Elctng Rsk Preferences: A Feld Experment on a Sample of French Farmers 1 Douada BOUGHERARA, Xaver GASSMANN and Laurent PIET INRA, UMR1302 SMART, F35000 Rennes, France. douada.bougherara@rennes.nra.fr Paper prepared for presentaton at the EAAE 2011 Congress Change and Uncertanty Challenges for Agrculture, Food and Natural Resources August 30 to September 2, 2011 ETH Zurch, Zurch, Swtzerland Copyrght 2011 by [Douada Bougherara, Xaver Gassmann & Laurent Pet]. All rghts reserved. Readers may make verbatm copes of ths document for non-commercal purposes by any means, provded that ths copyrght notce appears on all such copes. 1 We thank V. Leveau and JP. Ncolett (Arvals) for ther help n mplementng the feld experment and acknowledge fnancal support from ONEMA (Program Evaluaton et réducton des rsques lés à l utlsaton de pestcdes as part of axe 3 du plan Ecophyto 2018 ).
Elctng Rsk Preferences: A Feld Experment on a Sample of French Farmers Douada BOUGHERARA, Xaver GASSMANN and Laurent PIET INRA, UMR1302 SMART, F35000 Rennes, France. Abstract: We desgned a feld experment nvolvng real payments to elct farmers rsk preferences. Farmers are a very nterestng sample to study snce rsk has always played an mportant role n agrcultural producers decsons. Besdes, European farmers may face more rsky stuatons n the future. In ths context, t s very mportant for any economc analyss focusng on agrculture to correctly assess farmers behavour n the face of dfferent sources of rsk. We test for two descrptons of farmers behavour: expected utlty and cumulatve prospect theory. We use two elctaton methods based on the procedures of Holt and Laury (2002) and Tanaka et al. (2010) on a sample of 30 French farmers. The experment conssts n askng subjects to make seres of choces between two lotteres wth varyng probabltes and outcomes. We estmate parameters descrbng farmers rsk preferences derved from structural models. We fnd farmers are slghtly rsk averse n the expected utlty framework. In the cumulatve prospect theory frame, we fnd farmers dsplay ether loss averson or probablty weghtng, tendng to overweght small probabltes and to underweght hgh probabltes. In our study, expected utlty s not a good descrpton of farmers behavour towards rsk. Keywords: Rsk Atttudes, Feld Experment, Farmng. JEL Classfcaton: C93 (Feld Experments), D81 (Crtera for Decson-Makng under Rsk and Uncertanty), Q10 (Agrculture) 2
1. Background and motvaton Rsk has always played an mportant role n agrcultural producers decsons. Besdes, European farmers may face more rsky stuatons n the future for dfferent reasons. In partcular farm producton rsks may ncrease due for example to tghter envronmental regulatons and to the effects of clmatc change. The varablty of European farm prce s also lkely to be greater n the future due to the reforms of the Common Agrcultural Polcy. In ths context, t s very mportant for any economc analyss focusng on agrculture to correctly assess farmers behavour n the face of these dfferent sources of rsk. Recent contrbutons n the feld of expermental economcs may help to better assess ths farmer behavour. Ths approach enables to elct rsk atttudes both n the standard framework of expected utlty and n the framework of alternatve theores (Holt and Laury, 2002; Harrson and Rutström, 2008, 2009; Andersen et al., 2010; Tanaka et al., 2010). We desgned a feld experment to test for two descrptons of farmers behavour: expected utlty and cumulatve prospect theory. We also test for the mpact of context (output prce rsk and yeld rsk) on rsk averson parameters. We use two elctaton methods based on the procedures of Holt and Laury (2002) and Tanaka et al. (2010) on a sample of 30 French farmers. The experment conssts n askng subjects to make seres of choces between two lotteres wth varyng probabltes and outcomes. We estmate parameters descrbng farmers rsk preferences derved from structural models. We fnd farmers are slghtly rsk averse n the expected utlty framework and dsplay loss averson and probablty weghtng (overweghtng of small probabltes and underweghtng of hgh probabltes). In our study, expected utlty s not a good descrpton of farmers behavour towards rsk. Our paper s organzed as follows. In the next secton (secton 2), we descrbe the emprcal models derved from structural models. In secton 3, we descrbe the feld experment. In secton 4, results are presented and dscussed. Secton 5 concludes. 2. Emprcal models Followng Harrson and Rutström (2008) and Andersen et al. (2010), we use structural modellng to estmate rsk averson parameters for the farmers n our sample. 2.1. Estmaton of a structural model assumng expected utlty theory In the context of expected utlty theory, we elct a parameter (r) descrbng rsk atttude usng the followng CRRA utlty functon specfcaton (x s wealth) for ndvdual : u ( x) x 1 1 r = r r = x u xx u x. Ths leads to the followng values for r accordng to rsk atttudes: r>0 f ndvdual s rsk averse, r=0 f ndvdual s rsk neutral and r<0 f ndvdual s rsk lovng. The coeffcent of constant relatve rsk averson s the parameter.( ) In the experment, farmers faced seres of lottery choces j where a choce was made between { } two lotteres A and B: (, A, A );(, B, B j H L j H L ) p y y p y y. Lottery A (resp. B) offers a hgh outcome 3
A B y H (resp. y H ) wth probablty p j and a low outcome Lottery B has more varable payoffs than lottery A. For ndvdual and for a gven lottery k {, } ( ) ( 1 ) ( ) EU = p u y + p u y k k k j H j L A y L (resp. A B, the expected utlty wrtes: The dfference n expected utltes between the two lotteres wrtes: B EU = EU EU A B y L ) wth probablty 1 It provdes the rule for ndvdual choosng lottery B. We model the decson as a dscrete choce model (from here, we drop subscrpt to smplfy notatons). We consder a latent varable y = EU + ε that descrbes the decson to choose lottery B. We assume ε follows a standard normal dstrbuton wth zero mean and varance σ. y EU ε 2 = + wth ε Ν ( 0, σ ) Ths s equvalent to: p j. y σ 1 = EU + u wth u Ν ( 0,1) σ We do not observe y but only the choces ndvduals make so that: y = > y = 1 f y 0 0 f y 0 The probablty to choose lottery B s: ( ) y 1 Prob choose lottery B = Prob > 0 = Prob EU + u > 0 σ σ = Prob > = Φ where ( ) Φ s the standard normal dstrbuton functon. ( u EU σ ) ( EU σ ) We estmate the constant relatve rsk averson parameter and the varance σ usng maxmum lkelhood. The log lkelhood functon wrtes: ( ) ( ( ( σ )) ( )) ( ) ( σ ) ( ) ln L r : y, X = ln Φ EU I y = 1 + ln 1 Φ EU I y = 1 where I ( ) s the ndcator functon, y = 1 when lottery B s chosen and y = 1 when lottery A s chosen, X s a vector of ndvdual characterstcs. 4
2.2. Estmaton of a structural model assumng cumulatve prospect theory Under cumulatve prospect theory (Tversky and Kahneman, 1992), ndvduals dsplay dfferng behavours n the gan and loss doman. For ndvdual and for a gven lottery k A, B, the value functon utlty wrtes: v k { } k ( y ) k α ( y ) λ k ( y ) k f y > 0 = α k f y < 0 where α s the concavty of the utlty functon and λ s a loss averson parameter. Probabltes are transformed accordng to the followng weghtng probablty functon (Tversky and Kahneman, 1992): γ γ ( p) = p p + ( 1 p ) γ 1 γ π where γ s a parameter descrbng the shape of the weghtng probablty functon. γ < 1 (resp. γ > 1) mples overweghtng (resp. underweghtng) of small probabltes and underweghtng (resp. overweghtng) of hgh probabltes. The specfcatons used n ths secton collapse to the expected utlty specfcaton f λ = 1 and γ = 1. The structural specfcaton of ndvdual decsons under cumulatve prospect theory follows the same pattern as wth the expected utlty specfcaton. For ndvdual and for a gven k A, B, the prospectve utlty wrtes: lottery { } ( ) ( ) π ( 1 ) ( ) PU = π p v y + p v y k k k j H j L We estmate three parameters (α, λ and γ ) and the varance σ usng maxmum lkelhood. The log lkelhood functon wrtes: ( ) ( ( ( σ )) ( )) ( ) ( σ ) ( ) ln L r : y, X = ln Φ PU I y = 1 + ln 1 Φ PU I y = 1 where I ( ) s the ndcator functon, y = 1 when lottery B s chosen and y = 1 when lottery A s chosen, X s a vector of ndvdual characterstcs. We now turn to descrbng the feld experment. 3. Feld experment and sample descrpton We frst descrbe the feld experment and then the characterstcs of the sample. 5
3.1. Feld experment descrpton The feld experment took place n the summer 2010. Partcpants were face-to-face ntervewed. We used a multple prce lst procedure (see Harrson and Rutström, 2008 for a revew). We used two elctaton seres we call HL seres and TCN seres based on the papers of Holt and Laury (2002) and Tanaka et al. (2010) on a sample of 30 French farmers. The experment conssts n askng subjects to make seres of 65 choces between two lotteres wth varyng probabltes and outcomes (choce stuatons 1 to 30 correspond to the HL seres and choce stuatons 31 to 65 to the TCN seres). Choces were presented n the format of Fgure 1 where playng a lottery was framed as turnng a wheel (lke n the well known Wheel of Fortune TV show). The hghest potental earnng n the experment s 385 and the lowest s a loss of 6. Choce stuaton Probablty of earnng the hgh outcome Probablty of earnng the low outcome 1 1 out of 10 9 out of 10 Wheel A Wheel B I prefer turnng 200 385 Wheel A 160 10 Wheel B 2 2 out of 10 8 out of 10 200 385 Wheel A 160 10 Wheel B. 10 10 out of 10 0 out of 10 Wheel A 200 385 Wheel B Fgure 1. Example of choces faced by subjects n the feld experment: stuatons 1 to 10 based on Holt and Laury (2002) Indvdual choces between lotteres enable an estmaton of the parameters we descrbed n secton 2. There were three varatons as compared to the papers of Holt and Laury (2002) and Tanaka et al. (2010). Frst, n the HL seres, the fgures correspondng to gans are a hundred tmes hgher than n the baselne treatment of Holt and Laury (2002) (1.65$ becomes 165 ). Second, n the TCN seres, the fgures correspondng to gans and losses are 5,000 tmes lower than the experment of Tanaka et al. (2010) (40,000 Vetnamese dongs become 8 ). Thrd, the HL seres s played three tmes to test for pure framng effects: no context as n Holt and Laury (2002) (probablty of earnng a gven amount of money), prce context (probablty of sellng 10% of soft wheat producton at a certan prce per ton), and margn 6
context (probablty of gettng a certan margn wth a 15% fertlzer reducton). Table 1 shows the characterstcs of each of the 65 choce stuatons. Choce stuatons Seres Reference Framng Doman 1-10 Holt and Laury (2002) Baselne100 No Gan 11-20 HL seres Holt and Laury (2002) Baselne100 Prce rsk frame Gan 21-30 Holt and Laury (2002) Baselne100 Yeld rsk frame Gan 31-58 Tanaka et al. (2010) Gan TCN seres No 59-65 Baselne/5,000 Loss Table 1. Choce stuatons faced by farmers n the feld experment The ncentve of the experment s controlled by randomly drawng the choce stuaton (thus the lottery chosen by the partcpant) that wll be played for earnngs. Then, out of the 30 partcpants, 3 partcpants were randomly drawn for real payments. All partcpants receved a show-up fee (20 ) to cover ther expense for comng to the experment and to potentally cover ther expenses n the loss doman. 3.2. Sample descrpton We collected questonnares from 30 farmers. Table 2 gves summary statstcs. Farmers n the group are relatvely well educated. They perceve ther producton actvtes as very rsky n terms of output prces. Then, rsks related to nput prces and clmatc rsks are consdered as very mportant. Varable Descrpton #Obs Mean SD Mn Max Varables descrbng farmers AGE Age (n years) 30 41.90 9.36 23 56 EDUC =1 f baccalaureat dploma or hgher and 0 otherwse 30 0.70 0.47 0 1 Varables descrbng farms SAU UAA (hectares) 30 176.73 61.52 74 297 ETS =1 f company and 0 otherwse 30 0.60 0.50 0 1 GAEC =1 f partnershp and 0 otherwse 30 0.13 0.35 0 1 Varables on farmers percepton of rsk n ther producton actvty (1=not rsky to 5=very rsky) RISKPPROD Percepton of output prce rsk 30 4.60 0.67 3 5 RISKPINT Percepton of nput prce rsk 30 3.97 0.89 2 5 RISKCLIM Percepton of clmatc rsk (yeld) 30 3.63 1.10 2 5 RISKCOM Percepton of output marketng rsk 30 3.40 1.13 1 5 RISKPOL Percepton of rsk related to polces 30 3.00 1.31 1 5 RISKTECH Percepton of technologcal rsk 30 2.20 0.96 1 4 Table 2. Summary statstcs 4. Emprcal results We present and dscuss our results frst n the framework of expected utlty theory and then of the cumulatve prospect theory. 4.1. Econometrc estmaton of rsk atttudes under expected utlty theory We consder choce stuatons 1 to 58. As stuatons 59 to 65 nvolve losses and the CRRA utlty functon specfcaton does not allow for negatve wealth, we drop stuatons 59-65. Table 3 gves the maxmum lkelhood estmaton results usng clusterng for ndvduals. We 7
estmate the CRRA parameter along wth the varance. We allow for varance to vary as a functon of the seres (HL or TCN). A varable called TYPE enables us to get the mpact of the TNC seres as compared to the HL seres. Estmated parameters σ (1) (2) (3) Coeffcent P> z Coeffcent P> z Coeffcent (Robust SE) (Robust SE) (Robust SE) P> z r constant 3.768 0.000 3.732 0.000 3.711 0.000 (0.559) (0.553) (0.520) TYPE 5.811 0.000 5.987 0.000 5.788 0.000 (0.774) (0.807) (0.677) constant 0.125 0.203 0.114 0.251 0.133 0.198 (0.098) (0.100) (0.104) PRICEFRAME 0.009 0.792-0.005 0.868 (0.033) (0.033) MARGINFRAME 0.041 0.279 0.036 0.341 (0.038) (0.038) EDUC -0.070 0.137 (0.047) GAEC 0.054 0.448 (0.072) ETS 0.058 0.170 (0.042) #Observatons 1740 1740 1740 Log lkelhood -902.98 (ns) -901.63 (ns) -887.77 (ns) Table 3. ML estmaton of CRRA parameter and varance under EUT Stuatons 1 to 58 and clusterng for ndvduals The estmated parameter, the constant n model (1), suggests small rsk averson n the sample (r=0.125>0). The rsk preference parameter s elcted n three frames: no context, output prce rsk and yeld rsk. We control for framng effects by addng dummes (the reference s no frame) n model (2): PRICEFRAME equals one f output prce rsk frame and zero otherwse, and MARGINFRAME equals one f yeld rsk frame and zero otherwse. We fnd there are no sgnfcant framng effects. The constant gves an estmate of the CRRA parameter (r=0.114>0) when there s no context. Indvduals are stll rsk averse but slghtly less. We turn to studyng the effects of farm s and farmer s characterstcs on rsk averson n model (3). We use one varable descrbng the farmer (EDUC) and two varables descrbng the farm status (GAEC and ETS). The dummes for framng effects reman. The reference s no context and farmers wthout hgh school dploma, wth farms wth sole propretorshp. We fnd that the estmated CRRA parameter s now 0.133, whch s a lttle hgher but stll not sgnfcant. Framng has stll no sgnfcant effect on rsk atttudes. More educated people tend to be less rsk averse. Indeed, the varable EDUC has a negatve effect on the CRRA parameter although not sgnfcantly (p=0.137). The status of the farm has no sgnfcant mpact on atttudes towards rsk. 4.2. Econometrc estmaton of rsk atttudes under CPT We now consder all choce stuatons (1 to 65). Usng clusterng for ndvduals, the estmaton results are n Table 4. We present three models: baselne, wth framng dummes, and wth ndvdual characterstcs. We also test for parameters equalty to one. Recall especally that expected utlty theory mples λ = 1 and γ = 1. 8
Estmated parameters (4) (5) (6) Coeffcent P> z Coeffcent P> z Coeffcent (Robust SE) (Robust SE) (Robust SE) P> z σ constant 3.229 0.000 1.910 0.020 1.371 0.336 (0.786) (0.821) (1.425) TYPE 4.964 0.000 3.527 0.001 2.391 0.139 (0.853) (1.021) (1.617) α constant 0.803 0.000 0.605 0.000 1.002 0.000 (0.115) (0.136) (0.105) PRICEFRAME 0.255 0.047-0.089 0.252 (0.128) (0.078) MARGINFRAME 0.301 0.027-0.078 0.314 (0.137) (0.077) EDUC -0.004 0.962 (0.095) GAEC -0.439 0.061 (0.234) ETS -0.032 0.553 (0.054) λ constant 2.489 0.000 2.111 0.000 0.041 0.994 (0.697) (0.349) (5.512) EDUC 1.740 0.000 (0.483) GAEC 0.594 0.914 (5.500) ETS 53.377 0.242 (45.586) γ constant 1.036 0.000 0.884 0.000 0.048 0.000 (0.171) (0.146) (0.011) PRICEFRAME -0.535 0.000 0.218 0.055 (0.096) (0.114) MARGINFRAME -0.599 0.000 0.187 0.039 (0.103) (0.091) EDUC 0.025 0.429 (0.032) GAEC 0.531 0.000 (0.083) ETS -0.010 0.233 (0.008) #Observatons 1950 1950 1950 Log lkelhood -1025.35 (ns) -1013.07 (10%) -1096.83 (1%) Hypotheses can be rejected? α : constant=1 Yes (1%) Yes (5%) No λ : constant=1 Yes (5%) Yes (5%) No γ : constant=1 No No Yes (1%) Table 4. ML estmaton of parameters and varance under cumulatve prospect theory Stuatons 1 to 65 and clusterng for ndvduals Let us dscuss frst the results on the constants n models (4) and (5). We fnd that the value functon s concave n the gan doman and convex n the loss doman. The estmated α 9
parameter s 0.803 n model (4) and 0.605 n model (5). It s sgnfcantly dfferent from one (chsq test: 2.94; p=0.086 n model (4) and chsq test: 8.52; p=0.004 n model (5)). We fnd that farmers n the sample exhbt loss averson. The estmated λ parameter s 2.489 n model (4) and 2.111 n model (5) and s sgnfcantly hgher than one (chsq test: 4.56; p=0.033 n model (4) and chsq test: 10.13; p=0.002 n model (5)). However, there s no sgnfcant evdence of probablty weghng n both models. The estmated γ parameter s not sgnfcantly dfferent from one (chsq test: 0.05; p=0.832 n model (4) and chsq test: 0.64; p=0.425 n model (5)). In model (5), we control for framng effects. Note that framng effects were ntroduced n the feld experment only n the gan doman. They are controlled for n the estmaton only for the α and γ equatons. They appear to play a sgnfcant role. The prce frame and the margn frame mpact postvely the curvature of the value functon (5% sgnfcance) but negatvely the probablty weghng parameter (1% sgnfcance). Especally, farmers tend to overweght small probabltes and underweght hgh probabltes n the framng treatments. Fnally, we add ndvdual characterstcs to explan the parameters n model (6). We fnd that the value functon s lnear n the gan and the loss doman. The estmated α parameter s 1.002 and s not sgnfcantly dfferent from one (chsq test: 0; p=0.983). Contrary to the results of the prevous models, when ndvdual characterstcs are controlled for, we fnd no evdence of loss averson (chsq test: 0.03; p=0.862) but evdence of probablty weghtng (chsq test: 7280; p=0.000). Framng effects stll sgnfcantly mpact the probablty weghtng functon but not the curvature of the value functon. Now n a prce or margn frame, farmers tend to overweght less small probabltes. Indvdual characterstcs play a role n ths. We fnd the status of the farm mpacts the α and γ parameters. We also fnd that educaton tends to ncrease loss averson. 5. Concluson and dscusson In the context of ncreasng rsks n agrculture, we desgned a feld experment nvolvng real payments to elct farmers rsk preferences. We especally tested for two descrptons of farmers behavour: expected utlty and cumulatve prospect theory. We use two elctaton methods based on the procedures of Holt and Laury (2002) and Tanaka et al. (2010) on a sample of 30 French farmers. We estmated parameters descrbng farmers rsk preferences derved from structural models. We fnd farmers are slghtly rsk averse n the expected utlty framework. In the cumulatve prospect theory frame, we fnd farmers dsplay ether loss averson or probablty weghtng, tendng to overweght small probabltes and to underweght hgh probabltes. In our study, expected utlty s not a good descrpton of farmers behavour towards rsk. Ths study s a frst step nto a better understandng of farmers behavour towards rsky stuatons usng recent advances n feld experments. Several characterstcs of our study should be kept n mnd however. Frst, we used the multple prce lst procedure because t s easy to mplement and to understand for subjects. It may however nvolve framng effects (suggestng the mddle row and makng clear the experment objectve) though Harrson and Rutström (2008) ndcate the bas s not systematc. Second, our sample s small. We would need ether to ncrease the number of choces made by subjects or to ncrease the number of subjects. The frst proposton seems dffcult to mplement snce askng for 65 choces was already a lot for subjects. We showed that the varance ncreased n the TCN seres as 10
compared to the HL seres. Ths may also be due to fatgue effects, the HL beng played always frst. Our study would beneft from ncreasng the number of ntervewed farmers to better test for the effect of ndvdual characterstcs, to elct ndvdual parameters and to determne the effect of rsk atttudes on behavours such as producton choces and nsurance demand. Thrd, the loss doman s not easy to mplement n the feld. Indeed, one cannot ask partcpants n the experment to pay the expermenter f the lottery nvolves a loss. Ths s resolved by the show-up fee. But, ths fee n tself plays the role of an nsurance mechansm. Moreover, the experment mplctly sets the reference pont n the cumulatve prospect theory at a zero level. Ths s a hypothess. Future study ams at workng on these lmtatons and tryng to elct other parameters such as tme preferences and ambguty averson. References Andersen S., Harrson G.W., Lau M.I., Rutström E.E., 2010, Behavoral Econometrcs for Psychologsts, Journal of Economc Psychology, 31(4):553-576. Harrson G.W., Rutström E.E., 2008, Rsk Averson n the Laboratory, n: J. Cox and G.W. Harrson (Eds.): Rsk Averson n Experments, Research n Expermental Economcs 12:41-196, Bngley: Emerald. Harrson G.W., Rutström E.E., 2009, Expected Utlty And Prospect Theory: One Weddng and Decent Funeral, Expermental Economcs, 12(2): 133-158. Holt C.A., Laury S.K., 2002, Rsk Averson and Incentve Effects, Amercan Economc Revew, 92(5): 1644-1655. Tanaka T., Camerer C.F., Nguyen Q., 2010, Rsk and Tme Preferences: Expermental and Household Survey Data from Vetnam, Amercan Economc Revew, 100(1): 557-571. Tversky A., Kahneman D., 1992, Advances n Prospect Theory: Cumulatve Representaton of Uncertanty, Journal of Rsk and Uncertanty, 5(4):297-323. 11