marc WILLINGER «Wy my Participation Matters: Rent-seeking wit Endogenous Prize Determination» Mickaë BEAUD, Tierry BLAYAC, Maïté STEPHAN «Measurements and properties of te vaues of time and reiabiity» Tristan LE COTTY, Eodie MAITRE D HOTEL, Rapaë SOUBEYRAN, Juie SUBERVIE «Wait and Se: Farmer Preferences and Grain Storage in Burkina Faso» DR n : Antoine NEBOUT, Marc WILLINGER «Are Non-Expected Utiity Individuas reay Dynamicay Inconsistent? Experimenta Evidence» Edmond BARANES, Juien JACQMIN, Jean-Cristope POUDOU «Renewabe and non-renewabe intermittent energy sources: friends and foes?» Karizze PUZON, Marc WILLINGER «Do Maevoent Leaders Provoke Confict? An Experiment on te Paradox of te Penty»

50 DR n : DR n : DR n : DR n : DR n : DR n : : Pau BELLEFLAMME, Juien JACQMIN «An Economic Appraisa of MOOC patforms: Business Modes and Impacts on Higer Education» Edmond BARANES, Tomas CORTADE, Andreea COSNITA- LANGLAIS «Merger Contro on Two-Sided Markets: Is tere Need for an Efficiency Defense?» Nicoas GRAVEL, Brice MAGDALOU, Patrick MOYES «Ranking Distributions of an Ordina Attribute» Tierry BLAYAC, Vaérie CLEMENT, Grégoire MERCIER «Hospitaisation conventionnee vs prise en carge à domicie : anayse des préférences individuees par une experience en coix discret» Abdou Saam DIALLO, Afred MBAIRADJIM MOUSSA «Addressing agent specific extreme price risk in te presence of eterogeneous data sources: A food safety perspective» Lazeni FOFANA, Françoise SEYTE «Prévision du Risque de Contagion de six Marcés Financiers : une anayse prédictive par approce des Réseaux de Croyance Bayésienne non-paramétrique continu»

51 Contact : Stépane MUSSARD : mussard@ameta.univ-montp1.fr

52