The impact of attitudes toward risk on agricultural decisions in rural India

DISCUSSION PAPER Report No.: ARU 4 The Impact of Attitudes Toward Risk On Agricultural Decisions in Rural India Hans P. Binswanger, Dayanatha Jha, T. Balaramaiah and Donald A. Sillers May 1982 Research Unit Agriculture and Rural Development Department Operational Policy Staff World Bank The views presented here are those of the authors, and they should not be interpreted as reflecting those of the World Bank. The authors, in the order listed, are staff members of the World Bank, the Indian Agricultural Research Institute, New Delhi, the International Crops Research Institute for the Semi-Arid Tropics (ICRISAT), Hyderabad and the United States Department of Agriculture. Work on this project was initiated while the first three authors were employed by ICRISAT, and with its generous support. We are grateful to James G. Rayan and an anonymous referee for valuable comments on an earlier draft. Research Project No.: none Research Project Name: none w"b DISCUSSION PAPER Report No.: ARU 4 The Impact of Attitudes Toward Risk On Agricultural Decisions in Rural India Hans P. Binswanger, Dayanatha Jha, T. Balaramaiah and Donald A. Sillers May 1982 Research Unit Agriculture and Rural Development Department Operational Policy Staff World Bank br The views presented here are those of the authors, and they should not be interpreted as reflecting those of the World Bank, THE IMPACT OF ATTITUDES TOWARD RISK ON AGRICULTURAL DECISIONS IN RURAL INDIA by Hans P. Binswanger, Dayanatha Jha, T. Balaramaiah, and Donald A. Sillers In a recent paper attitudes toward risk among a sample of farmers in semi-arid tropical India were measured using experimental methods [3]. In these experiments, each respondent-s risk aversion was revealed by his choice among a set of risky alternatives such as those shown in Table 1, which were then played with real and fairly large monetary payoffs. The key findings of the earlier paper were: (1) that at high payoff levels virtually all farmers exhibited moderate levels of risk aversion, (2) that differences in risk aversion among farmers were not very large, and (3) that wealth had relatively little impact on measured levels of risk aversion. In response to these findings it was hypothesized that "differences in investment behavior observed among farmers facing similar technologies and risk cannot primarily be explained by differences in their attitudes but would have to be explained by differences in their constraint sets, such as access to credit, marketing, extension etc," [3, p. 406]. Since all farmers are risk averse, this does not imply that risk aversion has no impact on farming decisions, but rather that, within a given agroclimate region, it is unlikely that one can explain substantial differences in the behavior of farmers by differences in their risk aversion. -3- Using experimental reponses as a measure of underlying risk aversion, the present paper tests this hypothesis in a m6lel of several farming decisions involving risk. The overall model is divided into two parts: Model I considers the relationship among three "long-run" decision variables whose current values result more or less entirely from decisions made in the past: net household wealth, the proportion of the household-s crop land which can be irrigated with its current irrigation facilities, and the length of its experience in using fertilizer (as measured by the number of years since fertilizer was first used). Measured risk aversion is included as an independent variable in each estimated relationship. Model II examines the efect of risk aversion on several current decision variables: the level of fertilizer application as measured by three different variables, and the proportion of unirrigated land left fallow in years of adverse weather conditions. 1/ For the current decisions the values of the long run decision variables are assumed to be given, i.e., the overall model assumes a sequential decisi6n-making process. A separate investigation about sowing time is also briefly reported. For details on the regions studied, the sample, and the experimental techniques used to measure risk aversion, the reader is referred to [3]. 1/ Leaving land fallow avoids the risk of loss of investment in cultivation expenses. -4 I. MEASURES OF RISK AVERSION Binswanger [3] used the logarithm of partial risk aversion as a scalar measure of risk aversion, but discussed the various scaling problems involved. Following a suggestion from Pasquale Scandizzo in favor of a utility-free measure of risk aversion, we have adapted the concept of the "insurance premium" to the context of the risk aversion experiment. In this application, the insurance premium is simply the difference between the expected values of the high-risk option (that with the highest expected return) and the option chosen by the decision maker in the experiment; it is thus the choice of the preferred option that reveals the extent of risk aversion. Use of the insurance premium obviates the need to specify a utility function and eliminates all other scaling problems. In terms of the alternatives offered in the experimental game (see Table 1 [3], this insurance premium has the following values for a 5 rupee game.1/ In the previous paper it was found that the single most important variable accounting for interpersonal differences in measured risk aversion was the respondent-s "luck" in -revious rounds of the experimental sequence. This implies that our measure of risk aversion contains a random component: If in prior games an individual has been unusually lucky, his observed choice will tend to understate his "normal" risk aversion, and vice-versa if he has 1/ The specific indicator of the decision maker's risk aversion used here is the preferred alternative in experimental game number 7 at the 5-rupee scale. This game is selected because: (1) all household heads in the sample participated in this game; (2) the payoffs offered were large enough to motivate careful choice by most respondents; and (3) sufficient spread remained in the response distribution to make the use of this response as an indicator feasible, whereas responses in the 50-rupee payoff round were concentrated in only two response categories. -5- been unlucky. A luck variable equal to the excess of the number of the respondent 's wins over his losses in previous rounds is therefore introduced along with the risk aversion measure in the regression analysis which follows; the impact of the measured risk aversion variable is thus conditioned on prior luck. This procedure has the effect of "cleaning out" the random luck component in the estimation of the coefficient of risk aversion. Note f' ther that, where risk aversion is expected to have a positive coefficient in a regression, the luck variable is also expected to bear a positive sign: On average, measured risk aversion understates the "true" risk aversion of those with positive prior luck, and this effect should be reflected in a positive luck coefficient. Conversely, an expected negative sign on risk aversion leads to an expected negative sign for the luck variable. -6- II MODELS AND ESTIMATION PROCEDURES Model I, concerned with long-term issues, consists of a system of three simultaneous equations explaining net household wealth, irrigation intensity, and the decision to adopt fertilizer. The model is viewed as having the following underlying structure: (1) WEALTH = fl(IRRI%, EXP, RISKAV, LUCK, Z, Inherited Wealth) (2) IRRI% = f2(WEALTH, EXP, RISKAV, LUCK, Z, Inherited IRRI%) (3) EXP = f3(WEALTH, IRRI%, RISKAV, LUCK, Z, Father's Schooling), where the endogenous variables are: WEALTH = net household wealth in rupees (logarithmic form used in regressions); IRRI% = Percentage of gross cropped area which is irrigable; and EXP = number of years elapsed since the household's first use of chemical fertilizer. The predetermined variables in the system are: RISKAV = risk aversion of the household head, as measured by the insurance premium defined above; LUCK = previous luck in the experimental sequence; Z a vector of household characteristics consisting of: CASTRANK = an index of the household's caste in relation to -7- other households in the same village 1/; AGE = age of household head; EDUC = years of schooling attained by household head SEX = a dummy variable, equal to 1 if household head is female; VILLDUMi = a set of five village dummies, excluding Kalman village. The variables identifying the three equations are: (1): Value of inherited land, at current land prices (used in logarithmic form); (2): Percentage of inherited land which was irrigable when inherited; and (3): Years of schooling attained by household head's father, used as a measure of inherited human capital. The conceptual structure behind Model I is straightforward. Since the introduction of new seed--fertilizer technologies in the late sixties, use of fertilizer has provided farm households with a means to achieve increases in wealth levels. Lower risk aversion assumed to lead to increased wealth. 2/ Because data on the i,itensity of fertilizer use is unavailable for years prior to 1975-76, the length of the household's use of fertilizer 1/ This measure of caste follows a suggestion of Jere Behrman, and differs from the caste variable used in Binswanger [3] in that it reflects not only the household's relative caste rank in relation to that of other households in the same village, but also the proportion of households in the castes below the one of the respondent. 2/ A previous enquiry has demonstrated that for these households studies, wealth had little, if any, impact on risk aversion as measured in the experiment [4]. 8- (EXP) is used as a proxy for a more comprehensive measure of previous fertilizer use. The same changes in technology have raised the marginal productivity of irrigation water, and have thus increased the potential contribution of irrigation to the process of wealth accumulation. In the region considered the irrigation intensity possible on a given farm is determined by three factors: government investments in small-scale reservoir called "tanks" which cannot be built or operated by individual farmers 1/; the groundwater potential of the fields which the farmer owns; and his own decision to invest in digging wells or renting plots with access to irrigation. Experience in fertilizer use is presumed to increase the extent of the household's desired irrigation coverage, while households with greater wealth are presumed to be better able to make the large investments necessary to construct new irrigation wells. As noted below, construction of new wells in this region involves a sizeable financial risk because of a great uncertainty about the water yield potential of a well. Finally, more extensive irrigation is assumed to raise the incentives for adoption of fertilizer, while greater household wealth should allow the household to make the necessary investment more easily. It is widely assumed that farmers view the adoption of new techniques, such as the use of chemical fertilizer, as decisions involving risk. In the environment considered, many farmers irrigated no part of their farms; likewise, many had never used fertilizer. Thus, two of the three 1/ In the sample villages all such tanks date from the nineteenth or early twentieth century, ane are thus captured by the inherited irrigation variable. -9- endogenous variables in Model I are limited dependent variables with a large proportion of zero observations. The simultaneous structure of this model precludes straightforward application of standard Tobit regression techniques to equations (1) through (3); instead, we adopt the two-stage procedure proposed by Nelson and Olson [10] for estimating Model 1.1/ Instrumental variables generated in the first stage of the Nelson-Olson procedure may take on negative as well as positive values, a property which may in some respects be considered a liability in the present application. The first-stage predicted values of the fertilizer adoption variable EXP may be regarded as indices of farming ability, and as such negative values are clearly appropriate. An analogous argument for the admission of negative values of the first-stage IRRI% instrument is more difficult to make. The case for using the model in the present application rests on its low cost and computational tractability, in contrast to alternative models such as that proposed by Amemiya [1]. Furthermore Amemiya's model cannot handle the case where one predicted variable can assume negative values while the other cannot. The estimated relationships reported here, and particularly the effects of risk aversion on the decisions examined, have proved to be highly 1/ This procedure is a straightforward analogue of two-stage least squares. First-stage instrumental variables are formed by regressing WEALTH (by OLS), and EXP and IRRI% (by Tobit) on the vector of all predetermined variables, and taking the product of the parameter estimate vector and the predetermined variable vector for each observation. These instruments replace the right- hand endogenous variables in the structural equations 1 through 3, which are then estimated by OLS or Tobit as required. Following a suggestion by Nelson and Olson we use the standard errors generated by the second-stage estimates in testing significance, while keeping in mind the authors assertion that such standard error measures are probably biased upward (t-statistics biased downward). - 10 - robust with respect to substantial changes in econometric treatment and model specification. In particular, the qualitative results about risk aversion are unaltered when single equation Tobit techniques or two stage least squares procedures are used. This fact convinces us that any additional precision which might have been gained through the use of a technique that constrained first-stage IRRI% and EXP to non-negative values would not have justified the additional expense required. Model II examines the determination of several aspects of current production behavior, conditioned on the decisions previously made concerning the long term variables of Model I. (4) TOTRATE = (5) NRATE = fi(WEALTH, IRRI% EXP, RISKAV, LUCK, Z, (6) N-AREA% = Fertilizer price, RAINFALL), i = 4,5,6. (7) FALLOW = f7(WEALTH, IRRI%, EXP, RISKAV, LUCK, Z, RAINFALL). Equations 4 through 6 model the determination of three measures of current fertilizer application. The first is the total rate of application of nutrients per hectare of gross cropped area (TOTRATE), which measures the intensity of fertilizer application on a whole-farm basis. The second and third variables partition the overall application into a rate per unit area decision and an area decision. The second variable is the rate of nitrogen application per hectare of fertilized area (NRATE), and the third (N AREA%) is the percentage of area fertilized with nitrogen. Since phosphorous and potassium fertilizers are never used without nitrogen fertilizers in the villages under study, 1 AREA% is the percent of total area fertilized. - 11 - In addition to the three endogenous variables from Model I, the variables on the right-hand side (RHS) of equations 4 through 6 include appropriate measures of fertilizer price and rainfall during the period prior to sowing. The fallow decision is estimated in equation 7. In the regions considered, areas left fallow are primarily marginal lands, rather than high- quality land left fallow for crop-rotation purposes. Note also that fallow land is defined for present purposes as land not cultivated at any time during the year. Problems of simultaneity do not affect Model II. All right-hand-side variables are predetermined with respect to current fertilizer application and following decisions. However, the endogenous variables in Model II are both limited dependent variables, with many zero observations. Tobit estimation is therefore applied to equations 4 through 7. - 12 - III. DATA BASE The model is based on data from the Village Level Studies of the International Crop Research Institute for the Semi-Arid Tropics; fol details of these studies see Jodha, Ryan, and Asokan [8]. Binswanger [3] measured risk preferences of a sample of 240 heads of households included in the Village Level Studies; in addition to the risk aversion measures, the studies have accumulated data on many aspects of the socio-economic status and agricultural behavior of the included households. The sample used in this paper consists of the 144 cultivating household included in the Village Level Studies for whom data were available for the three consecutive crop years beginning in 1975-76. In Model II the analysis is based on data for all three years; in Model I, only third-year observations are used. The latter treatment is chosen (1) because one can compute fertilizer experience in the first two years from experience in the third year, (2) because wealth levels change very slowly from year to year, and (3) because the high initial cost and the durable nature of irrigation facilities make rapid changes in irrigation intensity unusual. Regional Characteristics The Village Level Studies cover househo, is in six villages -- two villages in each of three districts representative of major agro-climatic zones of semi-arid tropical India. Table 3 indicates some characteristics of the selected villages relevant to the decisions covered. Region I (Mahbubnagar District) is characterized by red soils with low soil moisture capacity (Alfisols), high irrigation intensity, low rainfall, and relatively small average land holdings. For unirrigated crops this is an area with high yield risks. Region II (Akola District) has black - 13 - soils with medium soil moisture capacity (Yertisols), stable rainfall, very little irrigation, and relatively large areas under unirrigated commercial crops. In this region yield risks are comparatively lower. Region III (Sholapur District) has deep black soils, and low and unstable rainfall; the cropping pattern is dominated by post-rainy season planting based on stored soil moisture, mainly of sorghum and chickpeas. Yield risks are high. The region-wise averages for the three fertilizer use variables (Table 2) indicate, as expected, the intensity of fertilizer use to be highest in Region I and lowest in Region III, with Region II occupying an intermediate position. Farmers in Region I also have a much longer history of fertilizer use (EXP) than those in the other two areas. Region II has the highest and most dependable rainfall and has virtually no fallow lands. Unirrigated fallow is highest in Region I, which also has the highest irrigation intensity. Village dummies are introduced into the regression analysis to take account of the non-homogeneity of error terms caused by the cluster sample design of the study, ai,d to capture village-specific differences in agroclimatic or infrastructural endowments. Since Kalman village of Region III is left out, the dummies capture differences between Kalman and each of the other villages. -14 - IV. RESULTS Household Net Wealth Collinearity problems in the structural equation for household net wealth required some departures from the conceptual model described in equation 1. When the full vector of explanatory variables in equation 1 was included in the regression (column la in Table 4), two apparent anomalies arose: irrigation intensity took on a significant negative coefficient, while inherited wealth had a coefficient near zero with a very low significance level. Collinearity diagnotics [2] applied to the regression suggested that the problem resulted from a strong dependency involving the instrumental variable estimates for irrigation and fertilizer experience, together with inherited wealth, age, and two of the village dummies. Exclusion of all village dummies and irrigation 1/ from the regression leads to column lb in Table 4, whereas exclusion only of irrigation leads to column Ic. Because we regard village effects as playing a somewhat secondary role in the process of wealth accumulation, and because column 1c (but not 1b) retains a high degree of collinearity, we view the specification shown in column lb as the most satisfactory. Exclusion of IRRI% and the village dummies from lb in the presence of known collinearity creates difficulties in interpreting the coefficient on fertilizer experience, since the estimated coefficient also reflects the impact of irrigation. We therefore refrain from an interpretation of this coefficient. 1/ Fertilizer experience rather than irrigation is retained in the regression but it makes little difference. Substitution of IRRI% for EXP in column lb leads to a coefficient estimate on IRRI% of .00534, significant at 5%. The coefficients and significance of other variables change very little. - 15 - According to column lb, households headed by older and more highly educated farmers tend to have accumulated more wealth than others, while inherited wealth has a strong positive impact on current wealth. The estimate suggests that higher caste households tend to have somewhat greater wealth, while female-headed households have somewhat less wealth than others, but neither of these effects is statistically significant. The coefficient on risk aversion is negative in all three specifications as expected; less clearly anticipated was the stroAg significance of risk aversion as a determinant of household wealth in equations (la) and (1b). Risk aversion may affect the process of wealth accumulation through a number of channels; we have only begun to explore the nature of these influences. First, risk aversion may affect investment in irrigation facilities or other fixed capital: the strong impact of risk aversion on irrigation investment is noted in the next section. Although an assessment of the effect of the induced change in irrigation investment is precluded by collinearity, this question requires further investigation. Second, risk aversion may reduce investment in fertilizer, labor, and other variable inputs to the household-a crops, resulting in reduced profits. Higher risk aversion is found below to induce a modest reduction in overall fertilizer input, and other inputs may be similarly affected. Third, risk aversion may inhibit the adoption of some new technologies despite the fact that below we can find no influence of risk aversion on fertilizer adoption. Fourth, risk aversion may affect cropping patterns, prompting farmers to plant subsistence crops rather than higher-value but riskier commercial crops; this is an issue that we cannot easily investigate due to the heterogeneity of the land base in the villages in question. Fifth, risk aversion may induce - 16 - conservative storage and other self insurance practices all of whic have a real or opportunity costs. Finally, risk aversion may reduce investment in human capital. When village dummies are included in the wealth regression (column 1c), the significance levels of all variables are reduced, including that of risk aversion. The uniformity of this drop in significance is an indication that collinearity is the source of the problem. Irrigation Intensity As in the wealth equation, inclusion of both right-hand side endogenous variables in the structural equation for irrigation intensity appeared to give rise to serious problems of collinearity. When collinearity analysis was applied to the least-squares analogue of equation 2, the problem was isolated as a single dependency among the two RHS endogenous variables, the village dummies, and the irrigable proportion of inherited land. Exclusion of either of the RHS endogenous variables appeared largely to resolve the collinearity problem, while the patterns of signs and significance in the two resulting equations were very similar. In particular, the coefficient value and t-statistic on risk aversion are quite robust with respect to the specification chosen, while in each case the RHS endogenous variables are insignificant and bear the "wrong" sign. The specification shown in column 2b was chosen on the basis of a priori judgement of the role of wealth in financing irrigation investment. Risk aversion is seen in column 2a and 2b to pose a significant hindrance to investment in irrigation capacity. Higher-caste households irrigate a higher proportion of gross cropped area, while female-headed households irrigate a smaller proportion; these effects may reflect - 17 - differences in access to credit for irrigation investment. Greater education leads to greater irrigation, possibly because of the higher demands placed on technical knowledge by irrigated agriculture. That risk aversion should reduce irrigation investment is at first surprising, because we tend to think of irrigation as a means of reducing yield risk due to drought stress. However, one must realize that in the areas studied, extension of irrigated area requires that the household dig open wells which involve large investment levels. Furthermore, these areas are not alluvial plains where fields are uniform and groundwater potential well known. Instead the farmer faces considerable uncertainty about the size of investment required to find water; wells dug in outwardly similar locations may encounter water at very different depths, while many of the wells initiated must be abandoned before water is reached at all. The negative risk aversion coefficient is consistent with this high level of risk in the initial investment decision. The large and highly significant coefficients on the village dummies reflect the strong region-specificity of groundwater potential in the Deccan plateau, together with the differential availability of government constructed irrigation tanks. Finally, as expected, the proportion of inherited land which was already irrigable is strongly associated with the proportion of gross cropped area presently irrigable. As far as can be seen from the econometric results, irrigation intensity is primarily a function of "predetermined" variables: the personal characteristics of the farmer (including his risk aversion), the intensity of irrigation on inherited land, and the agroclimatic environment of the - 18 - household's farm. On the other hand, the endogenous long-run decision variables -- wealth or fertilizer experience -- do not appear to play a significant role in determining irrigation investment. Fertilizer Adoption Irrigation intensity and household wealth are the predominant personal factors in the fertilizer adoption decision (column 3a in Table 4); the estimated signs conform to expectations. The village dummies also exhibit a strong effect on adoption. However, no other personal characteristics have statistically significant influence on the adoption decision; in each case except father'schooling, the "wrong" sign appears, and in the latter case the small coefficient size and t-statistic value run counter to expectations. Collinearity diagnostics applied to the least-squares analogue of column 3a identified a strong dependency among irrigation, wealth, the village dummies, and fathers education. Exclusion of wealth from the set of regression (column 3b) produces coefficient estimates with signs according to expectations, but only father's education attains statistical significance.1/ The resulting weak impact of personal characteristics on fertilizer adoption is probably due in part to the necessity of irrigation to achieve a positive payoff from fertilizer: until the household has obtained access to irrigation water (and only about half of the households had such access), personal characteristics have little relevance to the fertilizer adoption decision. Second, while risk aversion appears to inhibit current investment 1/ Elimination of irrigation produces a pattern of signs and significant Tevels similar to column 3a. - 19 - in fertilizer input (next section), the absence of an effect of risk aversion on fertilizer adoption may be related to the divisibility of fertilizer. Even a highly risk-averse farmer who viewed fertilizer investment as risky could experiment with it on a small plot for a minimal commitment of funds. Current Fertilizer Input As expected, households with greater wealth and with more extensive irrigation facilities used more fertilizer by each of the three measures of fertilizer use (columns 4, 5, and 6 In Table 5). Fertilizer application was also strongly influenced by the length of the household's experience with fertilizer. Each of these effects is highly significant and consistent across the three measures of fertilizer input. The coefficient of the fertilizer price variable is significant only in the equation for TOTRATE, where its sign is consistent with expectations; in the case of N AREA%, fertilizer price has the wrong sign but is not significant. Fertilizer price-thus appears to play a significant role in determining the level of total fertilizer investment among sample households, but does not affect the partitioning of the investment into the area fertilized and the rate of application on fertilized area. Rainfall has little impact on the fertilizer decision. Since the regressions contain village dummy variables, the rainfall coefficients capture the effect of deviations of rainfall in a growing season from its normal level for that village. We also know that farmers use most of their fertilizer on irrigated crops such as rice or sugarcane; the fact that these crops are not immediately dependent on rainfall may help to explain this finding. - 20 - Village dummies have been introduced in part to take account of the non-homogeneity of error terms caused by the cluster sample design of the study, but we believe that they capture important village-specific differences in agroclimatic and/or infrastructural endowments. Since Kalman village is left out, the dummies capture the differences between Kalman and the other villages. As may be seen in Table 2, the mean level of total fertilizer application per household is highest in Region I (Aurepalle and Dokur) and lowest in Region III (Shirapur and Kalman). In columns 4 through 6 the village dummies for Aurepalle are positive, while for Dokur they are positive for overall fertilizer input and negative for the other two measures. However, none of these dummy variables are significant, suggesting that the higher level of fertilizer use in Region I is accounted for by the differences in the levels of other included variables particularly irrigation good intensity and fertilizer experience. On the other hand, the Region II village dummies are consistently large and positive, and are highly significant in the case of Kanzara for all three fertilizer measures. This indicates that the assured rainfall received in Region II compensates for the lower intensity of irrigation among the households of that region. Education appears to have little or no impact of fertlizer input, aside from the indirect effects operating through wealth and irrigation investment. Similarly, the age, caste rank, and sex of the household head appear to have little or no direct influence on any measure of fertilizer application. In each of the fertilizer equations the risk aversion variable has the expected negative sign; the coefficient approaches the 10% significance - 21 - level in the case of overall fertilizer inestment, with much weaker effects on area fertilized and application rate. The near-significance of the risk aversion coefficient in column 4 suggests that risk aversion tends to restrain fertilizer investment, but that this direct effect is relatively weak. Since from an investment theoretic standpoint TOTRATE is clearly the most comprehensive of our three measures of fertilizer use, it is not surprising that the effect of risk aversion on TOTRATE should be most visible; similar comments apply to the effects of fertilizer price on the three measures of fertilizer use, cited above. Although risk aversion does ot appear to exert a strong direct influence on fertilizer input, it was seen above that risk aversion has significant effects on household wealth accumulation and on irrigation investment, each of which in turn strongly influences current fertilizer application. This suggests that, in addition to the "short run" model of columns 4, 5, and 6 where irrigation and wealth are taken as exogenous, we should examine as well the "long run" effect of risk aversion on fertilizer application, taking into account the indirect effects operating through wealth and irrigation investment. Column 4a of Table 5 presents such a long run model of overall fertilizer investment, where wealth and irrigation intensity have been dropped from the vector of explanatory variables in column 4. Risk aversion is seen to be a significant deterrent to fertilizer application when indirect effects are included, while the absolute value of the risk aversion coefficient is increased relative to that in the short run model. Education similarly becomes of significant long run importance for fertilizer use. - 22 - Fallow None of the included farms in Kanzara village (Region II) had any full-time fallow land during the sample period, so that the coefficient on the Kanzara dummy was not well defined. Observations for Kanzara were therefore pooled with those in Kinkheda, the other Region II village. As shown by the regression results in column 7 of Table 5, greater household wealth leads to a strong increase in the area left fallow. This presumably results from the fact that wealthier people are less dependent on income from marginal lands which they may own than are poor people. When viewed together with the strong positive impact of wealth oa current input use (columns 4 through 6), this result appears to reflect leisure preference and/or a preference among wealthy households for concentrating inputs on relatively high-quality land. A similar argument may be advanced to account for the positive impact of fertilizer experience on fallowing: if EXP is taken as an indicator of farming ability, its positive coefficient may reflect concentration of management resources on high-quality land and/or high-value crops. Irrigation intensity has no significant impact on the fallow decision. This may be due to the fact that, in general, the farmers in the sample irrigate the highest quality land and leave fallow the lowest quality land (if any land is fallowed), while cultivating a large proportion of the unirrigated land. Thus, only in rare cases would an increase in irrigation intensity directly affect fallowing practices. Caste rank, sex, and educaton had no impact on fallowing. However, older farmers tended to leave fallow a significantly lower proportion of their land than others. - 23 - Village effects played an important role in fallowing. The Dokur dummy was large and significantly negative; similarly, the dummy for the pooled Region II villages was significant and large in absolute value. In the latter case, the low degree of fallowing probably results from the assured rainfall in this region. Deviations from normal rainfall, on the other hand, resulted in no significant change in fallowing. Risk aversion has a strong effect on the proportion of land left fallow, while the luck variable has the corresponding positive sign as well. This finding is in accord with our interpretation of fallowing as a result of reluctance to risk inputs (labor, draft animals, seeds) on marginal land. Sowing time: The Response to an Unanticipated Event In May 1979 unexpected rainfall associated with an early typhoon in the bay of Bengal led to an opportunity to sow crops about one month earlier than usual in Aurepalli village. Higher yields are expected when sowing is advanced but there is a higher risk of death of seedlings in a post-emergence drought. In order to study the impact of risk aversion the sample of 40 households was increased to 100. Of the 68 cultivators growing the crops concerned 34, or exactly half the sample, had sown early. Risk aversion measures were taken again of the entire sample and farmers interviewed about their reasons for not sowing. Of the 34 farmers who did not sow only 8 refrained because they were "afraid of drought." For the others, the fields had not been prepared or they would not obtain draft animals in time (14); they were busy with marriages traditionally taking place in the season (6); they were busy with other work (4); or they experienced sickness or death in the family (2). A comparison of those who sowed with those who were afraid to revealed no statistically -24 - significant difference between them in any.personal characteristic. And in a multivariate logit analysis of the sowing decisions the coefficient of risk aversion was small with a t-value near zero. Just as in the case of adoption, we could not find any effect of risk aversion on the sowing decision. Instead this decision appeared to be conditioned by many other variable of temporary importance, and possibly by the subjective expected yield: The statement that one is afraid of drought may reflect either risk aversion or the subjective assessment of probability of drought, or both. The Risk Aversion Effects in Perspective Table 6 summarizes the magnitude of the effects of the RHS variables on Model I and Model IT decision variables in the form of elasticities evaluated at the mean levels of all RHS variables, 1/ These elasticities should be interpreted cautiously because (as can be seen in Table 2) many variables are highly skewed, with low means and very high coefficients of variation. Finally, in Table 7 we present a measure of the relative importance of the various RHS variables as sources of observed variation in each decision variable, computed as the product of the elasticities from Table 6 and the coefficients of variation of the RHS variables (Table 2). As noted above, risk aversion was found to play a significant role in the determination of irrigation investment and wealth accumulation. As measured by the elasticities based on wealth equation lb, the proportional 1/ Elasticities given for EXP and IRRI% are the elasticities of the expected mean E(Y) in the Tobit regressions [11]. The elasticities given for the wealth equation are calculated as usual. - 25 - impact of risk aversion on wealth accumulation is roughly similar to those of fertilizer experience and education. However, since farmer-to-farmer variation in experience and education exceeds the variation in risk aversion (as judged by their respective coefficients of variation), risk aversion tends to account for a smaller proportion of the observed variation in wealth than these endowments. On the other hand, the smaller variation in age among the sample is outweighed by the larger age elasticity of wealth, with the result that age also dominates risk aversion as a source of inter-household differences in wealth. Similar comments apply to the irrigation equations, although in this case the influence of caste exceeds that of risk aversion only slightly, while education overshadow both as a source of observed variation in irrigation intensity. In sum, although risk aversion plays an important role in the determination of household wealth and irrigation investment, it generally accounts for a smaller proportion of the inter-household differences in these variables than of other household characteristics found to have significant effects on wealth and irrigation. In the "short run" estimates for Model II, risk aversion has a significant coefficient only in the FALLOW equation 7. When elasticities and coefficients of variation are taken into account, risk aversion appears to play an important role in explaining differences in fallowing, exceeding the influence of age and rivalling that of fertilizer experience. However, variation in household wealth is the dominant source of variation in fallowing. Risk aversion approaches statistical significance as a "short run" determinant of overall fertilizer investment (TOTRATE, column 4), but does not affect the proportion of total area fertilized or the rate of fertilizer - 26 - application on fertilized area. The "short run" risk aversion elasticity based on this estimate is overshadowed by the higher elasticities and larger coefficents of variation for wealth, irrigation intensity, and fertilizer experience. On the other hand, when the indirect effects through wealth and irrigation are included, the "long run" effect of risk aversion on overall fertilizer investment (column 4a) reaches to statistical significance. Among the "long run" determinants of interpersonal differences in overall fertilizer use, the net effect of fertilizer experience exceeds that of all other variables, but in this case risk aversion appears to play a role which is comparable to that of fertilizer price, and only slightly less important than that of education. Finally, note that for most cases considered, some of the village dummy variables have large magnitudes, often doubling or tripling the level of the dependent variable from its overall mean. Thus the agroclimatic variation among villages clearly explains a larger proportion of the differences in behavior than variations in risk aversion, which in no instance have such large effects. Note further that, because of differences in their agroclimatic environments the villages differ significantly in the riskiness of farming (but not in the average risk aversion of sample farmers). Village dummies thus partially capture the impact of these differences in environmental risk. - 27 - V. Conclusion Contrary to our initial hypotheses, the results of the paper clearly indicate that interpersonal differences in risk aversion, as measured by the experimental method, lead to definite differences in agricultural decisions among the farmers studied. In the case of one major investment decision characterized by high initial costs and substantial financial risk (irrigation), risk aversion emerges as a highly significant determinant of investment behavior. Likewise, interpersonal differences in risk aversion appear to play a significant role in the process of wealth accumulation: a number of channels through which this influence may operate are suggested, including changes in investment in human and nonhuman capital, in input use, and in management practices. For the three measures of current fertilizer application used, risk aversion always has the expected negative effect, although only the "long run" effect of risk aversion on overall fertilizer application is statistically significant. Finally, interpersonal differences in risk aversion have a strong influence on fallowing behavior but not on the sowing time decision analyzed in a separate enquiry. As stated at the outset, these results are very robust with respect to changes in econometric treatment and model specification and to alternative scalings of the risk aversion measure. Nevertheless our original contention -- that interpersonal variations in risk aversion would not be able to explain a very large proportion of the interpersonal variation in agricultural decisions within a given agroeconomic environment -- is also supported. Effects of differential risk aversion on fertilizer use and fallowing are clearly dominated by differences in agroclimatic and other regional endowments, and by interpersonal differences in wealth, fertilizer experience, and irrigation intensity. - 28 - Moreover,differences in education dominate.differences in risk aversion in the decisions where the former are significant. This, of course, does not imply that variations in risk among techniques of production or across agroclimatic regions are unimportant. Our earlier work [7] has shown that virtually all farmers are risk averse, and are therefore likely to respond in rather similar ways to differences in risk. But in this paper we are concerned with interpersonal variations in risk aversion, not with differences in risk. We should also note that the demonstration that differences in experimentally measured risk aversion have an impact on wealth accumulation and a number of other decisions does not imply that the numerical magnitude estimates of risk aversion found in the game can directly be applied to all decisions. In Binswanger [5] it has been shown that the joint hypothesis of expected utility maximization and asset integration has to be rejected. 1/ While the experimental risk aversion measures appear to rank people in terms of risk aversion for a broad range of decisions, there is thus no guarantee that the numerical magnitude of risk aversion apply to all decisions. In the present paper we have attempted to measure the influence of individual risk aversion on a variety of agricultural production and investment decisions. The results presented here demonstrate that measured attitudes toward risk, as revealed by real gambling decisions, have 1/ Mark Machina has brought to our attention the fact that the test in Binswanger [4] maintains both Expected Utility maximization and Asset Integration. However, Machina's model [9] assumes both asset integration and a utility index which is not linear in probabilities. The test reported in [4] does not reject Machina-s model. Instead his model is one way to reconcile the experimental findings with some form of utility theory that - 29 - operational significance on agricultural decisions. However, we should not close the discussion without noting the recent growth of a body of literature that assigns to risk aversion a much more pervasive influence on rural institutions than previously hypothesized. According to this still-emerging line of thought, risk aversion, combined with problems of imperfect information, leads to incentive and moral hazard problems which exert a profound influence on the specification of land and labor contracts (reviewed in [6]), on the behavior of rural credit markets [7], and on other markets (see e.g. [5] on the failure of private crop insurance markets). We are hopeful that the development of this literature will provide fertile ground for further application of experimentally-measured risk attitudes. - 30 - REFERENCES [1] Amemiya, Takeshi. "Multivariate Regression and Simultaneous-Equation Models When the Dependent Variables are Truncated Normal." Econometrica, 42 (1974), 999-1012. [2] Belsley, David, Edwin Kuh, and Roy E. Welsch. Regression Diagnostics: Identifying Influential Data and Sources of Collinearity. New York: John Wiley and Sons, 1980. [3] Binswanger, Hans P. "Attitudes toward Risk: Experimental Measurement in Rural India." American Journal of Agricultural Economics, 62 (1980), 395- 407. [4] Binswanger, Hans P. "Attitudes toward Risk: Theoretical Implications of an Experiment in Rural India," Economic Journal, 91 (1981), 867-890. [5] . "Risk Aversion, Collateral Requirements, and the Markets for Credit and Insurance in Rural Areas," World Bank Studies in Employment and Rural Development No. 79. Washington: International Bank for Reconstruction and Development, 1982. [61 Binswanger, Hans P., and Mark Rosenzweig. "Contractual Arrangements, Employment, and Wages in Rural Labor Markets: A Critical Review," editors introduction to Rural Labor Markets in Asia: Contractual Arrangements, Employment, and Wages, New York: The Agricultural Development Council, forthcoming. [7] and Donald A. Sillers. "Risk Aversion and Credit Constraints in Farmers' Decision Making: A Reinterpretation," in Carl K. Eicher and John Staatz (eds.), Agricultural Development in the Third World, forthcoming 1982. [8] Jodha, N.S., M. Asokan, and James G. Ryan. "Village Study Methodology and Resource Endowments of the Selected Villages in ICRISAT's Village Level Studies." Hyderabad, India: ICRISAT, Economics Program Occasional Paper No. 16, Nov. 1977. [9] Machina, Mark J. "'Expected Utility' Analysis Without the Independence Axiom." Econometrica, 50 (1982), 277-324. [10] Nelson, Forrest, and Lawrence Olson. "Specification and Estimation of a Simultaneous-Equation Model with Limited Dependent Variables." International Economic Review, 19 (1978), 695-709. [11] Tobin, James. "Estimation of Relationships for Limited Dependent Variables." Econometrica, 26 (1958), 24-36. -31- Table 1: CHARACTERISTICS OF EXPERIMENTAL ALTERNATIVES Choice Bad-Luck Good-Luck Expected Risk Aversion Insurance Outcome Outcome Return Class Premium Prob=.5 Prob=.5 0 5 5 5 Extreme 5 A 4.5 9.5 7 Severe 3 B 4 12 8 Intermediate 2 C 3 15 9 Moderate 1 E 1 19 10 Slight or 0 neutral F 0 20 10 Neutral or 0 negative Source: [3] Table 2: VARIABLE DEFINITION AND THEIR MEAN LEVELS Variable name and definition Abbreviation Pooled file Mean Levels in Mean C.V. Region I Region II Region III (M1ahbub- (Akola) (Sholapur) nagar) 1. Average rate of N+P+K application TOTRATE 9.5 223.3 21.2 6.5 1.7 per hectare of cropped area in Kg 2. Rate of application of nitrogen NRATE 19.6 179.0 36.9 12.5 10.8 per hectare of fertilized area in Kg 3. Percentage of cropped area fertilized N AREA% 15.5 167.4 24.1 18.3 4.5 with nitrogen 4. Number of years since first use of EXP 5.2 134.2 8.9 2.3 2.9 fertilizers 5. Percentage of unirrigated land left FALLOW% 7.8 221.8 14.4 0.5 9.5 fallow 6. Caste rank of the farmer CASTRANK 56.8 47.5 61.6 54.7 54.5 7. Age of the respondent in the risk AGE 42.1 30.5 47.5 35.5 44.1 experiment in years 8. Education of the respondent EDTUC 3.0 116.7 2.0 4.6 2.2 in the risk experiment, in years 9. Sex of the respond in risk expt. SEX I for females and 0 for males 10. Insurance premium RISKAV 1.2 73.9 1.4 0.9 1.4 11. Luck in the experimental sequence LUCK 0.6 387.0 0.6 1.49 -0.2 12. Percent irrigable area IRRIZ 13.8 168.9 28.8 3.0 11.3 13. Net wealth of the household WEALTH 32102.4 103.7 31962.3 32843.8 31445.9 L4. Average price per Kg of plant NPKPRICE 3.6 14.5 3.8 3.6 3.5 nutrient 15. Price paid per Kg of nitrogen in Rs. NPRICE 4.1 3.8 4.2 4.1 3.9 16. Rainfall during May-November in m RAINFALL 605.1 39.0 579.2 704.3 523.9 17. (Five village dummies, excluding Kalman - 33 - Table 3: MAJOR AGROCLIMATIC FEATURES OF SELECTED VILLAGES Region District Major soil Normal Average Percent Major crops type annual size of irriga- village rain- holding ted (mms) (ha) area I MAHBUBNAGAR Aurupalle Shallow & 710 5.6 21 Sorghum, castor medium paddy Dokur deep 710 3.7 60 Paddy, groundnut, Alfisols II AKOLA Kanzara Medium- 820 6.5 5 Cotton, sorghum, deep groundnut Kinkheda Vertisols 820 6.7 4 Cotton, sorghum, groundnut III SHOLAPUR Kalman Deep & 690 8.5 10 Rabi sorghum, medium- chickpea, wheat deep pigeon pea Sholapur Vertisols 690 6.5 13 Rabi sorghum, chickpea, Wieat pigeon pea Source: [8] - 34 - :'aбie +• ST°UC'ПJR1L ^STZ'�АТЪ'S :УОЧ '!OOEL I 7escriptlon 1п('�Е1L:Ч) 1п('iE�L:it) 1п(нЕе�L:Н) :RR2ti 1RRI„ з:� г;{р (1а) (Lb) (ic) (2а) (2Ь) (За) (3b) 11(wЕец.2ц) ` - - 26.323 -6.2ВУ .105** - (-.7оз) (-.9о0) (г.а Ез) � 2.3н2т. -.О2ьs** - - - - .го8** .1sг* ('2.094) Г2.559) (1.848) ERP .126*** ,0278*** ,ОЫ з** Э.з47 - - _ (z.959? (2.625t (2.ова) (.54в) ' с�sт:�гг{ ,а057* .о0з4, .оозгz .zоз* .1яs* -,042ь .Ооьо (1.908) (1.з04) (1.1зо> (1.з8s) (1,з1о} (-L.z3s) (,21о) .�.Gc .0044 ,014Э*+* ,0100* .105 ,042в -,0235 ,0552 (.71о) (2.88о) (1,7во) (.sb5) (.г17) (-.за7) (1.эь3) �DUC ,ОЬ01** ,Об72*** .0545** 2,002* 1.819* -.42I .166 (г.ззг) (з.4о9) (г.о9ч) <1.4г8) (1.а44) (-1.zs2) (.ь7s> �г..$ -.553 -.Э87 -.224 -20.53Э -23.209* 3.912 -.581 (°1.5Ь5) (-1.321) (-.699) (-1.54Э) (-1,890) (.477) (-.160) 32SK<1ц -.154** -.142** -.118 -5.Z65* -4.838* 1.093 -.0446 (2.os8) (-г.озв) (-1.6ob) (-1.8в7) (-1,в17) (1.г45) (-.оь0) LL'С:С -.0363 -.0153 -.0087Э -1.502 -1.9Ib• .265 -,100 (-i.024) (-,48Э) (-,262) (1.115) (1.698) (,709) (-,289) AIIRE DUЧ -.550* - -.201 -i6.210 -й,625 4,266* !.826 (-1.4so> (-.87з) (-.7з0) (-.71в) (1.929) (.9ов) � ООК OL^,•I -,160 - -.522 +,123 ЭО.з08**• 1.651 6.914 (-.Э20) (-L.097) (.085) (3.536) (.Э44) (1.527) Х?.2i2_D[Rt -1.073** - -,151 -37.OL4** ,-27.439*** 8.Э65** 5.241 (-2.1ь9) ' (-.бы ) �.о18 � (.. ) (-э.о4з> (г.4_1) (1.зав> �I2iR_DLa -.736* , - -.00152 -30.004** �Э5.390*** 5.553 ,397 (-1.735) (-.006) C-2.t74) (д.069) (1.347) (,109) 5323 DI?t .2г6 - ,Э74* 2.42b -3.961 -1.575 .Э95 (1.оз6> (1.s1s) (.12э) С-1.2ьs) c-.6sz) (.179) 1п(г,'�г2тzn ,Оо74 ,0882*** ,OSSO** - _ - _ ;Е.аг..;г) (.2з5) ,.,.пz) (2.го7) ..`;дSгIгЕD .:IBI' - - - ,135 .т526*** _ - (,гг4) (з,азо) _лт•s�� зсаооtг:гс _ .Оь8л .77s*** ` - - - (.175). (2.4^_5) . гпсагсеос э.ь1;*** в.�о1*** з.зsz*** 2зо.sоl zs.o43 -бз.ьь8** -з,эзs (17.=.о1> (2s.�2a) (21.о4о) С.бо7) (,а18> (-2.ss6) (-1.зоз) г �д;ивсгд 3- ,:ь47 .:а23 .:+32 - - - _ :5Е ггот eecond згаgе .580 .544 .689 19.93Э 19.991 6.165 5.зС? :,onzero збserтations 14li 144 1G4 73 73 63 6Э Zгro ooвervatlons ) 0 0 71 ?1 д1 31 '�осв: Jne as[гrlsk 1nd:eaces slgпiгlcance ас '07.; сцо ascerlakв, at �'; firee ascerlsks, ас '_... .he аидЬеrз aopearlпg 1п narenchesas Se1ow che coefflсlепс гatloates дге the звsaciacad+t-staciacics. 35 Table S: STRUCI1TAL ESTIMATES FROM MODEL II TO171ATE -LONG RUN," NIRATE N-ARF-A% FALLOW' (4) (4 a) (5) (6) (7) ln(WEALTH) 5.4 71,~ 11.333*** 9.117*** 9.4 7 9*** (2.689) (3.061) (3.168) (3.01.1) rRPIZ 582** .913*** .556*** -.0689 (6:7221) (5.621) (4.362) (-.517) Vw 2.296*** 3.289*** 5.107**ý. 3.707*** 1.200** (6.281) (9.265) (7.538) (6.948) (1.313) CASTRANK -.0106 .0140 .119 -.070 .0668 (-.164) (.214) (1.012) (-.772) (.675) AGE 0832 .0977 .174 ~.125 -.4 07 (.629) (.694) (.725) (-.658) (-2.063) EDUC 4078 1.073** .116 -.218 -.385 (:792) (2.036) (.124) (-.299) (-.471) SEX -1.966 -8.219 -1.933 2.419 -3.580 (-.221) (-.895) (-.121) (.200) (-.337) RISKAV -2.421 -3.216* -1.145 -2.709 7.575*** (-1.391) (-1.689) (-.358) (-1.101) (2.994) LUCK -.504 -1.178 2.822* -.112 4.006*** (-.611) (-1.342) (1.876) (-.096) (3.482) AUREE DUM 7.571 3.644 8.232 8.597 4.702 (1.405) (.634) (.8411) (1.105) (.721) DOK DUM 7.202 26. 244 *** -20.700 -9.939 -25.108** (1.001) (3.859) (-1.513) (-.926) (-2.549) KANZ DUM 29.207*** 24.148*** 41.982*** 51.183*** -70.692*** (5.474) (4.208) (4.325) (6.928) (-7.237) KINK DUM 11.4 SO** 6.177 12.84-1 12.846 -a (1.946) (.972) (1.220) (1.566) SHIR-DUM -.367 5.499 8.571 5.041 -8.044 (-.063) (.898) (.854) (.6172) (-1.256) 17ERT PPRICE -7.344** -5.267* -6.487 4.745 - (-2.449) (-1.653) (-.775) (.727) RAINFALL -.00179 -.00084 -.00280 .0132 .0188 (-.229) (-.103) (-.203) (1.225) (1.554) Intercept -52.629** -12.635 -146.003** -138.382*** -106.177*** (-2.225) (-.766) (-2.794) (-3.392) (-3.347) MSE from aecond 22.230 24.270 41.987 32.863 31.883 stage Nonzero 183 183 183 183 144 observatlons Zero observations 249 249 249 24 9 288 a Observations from Kanzara and Kinkheda are pooled in column 7. INotp: One asterisk indicates significance at 10%; two asterisks, at 3%, three asterisks, at 1%. The t-statistics appear in pareutheses. Table 6: ELASTICITY ESTIMATES WEALTH IRRI% EXP TOTRATE "LONG RUN" NRATE N AREA% FALLOW % (lb) (2b) (3b) (4) (4a) (5) (6) (7) WEALTH - -.373 - .368*** - .387*** .395*** .504*** IRRI - - .341* .538*** - .429*** .331*** .046 EXP .143*** - - .914*** .979*** .803*** .739*** ..289** CASTRANK .196 .635* .056 -.061 .0524 .232 -.172 .196 AGE .618*** .109 .385 .236 .266 .250 .229 -.828** EDUC .201*** .324* .080 .082 .208** .012 -.028 .052 RISK -.175** -.355* -.009 -.201 -.250* -.048 -.145 -.467*** AVERSION FERTILIZER -1.792** -1.237* .902 .837 PRICE Note: Asterisks indicate significance levels of corresponding coefficient estimates; see note te Tables 4 and 5. Table 7: RELATIVE IMPORTANCE OF EXPLANATORY VARIABLES PRODUCTS OF ELASTICITIES AND SAMPLE COEFFICIENTS OF VARIATION WEALTH EXP TOTRATE "LONG RUN" NRATE N AREA% FALLOW % (lb) (3b) (4) (4a) (5) (6) (7) WEALTH -- 38.2.*** - 40.1*** 41.0*** 52.3*** IRRI % - 57.5* 90.9*** - 72.5*** 55.9*** 7.8 EXP 24.2*** - 154.4*** 165.4*** 135.6*** 124.8*** 48.8** CASTRANK 9.3 2.7 -2.9 2.5 110.2 -9.2 9.3 AGE 29.4*** 18.3 11.2 12.6 11.9 10.9 -39.3 EDUC 23.5*** 9.3 9.6 24.3* 1.4 -3.3 6.1 RISK AVERSION -12.9* -.7 -14.9 -18.5* -3.5 -10.7 34.5*** FERTILIZER - - -26.0** -17.9* 7.9 7.4 PRICE Note: Asterisks indicate significance levels of corresponding coefficient estimates; see note to Table 4.