Attitudes toward risk : experimental measurement in rural India

World Bank Reprint Series: Number 179 Hans P. Binswanger Attitudes toward Risk: Experimental Measurement in Rural India Reprinted with permission from American Journal of Agricultural Econotnics, vol. 62, no. 3 (August 1980), pp. 395-407.  Attitudes toward Risk: Experimental Measurement In Rural India Hans P. Binswanger Attitudes toward risk were measured in 140 households using two methods: an interview method eliciting certainty equivalents and an experimental gambling approach with real payoffs which, at their maximum, exceeded monthly incomes of unskilled laborers. The interview method is subject to interviewer bias and its results were totally inconsistent with the experimental measures of risk aversion. Experimental measures indicate that, at high payoff levels. v-irtually all individuals are moderately risk-averse with little variation according to personal characteristics. Wealth tends to reduce risk aversion slightly, but its effect is not statistically significant. Keyv words: India, psychological experiments,, risk aversion, semi-arid tropics. The research reported here was carried out in F.arlicr- experimental work on measure- the semi-arid, tropical areas of India, charac- ments of attitLdes toward risk was carried out terized by high climatic risk for agriculture. It primarily by exper imental psychologists and is was initiated to determine whether differences reviewed by Luce and Suppes. Where actual in behavior between farmers of different gambles were involved, payoffs and sample wealth levels are the consequence of different sizes were small. In this study, payoffs varied attitudes towards risk or of different constraint from very low levels to levels exceeding the sets such as limitations on credit or on access monthly incomes of unskilled rural laborers. to modern inputs. This question is of consid- The total sample size was 330. erable policy importance because policy pre- Agricultural economists have measured pa- sumably can affect credit and other con- rameters of utility functions by simulated straints faced by low income farmers more gambling situations rather than actual ones. easily than their attitudes toward risk. The Officer and Halter, O'Mara, and Dillon and basic approach is experimental. It measures Scandizzo used approaches based on utility attitudes by observ ing the reactions of indi- theory and elicitation of certainty equivalents. viduals to a set of actual one-period gambles. Kennedy, instead, used a method based on It must be recognized that extrapolating the focus loss. Only Dillon and Scandizzo used findings of such an approach to real farm deci- simulated farming pr-oblenms rather than pure sions may face theoretical challenges.' simulated gambles. Hans P. Biriswanger is an associate of the Agricultural Develop- ment Council, stationed at the Economic Growth Center, Yale The Experimental Sequence University. ICRISAT Joumal Article Approval No. 116. The experiment on which this paper is based was carried out The experimental method based on one-period while the author was stationed at the International Crops Research ambles was developed after reSultS of a sur- Instituteforthe Semi-AridTropics, Huderahad. India, and with its g generous support. vey using the Dillon-Scandizzo approach sug- The author would like to thank B. C. Barah, R. r). Ghodake, gested that their method was subject to inter- S. S. Badhe, M. J. Bhende, V. Bhaskar Rao, T. Balaramaiah, N. B,. Dudhane, Rekha Gaiki, K. G. Kshirsagar, Madhu Nath and Usha XVieWzei biases (fourth section).2 To overcome Rani, who helped in carrying out the experiment. James Roumas- set, University of Hawaii, and an anonymous referee made par- an apparently risk-averse indirect utility function for one-period ticularly helpful comments on an earlier draft. money because of capital market imperfections, and therefoie the Masson and Roumasset (1978b) point out that under fairly attempt to separate attitudes from constraints may be impossible restrictive assumptions, a utility function in "one-period money using one-period gambles. may be viewed as an indirect uhility function that reflects the 2 The author is personally indebted to John Dillon and Pasquale interaction of a'lifetime utility function of consumption with bor- Scandizzo for encouraging him to start work on risk aversion with rowing and lending opportunities. An individual who is risk-neu- large samples. He is indebted also to J. G. Ryan and Matthias von tral with respect to utility function in lifetime income may exhibit Oppeti for later encouraging a shift to experimental methods. Copyright 1980 American Agricultural Economics Association  396 August 1980 Anmer. J. Agr. E't-oi. moral problems confronting low income ual who chose 0 simply got Rs.50; i.e., par- people involved in gambling, the gambling was ticipation in the game resu.ied in an automatic limited so that the worst possible outcome was and sure increase in wealth by Rs.50. An indi- a zero gain, and it thus involved gifts to the vidual choosing C received Rs.30 on head and respondents. Because many respondents were Rs. 150 on tail. By not choosing 0 he stood to illiterate, the experiment had to be simple. lose Rs.20, but could gain Rs.100. Compared Also, because farming decisions are often to B, which was more relevant, the potential taken on an annual or crop-cycle basis and in losses and gains in going to C were Rs. 10 and consultation with relatives and friends, the Rs.30, respectively. Finally, by choosing F the experiment was designed to allow long periods individual received either no money or Rs.200; for reflection and opportunities for consulta- F had the same expected return as E, but a tion. higher variance, so only a risk-neutral or Only minimal theoretical commitments risk-preferring individual would make the step were to be made at the outset. The set of from E to F. choices should be ranked as more or less risky At the simplest level the choice of any alter- in a unique way, almost regardless of the native 0 to F classified the individuals into a definition of risk one might want to adopt. risk aversion class to which a name was given (For a review of problems of defining risk, see to simplify discussion. Interpreted in the Roumasset 1978a.) The subjects were not to framework of expected return-variance analy- be confronted with any budget constraints that sis (which is useful when decision makers are would rule out certain choices. One cannot, in confronted with normally distributed out- measuring pure attitudes to risk, propose comes), the game consisted of offering indi- games to individuals for which the worst pos- vidualk a set of alternatives within which sible loss exceeds their current cash holdings. higher expecte(i returns could only be "pur- If one does, he nmay measure the impact of a chased" at the cost of higher variance (or cash- or budget-constraint rather than the pure standard de'viation), and this tradeoff could be attitudes towards risk (Masson, Lipton). As measured by the slope Z in table 1. Interpreted far as possible, respondents should perceive in a utility framework, risk aversion could be the samc probabilities; therefore, the game measured by partial risk aversion S, which is was based on coin tosses. fixed regardless of the level of payoff Table 1 explains the basic method. Several (Menezes and Hanson, Zeckhauser and days ahead of any given game, individuals Keeler).3 To each risk aversion class corre- were given forms (which they could keep) sponded anl interval of partial risk aversion S. with the numbers of panel A on table 1. They had to choose from alternatives 0 to F. Once It is defined on a utility function U in terms of certain wealth W they chose, a coin was tossed and they got the as follows: let M be the certainty equivalent of a new prospect and left-hand amounts if heads came up or the evaluate derivatives at W + M; then, right-hand amount if tails came up. An individ- s(w + M) = -MU"(W + M:uI, "I1' + M), Table 1. The Payoffs and Corresponding Risk Classification Panel A S Approximate Heads Tails- Risk P)arlial Risk Low High Aversion Aversion z h (hoice Payoff Payoff ('lass (Collicienl" / s T, O 50 50 Extreme - to 7.51 1 to 0.80 A 45 95 Severe 7.51 to 1.74 0.8 to 0.66 B 40 120 Intermediate 1.74 to .812 0.66 to 0.50 D* 35 125 Inefficient C 30 150 Moderate .812 to .316 0.50 to 0.33 1) 20 160 Inefficient E 10 190 Slight-to-neutrall .316 to 0 0.33 to 0.00 F 0 200 Neutral-to-negaltive 0 to 0 to --x For reasons that are explained in Binswanger (1978c), a constant partial risk-aversion function on gains and losses was used to approximate S for the games. See footnote 4 for more details. b Z is the trade-off between expected returns and standard deviation of two games.  Bill wan 11'e0 MeasuIreme'nt of' Attitud(es' toward RisA 397 In the experimental sequence (table 2) the derabad, lindia. (For more details, see Jodha, individual was not presented immediately with Asokan, Ryan; Binswanger and, Jodha.) the alterniatives of table 2, called 50-rupees These stuidies are located in the semiarid game;, instead he went thro,ugh a sequence of tropical tracts of Maharashtra and Andhra games and hypothetical questions at various Pradesh, some of the poorer regions of India. game levels. All game levels were der-ived TFhe average physical wealth of the houise- from the 50-rupees game by multiplying all holds, approximately Rs.22,000 (US $2,750), amounts by a constant, which is 11100, 1110, is very low by international stand(ardLs, Buit and 10 for the 1/2-rupee, 5-rupee, and the 500- there were large variations in wealth in the rupee game levels, respectively. The sequence sample, as indicated by a coefficient of varia- started with five games at the Rs.0.50 level to tion of physical, wealth of 137c. The average teach participants the rules of the game and to schooling level was only 2.6 years hut had a convince them that they would receive the coefficient of variation of l20r- engarn money when promised. To help illiterate dom sample of the entire population engaged people, the payoff structure was shown as a in aigricultujre as laborers or farmers, variation photograph with the sums of money to be re- in other personal characteristics was also ceived indicated by coins placed in each field. large. The photographs were handed out to each Up to the Rs.5 level, the sequence was player and left with them through the entire 5- played with all 240 household heads of the to 6-week period of the experiment, sample (of which 20 were women), although The study was carried out in the 240 rural temporary ahs,ences from villages made some households included in the village level Stuidies of the sequences incomiplete. In three of the of the International Crops Research Institute six villages ( 118 110Lseholds) the full seque:nce for the Semi-Arid Tropics (ICRISAT), Hy- was played. In addition, in two villages the where U' and U' are the first and seconld derivatives of the utility moist imortusanlytdepwiendn femalesof thlued function. Other utility based measures of risk aversion are dis- hueod sal h ie a loicue cussed in Binswanger (1978a) but S was the most convenient one. in the experiment up to the Rs.5 level (thie Table 2. Sequence of Games and Hypothetical Questions Minimum Delay Game Since Last Game Real or Number Event' Level (Rs.) _ H) poEheuical Village', IFirst Day 0.50 Real All 2 One day 0.50 Real All 3 One day 0.50 Real All 4 One day 0.50 Real All 5 One day 0.50 Real All 6 Two weeks 50.00 Hyputhetical Shir-apur excluded 7 Same day 5.00 Real All Same day Hand out Rs.5.00 for next day game 8 One day 50.00 Hlypothietical Shirapur excluded 9 Same day 5.00 Real All 10 Same day 5.00. Hypothetical All I1I Two Weeks 500.00 Hypothetical )( ) Shirapur 12 Same day 50.00 Real ) )( Kanzara 13 Same day 50.00 Hlypoithetical ( (AuJrepalle only 14 Same day 50.00 Hypothetical )( ) Kalman )( ) Kinkheda 15 Same day 5.00 Hypothetical )( I Dokur only 16 Two weeks 500.00 Hypothetical y( ) Shirapur II IC Kanz:ara 17 Same day 50.00 Hypothetical ) )(Aurepalle only aIn many cases these minimum delays were extceded by a few days. There are six viUlages, two eachi in three districts: Shiolapur district-Shirapur and Kalman, Akola district-Kanzara and Kinkhed1a; Mahboobnagar district-Dokur and Aurepalil. Each village contans a panel of forty households and households heads were included in all viliages. In Yinkheda and Dokur the most important dependent female in each household was also included in the experiment in addition to the head of household who, on occasion, was female.  398 AuguAsl 1980 .Amer. J. AgA, P,c(onl. dependent female sample). In five villages a could then use the hypothetical answers as if nonrandom sample of the three "most pro- they were real choices. Hypothetical games 6. gres,sive" farmers of the village was added (the 8, and 13 at the Rs.50 level were introduced in progressive farmer sample). Progressive two villages (Aurepalle and Kanz.ara) for com- farmers are early adopter s of new techniquLes. parison with the real 50-rupee game. Chi- They were identified by the resident inves- square tests at the 0.5 level showed that, be- tigators on the basis of the investigator 's fore plhaing the 50-rUpee game, people be- knowledge of the villages. For all gamnes ex- lieved that they would act either more cept at the Rs.0.50 level, respondents' choices aversely or less aversely to risk than they actu- were ascertained by a first investigator and ally (lid in the real game 12, i.e., the risk-aver- verified with the respondent by a second in- sion distribution was far more dispersed in the vestigator. In about 250 games, including all early hypothetical answers than in the real the 50-rupee games, the author was the second game. However, once the 50-rupee game was investigator. In only two cases did the respon- played, there was no statistically significant dent change his mind. It was clear that the difference between the real choices in game 12 respondents enjoyed the game. No attempt and the hypothetical answers to games 13 or was made to isolate the respondents from their 17. The data also indicate that the ability of peers except for the second verification. Ag- respondents to predict their actual behavior in ricultural decisions are also observable in the a hypothetical question increases as the game village context and their outcomes are known sequence piroceeds, even before the 50-rupee to all. game is played. Therefore, from this point on, the hypothetical 500-rupee game number 16 will be interpreted as if it really had been Reliability Tests played, albeit with caution. The third test was to investigatte whether The first test was concerned with whether be- individuals, when confronted with a game havior with gift money differs from behavior such as in table 1, had an automatic tendency with own money. (A fuller account of these toward alternatives in the center of the dis- tests is given in Binswanger 1978c.) To pretest tribution. Table I contains two risk inefficient the method. ten individuals were at one stage alternatives D and D*, which are derived from asked to play the game with their own money, C and F, respectively, and have the same and nine out of ten chose the sanme alternative means but higher variance. No risk-averse in- as in the immediately preceding game, while dividual should choose these alternatives, and one respondent became more risk-averse. they were introduced precisely to test whether With the household heads of the full sample a people could detect stochastic dominance in different test was carried out: one day prior to this simple context. game 9, Rs.5 were given to the respondents Note that in a game structure coritaining D and they had the choice not to come to play but not D*, alternative C is the most central game 9 (such a choice was interpreted as the alternative and, under the "central tendency riskless choice 0). If they chose to play game hypothesis," should be the most preferred 9, they had to pay back any losses relative to one. On the other hand, if D is deleted from the Rs.5 of that bet. If after gift money was in table 1, alternative D* becomes the most cen- their possession for one day the respondents tral one. In three villages half the respondents considered it their "own," comparison of the were given the game structure containing the risk aversion distribution of game 7 and game alternative D, while the other half were given 9 is a test of differences in behavior with gift the game structure containing D*. It was and one's own money. A chi-square test of found that for both games 9 and 12, the fre- differences betwcen games 7 and 9 in the dis- quency distributions associated with the two tribution of choices over the alternatives was game structures could not be distinguished not significant at 0.05 level. statistically. The second test concerned the usability of There were three potential learning effects answers to hypothetical games included in the in the experiment. The first one concerned the sequence. It was hoped that after playing the ability to know risk preferences when the par- full sequence up to the Rs.50 level, individuals ticipant is faced with a hypothetical question would acquire the introspective ability to tell without making an actual decision, which was how they would play at the Rs.500 level. One discussed above. A second potential learning  Bina.sianeiii. r Measurement of Attittudes towvard Risk 399 effect was revisions of personal probabilities found between the risk-aversion distributions of heads and tails in coin tosses, which will be of the two subsamples and investigator bias discussed later. A third learning effect con- appearekd to be less of a problem using the cerned the rules of the games. How many game method than with interview methods. games did one have to play till one was sufficiently familiar with the rules? A chi- square test of the differences in risk aversion The Main Experimental Results distribiution was performed between the suc- cessive 0.5-rupee game; these tests were not The risk-aversion distributions corresponding significant, although there was a trend toward to different game levels are given in table 3, in less risk aversion as the games proceeded. the first panel for those villages where the Respondents thus appeared to familiarize game was played up to the 50-rupee level (with themselves quickly with the rules. a hypothetical answer at the 500-rupee level) When using the Dillon and Scandizzo inter- and in the second panel for all '.he households, view method (to be discussed in a later section including those where the game was played of this paper), two investigators were iden- only up to the 5-rupee level. Observe that at tified who tended to elicit substantially differ- low levels of the game the distribution was ent certainty equivalents while interviewing fairly evenly spread across the four classes of the same respondents. These investigators intermediate risk aversion to risk neutrality. were assigned to two different subsamples- As the game level rose, the distribution shifted fcrty respondents each, twenty in each of two to the right and became more peaked, i.e., risk villages-for the entire game sequence. No aversion increased. statistically significant differences could be Consider the slight-to-neutral and neutral- Table 3. The Effect of Payoff Size on Distribution of Risk Aversion Payoff Level and Game Slight-to Neutral to Number Extreme Severe Intermediate Moderate Neutral Negative Inefficient Sample Size ----------------- ---- Household Heads: Shirapur, Kanzara, Aurepalle A 0.50 No. 2 1.7 5.9 28.5 20.2 15.1 18.5 10.1 119 B 0.50 No. 4 + 5 1.7 8.1 14.5 29.3 21.3 16.6 8.5 235 C S No. 7 0.9 8.5 25.6 36.8 12.0 8.5 7.7 117 D 50 No. 12 2.5 5.1 34.8 39.8 6.8 1.7 9.3 118 E 500 H No. 16 2.5 13.6 51.7 28.8 0 0.9 2.5 118 --------------------------- ---All Household Heads ------- F 0.50 Games 2 + 3 1.7 7.6 18.5 22.7 17.1 18.7 13.7 475 G 0.50 Games 4 + 5 0.9 8.2 12.9 27.5 22.8 18.4 8.3 473 H 5.00 Games 7 + 9 0.8 8.1 23.8 36.5 11.9 9.8 9.1 471 Distributions tested x2 df 2 0.05 A vs. C vs. D vs. E 85.68 18 28.87 C vs. D vs. E 48.49 12 21.03 A vs. C 11.91 6 12.59 B vs. D 44.22 6 12.59 D vs. E 23.46 6 12.59 A vs. B 13.17 6 12.59 F vs. G 16.30 6 12.59 G vs. H 50.02 6 12.59  400 August 1980 Amer. J. Agr. Econ. to-preferred classes: at the Rs.0.50 level, the follows. For individuals with initially low risk percentage in each of these classes is around aversion, it tends to rise fairly rapidly as game 15 to 20, and it falls monotonically to near zero levels start to rise beyond trivial levels. For as the payoff level rises to Rs.500. ML tile mod- individuals who inititally have intermediate to erate risk-aversion class, we initially find moderate levels of risk aversion, the level in- around 20% of the individuals. This percent- creases slowly or remains fairly constant as age first rises at the Rs.5 and Rs.50 levels game levels rise. As can be seen from the because people enter this class when leaving chi-square tests (bottom of table 3), these the lower risk-aversion classes. But between trends are statistically significant and evident the Rs.50 and Rs.500 level, the number of in both the reduced sample and the full sample entrants from lower risk aversion is lower than of households. the number of individuals who become more Interpreted in the utility framework, the risk-averse and the frequency in this class de- evidence suggests that all but one of 118 indi- clines. The intermediate risk-aversion class viduals have nonlinear, risk-averse utility starts out with 28.5% of individuals in game 2 functions, which exhibit increasing partial risk at the Rs.0.50 level. As that game is repeated aversion.4 It has been shown elsewhere people prefer to play at higher stakes. But as (Binswanger 1978c) that the results also imply the payoff level rises again, more people enter decreasing absolute risk aversion. Relative this class from the lower risk-aversion classes risk aversion first decreases and then in- and at the Rs.500 level more than 509% of indi- creases. viduals are concentrated in this single class. The 500-rupee game corresponded to payoffs in the order of substantial fertilizer invest- Interviews versus Gambling Experiments ments for these households, and many were too poor to undertake them. For some house- The most immediately comparable study to holds it even exceeded net wealth. the present one (and the one which initially The extreme and severe risk-aversion inspired it) is by Dillon and Scandizzo for a classes together contained less than 10% of the semi-arid tropical region of Brazil. It had a individuals for all levels except the Rs.500 sample size of 103 farmers. Prior to the gam- level, in which the percentage rose to 15. bling experiment, the author executed a similar There appears -to be an upper barrier to risk interview-based survey in the Indian SAT vil- aversion that is exceeded only very slowly at lages. In this section the author describes the high stakes. problems encountered with the Dillon-Scan- In any given game, around 10% of individ- dizzo method and then compares the results of uals chose one of the inefficient alternatives. the two surveys with each other as well as This is clearly lower than the percentage of' with the experimental results. individuals who would choose it on a random Dillon and Scandizzo describe their method basis. Consider game 12. Inefficient alterna- as follows: "The farmer's risk attitudes were tives exist between the intermediaite and mod- appraised via their choices between hypothet- erate and the moderate and sliglht-to-neutral ical but realistic farm alternatives involving alternatives. These three classes and the in- risky versus sure outcomes. These questions efficient ones contain 90.7^. of individuals. If - people fell into the two inefficient and three 4 To obtain uniquJe measures of partial risk aversion associated efficien. classes at randomn, the two inefficient with the indifference points between two alternatives, a constant partial risk-avcrsion function (CPR) of the form l (1 S)M I classes would contain at the very least one- was used. Giiven the evidence of increasing partial risk aversion fifth of the 90.7% observations, i.e., 18.1%, but one might otbject tiat an incrcasing partial risk,aversion function (ICPRAI should have been used tB'nsuanger 1978bi. H-owe'.er. the the actual percentage was 9.3. partial risk-aversion coefticient for any indifference point will then Who chooses inefficiently varies m]luch not be unique but will depend on the rate at which partial nsk- across games. Two hundred and eighty seven aversion increases, i.e., on the choice paths across the game scale. Therefore, partial risk-aversion coefficients were computed for individuals played all the games from 1 to 9. Of each indifference point at each game scale and for e%ch feasible those, ninety-four (or 33%) chose one of the choice path given a smooth lCPRA titility function. Because in- inefficienit alternatives at least once, i.e . they come varies more across game scales than within cach game scale. S values associated with thesc I('PRA ililicred by less than 2X did not recognize that they were stochastically from those associated with the CPR functions, cxcept for the dominated, or did not care about it at least indifference point between alternative ) and A. where the largest difference was 15' .. Because few respondents chose alternative 1 once. to A, the results of this paper would not he subsiainii:ally affected The evidence can thus be summarized as by using S values from an lCPRA function.  Binswonger Measuremetit of Attitudes towvard Risk 401 form the basis of our empirical analysis and coefficients differed sharply. For table 4, the were geared to finding the certainty equiva- elicited survey results were converted into lents of risky prospects involving stated prob- partial risk-aversion coefficients using a con- abilities. Two types of risky prospects were stant partial risk-aversion function (see foot- used, yielding two subsets of responses for note 4) and grouped into the same classes as each group of farmers. The first type involved those of the experimental study, except that only payoffs above household subsistence re- the intermediate and moderate classes were quirements. In these, while the level of total pooled. The second and third line of table 4 income was at risk, subsistence was assured. (Shirapur First and Kalman First) compare The second type of risky prospect included the the results for the first survey carried out by possibility of not producing enough to meet inpv,stigators A and B, respectively. Shirapur subsistence requirements. Both types of risky appears to be more risk-averse and the differ- prospect involved only two possible outcomes ence is statistically significant. whose probabilities were specified as invariant The villages vwere then resurveyed, switch- frequencies" (Dillon and Scandizzo, p. 427). ing investigatorj, and the results are given in These frequencies were 0.75 (-3 years out of the line I and line 4 of table 4. Comparison of 4") for the "good" outcome and 0.25 (" I year line 1 with line 2 and line 3 with line 4 clearly out of 4") for the "bad" outcome. shows that in each village investigator B In the Indian study the "good" outcome classifies respondents as more risk-averse and the "bad" outcome of the uncertain pros- than investigator A, and these differences are pect are fixed so that the expected value of the statistically significant. This cannot be caused uncertain prospect was one-half of subsistence by the time lag of more than a month between income and twice the subsistence income, re- interviews because the time sequence of in- spectively. Subsistence income previously vestigators was reversed betwveen the villages. had been established for each household indi- Thus, the interview technique is subject to vidually by asking householders, item by item, severe interviewer bias. Resurveys also were their minimum annual requirement of all food carried out in other villages. By analyzing all and clothing. Subsistence income ranged from resurvey results, it was found that in more Rs.462 to Rs. 14,117. The certainty equivalent than 20% of the cases individuals were reclas- of the prospect was then found by vaLrying the sified radically between extreme risk aversion certain income until indifference with the un- and neutrality or negative and positive risk certain prospect was attained. aver.sion. In the game results, such radical re When analyzing the results of the Indian classification in successive games at the same survey, several problems and inconsistencies level is rare (Binswanger 1978a). were encountered. The most serious was that Table 5, lines A and B, show the distribu- in two neighboring villages, Shirapur and tions for the 50- and 500-rupee games, while Kalman, the distributions of risk-aversion lines C and D show the India interview results Table 4. Survey Results in Shirapur and Kalman Risk Aversion Distributions Obtained by Different rnvestigaltmis in Two Vill;iges' Risk-Aversion (lass Village Intermediate Slight and S;urvey or or or Number of Sur'.e) Investigator Resurvey Extreme Severe Moderate Neutral Negative Observations Shirapur A Resurvey 1(0 9 4 5 5 33 (second) Shirapt" B Survey 20 10 3 0 0 33 (first) Kalman (first) A Survey 4 5 5 11 4 29 Kalman (second) B Resurvey 11 12 1 2 3 29 Relevant chi-square tests, all significant at better than 0.01 level. a In absolute numbers.  402 August 1980 Amer. J. Agr. Econ. Table 5. Comparison of Interview-Based and Experimentally Based Distribution of Risk Aver- sion Intermediate or Slight or No. of Extreme Severe Moderate Neutral Negative Inefficient Observations India A. Game no. 12; Rs. 50 2.5 5.1 74.6 6.8 1.7 9.3 118 B. Game no. 16; Rs. 500 2.5 8.2 85.9 0 0.9 2.5 118 C. Interview Subsistence-at-risk" 27.0 34.3 18.0 6.3 14.4 n. appl. 222 D. Interview Subsistence-assureda 18.2 43.6 15.5 9.1 13.6 n. appl. 220 Dillon and Scandizzo's Interview Based Results from Brazilb E. Subsistence-at-riska 26.2 57.3 0 16.5 n. appl. 103 F. Subsistence-assured, 32.0 32.1 8.7 27.2 n. appl. 103 (A) vs, (C) or (A) vs. (D) Chi-square > 95; X'(4,0-05) = 9.49 Note: Comparisons are in percentage of number of observations. ' Subsistence-at-risk and subsistence-assured refer to two different payoff level). In the first, the "bad" outcome would result in the farmer not being able to meet his subsistence income while in the second case the bad year outcome would exceed the level. b Computed from tables 2, 3, and 4 by combining the data for sharecroppers and small farmers. The 103 respondents do not include 15 respondents who were not willing to answer the questions or whose answers were internally inconsistent, as judged by the interviewers, Similarly, the 222 farmers in the Indian interview studies excludes roughly 10 respondents on similar grounds. for the Rs.50 and Rs.500 levels, which come comes is skewed in the interviews but sym- closest to the usually higher payoff levels used metric in the games. in the interviews. The interview results On the other hand, one should not under- classify more than 50% of individuals as ex- estimate the problems associated with any tremely or severely risk-averse and close to interview method. In the third section, it was 15% as neutral or negative. This is in sharp shown that at the early stages of the game contrast to the game results for the same sequence the respondents' replies to hypothet- households. Dillon and Scandizzo give explicit ical questions at the Rs.50 level differed sig- data on the slight-to-neutral and negative nificantly from the real choices and implied classes of risk aversion, but not on the "ex- much more dispersed risk-aversion distribu- treme" classification. In table 5, lines E and F tions. Furthermore, the distributions also show individuals in the extreme class who were more widely spread at the very low game opted for the highest possible certainty equiva- level of one-half-rupee than at high game lent in their study. Interestingly, the interview levels. Interview methods are inevitably faced results for Brazil are somewhat similar to with the problem that individuals may not be those for India, identifying substantial pro- able to reveal their attitudes towards decisions portions of individuals with extreme and they have never taken or seriously contem- negative risk aversion. Other interview-based plated. And even if the payoffs discussed in studies also appear to find higher dispersion of hypothetical questions are high, there are no risk-aversion coefficients than those identified real payoffs or penalties associated with re- here (O'Mara, Kennedy). vealing a preference which may or may not cor- Given the clearly documented interviewer respond to how one would act when faced biases and high instability of interview results with real choices, i.e., true payoffs are relative to game results, one is tempted to even lower than those in the one-half-rupee dismiss the interview studies as unreliable and game. potentially misleading. Some caution may be necessary, however, because the in:erview methods differ in significant ways from the Correlation of Risk Aversion with game method. First, the interviews about an Personal Characteristics income stream from assets or occupations, while the game results are about one-period Empirically, virtually nothing is known about gambles. In the light of footnote 1, it is con- how personal characteristics of individtials are ceivable that the two methods measure differ- correlated with risk aversion. This section is ent concepts. Second, the distribution of out- concerned with correlations of risk aversion  Bill. wolnger Nica UrCIfelcfn( JfAii,h oicard I?MA 403 with personal character-istics regardless of the vairiables and transformations had little impact causal nature of the relationship and therefore on the sign patterns of the coefficients, but the can look at personal characteristics that may regressions using In S had, on an average, the be determined jointly with risk aversion. In highest JR2, and ar-e ther-efor-e r-etainled. Fur- order to use multiple regression, a number of thermore, the full data set was divided into scaliing decisions have to be made to assign subsets of differ-ent villages and for males and risk-aversion '1numbers" to the discreet femiales separately. F-tests indicated that classes. At the simplest level, numbers zer-o to these sets could be comibined for- all gaimes, five are given to the choices 0-to F, and they i.e., coefficients did not differ- significatntly are used as regressors. Other scales are based across data subsets. The regressions in.table 6, on the tradeoff Z and on par-tial risk aversion however, exclu~de the dependent females data S. A substantial number of regressions were because their observations are not indepen- performed using these three variables and dent of those of the houisehold heads. Signs functional transformations thereof. These and signiificant levels of coefficients were fairly Table 6. Regression of Personal Characteristics on Partial Risk Aversion 0.5 Rupees 5 Rupees 50 Ruipees 500 Rupees No. 2 No. 5 No. 7 No. 9 N o. 12 No. 16 ______(1) (2) (3) (4) (5) (6) Intercept -2.975 -- 1.894 0.238 3.498 0.202 0.421 Village 1 0.734 -0.018 0.320 1.859 0.404 -0.314 (1.194) (0.032) (0.696) (3.792), (1.295) (1.804)* Village 2 1.569 - 0.526 -0.776 1.809 (2.663) (0.873) (1.7661* (3.851)1 Village 3 1.576 1.286 0.252 2.34-3 0. "'-3 - 0.16.5 (2.620r (2.1121* (0.567) (4.938)* il.9651* (1.010) Village 4 0.918 --0.484 - 0.304 1.378 (1.563) (0.797) (0.686) (2.880)* Village 5 - 0.387 1-1.165 - 0.918 1.254 (0.692) (2.0511* (2.222r, (2,838)* Women 0.810 1.10 0.204 0.878 -0.073 -0.027 (1.337) (1,17851* (0.456) (1.8321* (0.184) (0.122) Progressive farmer dummy -.0.245 -1.187 - 1.141 0.088 -013 - 0.320 (0.391) (1.8691* (2.4731* (0.179) (0.424) (1.259) Working age adults 0.452 -- 0.761 0.092 1.070 0 081 0.328 (weighted share age 15-59) (0.594) (0.992) (0.167) (1.794) (0.161) (1.167) Salary (Rs. 1000/month) 0.232 - 0.051 --0.493 - 0.294 - 0.141 -0.208 (0.769) (0.164) (2.213)* (1.232) (0.645) (1.7001* Land rented (hectares) - 0.092 ---0.233 -- 0.049 0.012 0.053 0.0008 (1.232) (3.0721* (0.891) (0.210) (0.7481 (0.000) Gambler- dUMMY --1.087 -0.591 0.381 - 130 -- 0.125 0.210 (0.837) (0.447) (0.397) (1.268) (0.195) (0.583) Age (years) 0.017 0.023 0.009 0.021 --0.016 - 0.0025 (1.202) (1.573) (0.848) (1.894) (1.648) (0.465) Schooling (years) 0.061 --0.027 - 0.105 --0.012 -- 0.038 -0.037 (0.984) (0.424) (2.311)* (0.241) (0,915) (1.586) Assets (in 1000 Rs.) --0.019 --0.0055 ---0. 004 1 -0.012 0.0032 -0.001 (2.491)' (0.735) (0.744) (2,0681* (0.568) (0.345) Net transfers -0.247 -0.~502 - 0.388 -0.241 - 0.055 0.005 (received in (000 Rs.) (1.021) (2.0481* (2. 176)* (1.265) (0f437) (0.071) Luck -0.240 -0.269 -0.156 -0.145 - 0.133 -0.043 (1.428) (3.015)* (2.549)* (2.399)* (2.641 )* (1.672)* R2 0.110 0.179 0.202 0.205 0.034 0.088 F 2.762 4.096 4.598 4.653 1.302 1.814 N observations 228 228 2 228 228------1I -ill Note: Asterisks denote significance at the 10%A level of prot'ability.  404 4ii,i':a1 IY() Anmcr. J. Agl%. Econ, IrObuISt in theNe e.xpCeimlents with functional the sample (first line, underlined values). The forms, and, where that waIs not the case, it will predicted S is computed as follows; add to the be signalled in the text.' average S the shift implied by the regression For the partial risk-aversion coefficient S, coefficient for a move fiom the average value the following scaling decikions, are involved. of the indcpendent variable to the largest value lThe choices of an alternative indicate a range observed in the sample. Table 7 also shows only for S. Ihe geomeliric mean of the end which choice would be implied by the new points is assigned as the measure of,S 6 In the value of s. catse of alternative ', a %aline of zero is given T'hirteen variables are included in the re- to S N llhough it could be negaltive. Given the gressions, apart from the village dummies, result that practically no one prefers risk at which are included to take account of effects high game levels, a value of zero is not unrea- on risk asersion of such variables as agro- sonable.7 fIor alternaties (0, the upper bound clinmltic differences, and others, for S is equal to infinity, while its lower bound In the regre ,sions, wealth is nmeasiured by is 7.50. Because in the e\perinicnt very few gross sales value of physical assets. It would ind idua1ls chose alternative 0, it is reason- have been better to use net worth rather than able to assulme that their partial risk aversion gross wvealth. However, the data on borrow- shouild not exceed 7.5 by very much, anid this ings and lendings are scanty, but imply that at Walue ws inCreasled by 12%' to give a value of higher wealth levels borrowings were a small 8.4. It is easy to find fault with any of these fraction of gross wealth. In these households, scaling decisions, and they can be (lefended on an average, 69%, of physical wealth was onily by the anparent insensitivity of resuilts to held in the form of land. The weakness of the alIeIn! ti.e scalings, relationship between physical assets anid risk In table (. the coefficients ol the variiables aversion is sutrprising. given the fairly strong with ln S are giveni. TIo juidge the magnitude of eflect of the garme size. Across games the sign the effects implied, table 7 comnpultes a pre- of the coefficient is consistently negative, but Liicted S for the Rs..5 and Rs.50 levels and not always statistically significant. The (statis- comnpares it with the geoometric average S in tically nlot significant) coefficient of --0.0041 in the 5-rupee game 7 implies that a shift from A decision iNsi' had ito be taken as to what to do with the average wealth to the largest wealth observed -inetffLtent choices ' I) and I* l.eaving out everyone who in the samniple is just sufficient to bring an indi- Lhose in iicthl e iii lici n.risit leat once Aould have drasticails VidUal from choice C to risk neutrality. It ,i-t the sarnple \ otnparison ot regre,sion where thev were left otit withi iegic-ion, where choice 1. ws treatedas its tLiglhit.ing w-ould not be sufficient to move an individLial choice It and chotte D)as cl,to:ce ( resealcd no Itileren, in sign patterns and .. sil , n st/e but redtuced standard errors, 'I'he I Plredicted resulls reported thus incIltde the inefficient choices I For alteinatise I at one of rte e-ndpoints. S () and the geOnietric mean ot' hoth endpoints would he zero 'Iherefore, the S -z exp - log S)i + exp [h,iXj.m. X.jl, .irithnietl. Ine.n ias chosen in thIs cise n lot log.irnthimn tr,insformantons. salute of zero is inadmissi- where / is the sample size. and A; thejtlh indpendent variable, kJ hie It was therefore rather .irbita,itls set at I) ()(X)7 is the arithmetic mean. and h, is its estimated coefficient, T'able 7. TI'h' Largest Possible Sllts in Choices Implied by the Regression Results Maximum Pre(licted Predicted [xplanator'N Minius Mean .S at Rs.5 Choice S at Rs.50 Chloice \'VtIIle.11C ValLe' l evel Implied( Level Implied Asci age .5 0.483 C 0.705 C Wotmien 1 0.592 C 0)758 C PIt Ltcsltc' I )0.154 E 0.581 C Wvorkiing .idutlts (sh.tie atge. 15-s9i 0 0.506 C 0,734 C S.tlaty (Rs 1000) Rs,5.t)69 0.040 k 0.345 C Age 38 yeatrs 0.680 C 0.384 C Schooling 12 years 0.137 E 0.447 C .Asset. iRs. 1(0(00) 185.277 0.226 E F t Iransnfer income (Rs.lt)I)ti 6h224 0.043 E 0.501 C I sick 5 0.221 Es 0.363 C Nor dlummy variables the *alue tiken was one Antilog of aserntge of In S o( ticient has wrong sign.  Bins ivanger MAeasuiremenlt otf Atiiudv.s toward Risk 405 who initially was indifferent between A and B alternatives defined on it, Psychologists, on to choose alternative E. the other hanid, would not find this surprising, For the crucial 50-rupee game, the and the present experiment suggests a strong coefficient is usually of the unexpected sign impact of prior luck. Past experience, or luck, (positive, close to zero, and not significant). is defined as >X,, where i is the game number Contrary to expectations, wealth has little im- 1, 2,3, 4,5, 7, 9, and 12, and X takes a value of pact on individuals' behavior at game levels I when the person wins, 1 when he luoes, that are commensurate with monthly wage and zero when he neit:her wins nor loses (al- rates or small agricultural investments. ternati e) he ceiien is cosistenly Another form of wealth is human wealth and negative and awy statistcly sigicnt. "schooling" is a proxy variable for it. Average note als atwits sietenstoclineias the schooling in the sample is two years, but the maximum is sixteen years, i.e., the distribu- game level rises, i.e., its impact is weaker the tion is highly skewed. At low game levels ths higher the stakes. Nevertheless, at the Rs.5 * level (after seven games), a person who had variable had little influence on risk aversion, consistently won (luck = +7) would have a but at the Rs.5 level and above, it generally greater tendency to shift from playing alterna- reduced the level of risk aversion and was tive C to playing alternative E than a person often statistically significant, although not who had had an equal number of gains and generally so in the regressions using log S. But losses. Finally, past experienice does not wear again, the impact of schooling was not mas- off rapidly. The answers to the 500-rupee sive. In the 5-rupee game, the coefficient size game were collected two or more weeks after of -0.0432 implies that an individual who has the last game had actually been played. fourteen years of schooling rather than one Whether the infuencing of this variable re- would fall into the slight-to-neutral class rather fleets revision of personaf probabilities, or than the intermediate class. At the Rs.50 level, learning about them, or some other effects the same difference is not sufficient to shift the cannot be answered by this experiment.9 Be- individual's risk aversion by an entire class cause "luck" in this experiment is a i-andom interval. variable uncorrelated among individuals it has Two variables that are correlated with impact on individual choices but not on the schooling are the amount of income received risk-aversion distributions. However, farmer.s in the form of salary (i.e., from a secure Job) in a given area race highly correlated weather and a dummy variable for progressive farmers. outcomes. That past experience should have Salary employment, with some exception,, is such an impact on risk aversion suggests that restricted to individuals with schooling, and farmers would be more reluctant to invest totally illiterate individuals have no access to after a series of droughts (even if they had the it (58%r of the household head sample had no same wealth levels as before the drought) than schooling). Progressive farmers are those they normally would on account of their own whom the resident investigators designated as average risk aversion. the early adopters of new techniques (five In Age has a positive sign in games up to the each village). Schooling is again correlated Rs.5 level but a negative sign at the Rs,50 and with this variable and can be expected to con- Rs.500 level At the Rs.50 level it is statisti- tribute to it. Note that in regressions where cally significant but not at the Rs.500) level. Is these two variables were suppre.sed, school- it possible that young people are more wvilling ing did become statistically significant, to engage in risky games at low stakes, "Salary employment" by itself tended to whereas older people having dealt much more decrease risk aversion, the -sign t->ing fairly in risky economlpic games at high stakes might consistently negative, although it was not be more willing to take risks at high levels? statistically significaint at the Rs.50 level. Simi- But at the Rs.50 level, the quantitative impact larly, the progressive farmer dummy had a fairly consistent negative sign, but at the high game levels its coeffi:ient was so small that it Psychologists working expenmentally in the area have found snot s ific that individuals exhibit preferences for heads or tails in coinl toss- was ,,g t es. Because the winning sign of the coin was charged for each Economists would not usually expect that game level. such preference cannot account for the observations past experience with a random process, which on the luck variable. Buit it is p.msihle that the preferences for one s ide ofthe coin seen in earlier experimenili, work might he caused aby a peron having had a winning or losing streak on one ide of a strong impact on a person's next choice over the coin.  406 Au<gust 1980 Amiier. 3. Agr. Eco,. of even thirty-eight years of age difference is sign, which is consistent with the hypothesis not sufficient to shift an individual's choice by that the possibility to rely on income transfers an entire class interval. reduces risk aversion because it insures The "women" dummy variable exhibits in- against adversity. It is not a good measure of consistent coefficient signs. At high game "insurance" via transfer mechanisms because levels it does not appear to affect behavior at it measures what has actually been received all. Clearly, there is little support for the hy- rather than what can potentially be received, pothesis that women are less willing to take yet it is the best that can be done at this stage. risks than men, once adjustment is made for The individuals who liked to gamble (by variables such as schooling. In tabular analy- buying lottery tickets or by playing cards, with sis it was noted that, on an average, women and without money) were identified. Less than were slightly more risk-averse than men 5% of individuals fell in this category, and the (means not significantly different). At best, variable leads to contradictory results. one can explain this by the fact that, in the Table 5 shows that coefficient sizes were environment studied, women did not have generally smaller at the Rs.JO level than at the equal access to education as men. Not a single Rs.5 level. This is not surprising because the woman in the sample ever attended school. distribution of risk-aversion coefficients is The variable "working age adults" approx- more concentrated at the Rs.50 level than at imates the proportion of productive individ- the Rs.5 level. uals in a household: it varies on the unit inter- val, i.e., it is the weighted number of adults between the ages of fifteen and fifty-nine years divided by the weighted sum of family mem- Gambling Results and Farming Decisions bers.'0 The lower this ratio, the higher the proportion of individuals whom the working As measured by the gambling experiment, the age adults have to support. One would thus main conclusions of this study are as follows: expect the variable to have a negative sign by (a) At very low payoff levels, risk aversion is saying that those with few dependents can af- fairly widely distributed from intermediate ford to take more risk. This hypothesis is not levels to risk neutrality or preference. (b) At supported by the data. The coefficient shifts in payoff levels in the neighborhood of monthly sign and is hardly ever significant. At higher labor incomes or small agricultural invest- game levels it is consistently positive, i.e., of ments, risk aversion is highly concentrated at unexpected sign. the intermediate and moderate levels, and risk A portion of the new literature on tenancy neutrality virtually disappears. (c) At these assumes that share tenancy is used to spread high payoff levels, wealth does not appear to the riskin'!ss of farming (Bardhan and Sriniva- influence risk aversion significantly, although san). I; . ieasoning is not based on differential at low game levels such an effect appears to risk avLrsion between landlords and tenants, exist. but it would be strengthened considerably if If these results can be extrapolated to farm- tenants were generally more risk-averse than ing decisions, they suggest that differences in landlords. The "land rented" variable mea- investment behavior observed among farmers sures the net area leased by a household re- facing similar technologies and risks cannot be gardless of the form of contract. It is negative explained priimairily by differences in their at- for landlords and positive for tenants. At low titudles but would have to be explained by game levels there was some indication that differences in their constraint sets, such as tenants were less risk-averse than landlords, access to credit, marketing, extension. etc. It not vice-versa. At high game levels there ap- is not the innate or acquired tastes that hold peared to be no difference. the pcor back but external constraints. Policy "Net transfers received" measures the net in support of poor farmers and landless labor- amount of income transfers received from rela- ers will have to be geared toward removing tives and other sources between 1 July 1975 these constraints rather than being risk- and 30 June 1976. It was negative for those specific. who sent transfers. It usually had a negative 0 In computing the ratio, adult males (above 15 years of age) [Receivedl May 1979; .evjisioii accepted were given a weight of i; adult females, 0.8; and children, 0.5. Januarby 1980.1  Binswanger Meassuremenit of Attituides toward Risk 407 References Council and Southeast Asian Regional Center for Graduate Study and Research in Agriculture, 1978. Bardhan, P. K., and T. N. Srinivasan. "Crop-Sharing Luce, R. D., and P. Suppes. "Preference Utility and Tenancy in Agriculture: A Theoretical and Empirical Subjective Probability." Handlbook of Mathlematical Analysis." Amer. Econ. Rev. 61(1971):48-64. P.cs,vhoi gy. ed. R. D. Luce et al. New York: John Binswanger, Hans P. "Attitudes towards Risk, Experi- Wiley & Sons, 1965, mental Measurement in Rural India." New Haven, Masson, Robert T. "The Creation of Risk Aversion by Conn.: Economic Growth Center Disc. Pap. No. 285, Imperfect Capital Markets.' Anmer. Econ. 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James A. Roumasset, Jean-Mark Boussard, and Dillon, John L., and Pasquale L. Scandizzo. "Risk At- Inderjit Singh, pp. 3-22. Laguna, Philippines: Ag- titudes of Subsistence Farmers in Northeast Brazil: A ricultural Development Council and Southeast Asian Sampling Approach." Amer. J. Agr. Ec-on. 60 Regional Center for Graduate S'uidy and Research in (1978):425-35. Agriculture, 1978a. Jodha, N. S., M. Asokan, and James G. Ryan. "Village - . "Risk Aversion, Indirect Utility Functionn and Study Methodology and Resource Endowments of Market Failure." Uncertaint 'v antd Agricultiurail De'- the Selected Villages in ICRISAT's Village Level velopment. ed. James A. Roumasset, Jean-Mark Studies." Hyderabad: ICRISAT, Economics Pro- Boussard, and Inderjit Singh, pp. 93-114. Laguna, gram Occas. Pap. No. 16, Nov. 1977. Philippines: Agricultural Development C'ouncil and Kennedy, John 0. S. 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Lit. 15(1977):24-55. Mark Boussard, and lnderjit Singh, pp. 341-79. Zeckhauser, R., and E. Keeler. "Another Type of Risk Laguna, Philippines: Agricultural Development Aversion." Economnetrica 38(1970):661-65. Reprinted from AMERICAN JOURNAL OF AGRICULTURAL ECONOMICS Vol. 62, No. 3, August 1980  THE WORLD BANK Headquarters: 1818 H Street, N.W. Washington, D.C. 20433, U.S.A. European Office: 66, avenue d'Iena 75116 Paris, France Tokyo Office: Kokusai Building, 1-1 Marunouchi 3-chome Chiyoda-ku, Tokyo 100, Japan The full range of World Bank publications, both free and for sale, is described in the World Bank Catalog of Publications, and of the continuing research program of the World Bank, in World Bank Research Program: Ab- stracts of Current Studies. The most recent edition of each is available with- out charge from: PUBLICATIC; IS UNIT THE WORLD BANK 1818 H STREET, N.W. WVASHINGTON, D.C. 20433 U.S.A.