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NO. 6, September 1996
by Romano Pantanali
Table of Contents4. Implications for project design
This paper was prepared by the Investment Centre Division of the Food and Agriculture Organization of the United Nations (FAO), Rome, Italy, in the context of a mission to Lesotho carried out under the Cooperative Programme with the International Fund for Agricultural Development (IFAD), Rome, Italy. The views, findings, interpretations and conclusions expressed in this paper are entirely those of the author, and should not be attributed in any manner to FAO or IFAD. The designations employed and the presentation of material in this publication do not imply the expression of any opinion whatsoever on the part of FAO or IFAD concerning the legal status of any country, territory, city or area, or of its authorities, or concerning the delimitation of its frontiers or boundaries.
1. This note is based on information gathered by an FAO Investment Centre mission which visited the Districts of Thaba T'seka and Qacha's Nek in Lesotho in November 1995 on behalf of the Government and the International Fund for Agricultural Development (IFAD). The mission's task was to identify a Sustainable Mountain Agriculture Programme for possible IFAD financing. It is expected that this programme would form part of the forthcoming Agricultural Sector Investment Programme (ASIP) for Lesotho. The present note sets the background and the justification for deepening the search for a valid technological basis for a sustainable mountain agriculture development programme. This search is the subject of a complementary note on the Machobane system 1, produced as a result of a second FAO mission undertaken in July 1996. Observations of farmers' attitudes and behaviour as well as socio-economic data have been collected by a Socio-Economic and Production System Study (SEPSS) 2 carried out in February 1996 in several villages of the two Districts.
2. In Lesotho externally financed agricultural development projects appear to have been particularly prone to failure. One reason for this may be that, when they have been designed, projects have not been subjected to sufficiently rigorous analysis, particularly with regard to expected farmers' response to extension messages. The thesis of this note is that the impact of high inter-annual fluctuations in crop yields (and of crop prices) on farmers' expectations plays an important role in producers' decision-making, and that this can be measured with sufficient approximation to assess the prospects for the successful introduction of "improved" cropping technologies in small farmers' communities. Stochastic Efficiency Analysis has been used for this purpose. The analysis has been applied to the mountain areas of Lesotho, where natural conditions are particularly harsh, but it has wider applicability in project formulation.
3. The background section briefly presents the statistical evidence. The second section describes the methodology 3. The results presented in the third section are based on the available empirical data. Three major crops have been selected for the analysis: two cereals (maize, the locally preferred crop, and wheat, a crop much better suited agronomically to local conditions than maize, the promotion of which is one of GOL objectives), and one legume (pinto beans, selected as a proxy for pulses). The analysis has been carried out for most Lesotho Districts; however the presentation is limited to the case of Thaba T'seka. The fourth section draws conclusions relevant to agricultural development policy design for the area.
4. In section 5, an empirically derived relationship between the expected crop price, the increase in crop yields (over those of traditional technology) which would be expected to bring about a target average increase in returns to labour, and the increase in yields which would ensure stochastic dominance of a new technology has been estimated with reference to maize. In the last section, a possible short-cut method to assess farmers' potential response, in the absence of detailed information, is explored. This method assumes that unknown frequencies of independent variables (such as yields or prices) would follow a triangular distribution of probability frequencies, defined by the MIN, MODE and MAX values of the variables. The results obtainable with such a method have been compared with the results of the analysis based on actual data. The case of maize yield fluctuations has been used for this purpose. While the specific results obviously differ in absolute value, the orders of magnitude, the relative importance, and the sign of the indicators are confirmed, and lead to similar conclusions. This suggests that the procedure is applicable when data are not available over an adequate time series, provided that a good insight is obtainable on the MIN and MAX values of the variable concerned.
5. Agricultural statistics of Lesotho include data over a 15 year period on the yield of the major crops on a District basis 4. These data have been analysed and elaborated to explore the implications for investment decisions in farming.
6. No significant technological change has taken place in the Lesotho mountain areas in the last 15 years. Production is by small farmers, almost exclusively for home consumption. The annual yields of all crops fluctuate widely, so that the average over the period is not statistically significant. Nor can any statistically significant trend line be detected. All crop yields generally fluctuate in the same direction in the same year (Figure 1) 5. Yield fluctuations are due mostly to different climatic factors: rainfall, hail, and frost: particularly time and duration of rainfall, time and intensity of hail, time and duration of frost.
7. Yield data refer to quantities produced related to area sown, as distinct to area harvested. Lesotho statistics also show the percentage of area sown to different crops which is not harvested (an indication of total crop failures). These are not published on a District basis, but refer more broadly to lowland, foothill and mountain areas. The latter information, covering a 19 years period has not been separately included in the analysis 6, since its impact is reflected in the yield data.
Figure 1
8. Investment decisions by farmers, particularly decisions regarding the switch to so-called improved technologies, would be expected to depend on their perception of the risks involved relative to the possible benefits. This involves expectations about three uncertainty factors: (i) the average yield increase that the switch would bring about; (ii) the extent of fluctuations in crop yield and in returns to labour that would result from the adoption of improved technology compared to continuing with the traditional technology; and (iii) the crop prices. As against these uncertainties, the differential costs which would be incurred are reasonably firm.
9. To deal with the first uncertainty, several assumptions about farmers' perceptions of the expected land productivity increases have been tested. Since the statistical evidence is that average yield data are not significant, those assumptions have been combined with an analysis of the second uncertainty factor. The basic assumption in dealing with the latter is that farmers' expectations about the future fluctuations of crop yields will be influenced by the pattern of past crop performance in their area. It must be emphasized that the models are behavioural models and are not designed to predict precisely what will happen to crop yields in the future, but to assess possible farmers' responses to proposals concerning the adoption of new technologies.
10. In order to do that, stochastic efficiency analysis has been applied. In this procedure, the stochastic dominance concept is used as a measure of the probability of obtaining better results from one technology vs. another, given the probability distribution of a set of outcomes resulting from the application of either one of the two. Stochastic efficiency analysis requires the estimate of the cumulative distribution function (CDF) of the probabilities of a selected index of profitability. In a small farmer, food security oriented setting, gross returns to labour (revenue less cash costs) are an adequate indication of crop profitability.
11. To construct the CDFs, the yield data series have been arranged in ascending order, and correlated to the probability of occurrence, such probability being measured at 1/15 for each value of the series which are made up of 15 observations. From these p values, a cumulative probability series has been calculated.
12. The data have been applied to two crop budget models: one represents the traditional technique applied by the farmers (result of the SEPSS investigation), and the other the modern "low input" improved technology recommended by the GOL. Two series of gross returns to labour have been calculated, each having 15 values. The series are constructed on the basis of the corresponding crop budgets, keeping cash costs constant and applying the pattern of yield outcomes to crop prices to obtain a series of revenues. The difference between the revenue series and the fixed cost has been associated with the cumulative probabilities series.
13. Two CDF of returns to labour from maize farming are presented in Figure 2 and 2bis. Given the way that data have been arranged in the graphs, each point of the CDF curve lying above the other has stochastic dominance, i.e. results in higher returns for the same probability value 7. At each point on the CDF the probability that returns to labour (plotted on the y axis) would be more than the corresponding cumulative probability value plotted on the x axis is = (1 - x). Thus the probability of better returns than the maximum value is (1 - 100% = 0); the probability of better returns than the minimum value is (1 - 7% = 93%). In the case of maize, for example, the probability of exceeding a "modal" value of M300 (corresponding to about 900 kg/ha with the improved technology) is (1 - 43% = 57%); and so on.
14. The model uses a percentage yield increase factor, applied as a constant to all historical yield data, to estimate the impact of the improved practice. This procedure switches the yield profile of the improved technology upward by the same proportion in each point of the curve. The yield increase factor can be changed (as well as the crop price) to simulate the impact of different assumptions.
15. The above condition, and the assumption of constant production costs, may seem an oversimplification. In reality, with adverse dry farming seasonal conditions, production costs such as harvesting and fertilizers application will be less, but the yield of more sophisticated crop varieties may well be also considerably lower, the net impact on returns to labour being difficult to estimate. With very good conditions, harvesting and perhaps weeding costs will be more, and yields may well be proportionally higher with improved technologies 8. Such differences would be important if one was building models that would attempt to predict precisely what would happen to returns to labour. In our case, however, we are trying to identify the general conditions which would persuade a farmer to adopt or reject a new technology, and this would not be influenced much by relatively marginal adjustments.
16. Comparison of the two CDFs (the one corresponding to the traditional technology and the one corresponding to the improved technology) gives an indication of the stochastic dominance of one technology over the other, i.e. of their relative stochastic efficiency. The sum of the differentials (returns to labour with traditional technology less returns to labour with improved technology) over the entire range of observations, or 1/15 of that value on a per annum basis, gives a first indication of the preferred technology. Negative values of this sum suggest preference for the traditional technology.
17. In the case of stochastic dominance of the first degree (one of the two curves is higher than the other in all its points, as in Figure 2), the technological preference is straightforward.
18. In the case of stochastic dominance of the second degree (the two curves cross somewhere) the problem is more complex. Other indices have been worked out to explore these situations. A relevant factor in decision making of small farmers would be the size of the negative values resulting from the application of one technology vs. the other, reflecting the high liquidity preference of these producers (fear of losing money). When the sum of the differential is = 0, the two technologies may be indifferent, but if the size of the sum of possible negative values is larger for one technology, the other would be normally preferred.
19. By assuming different values of the yield increase factor, it is possible to work out the relationship between the percentage increase in yields and the gross return to labour resulting from the stochastic efficiency profiles. From this, the minimum increase required to bring the two technologies onto an indifference level can be read, and reading it in conjunction with the CDF graphs, suggests what the minimum yield required to induce farmers to make the shift might be.
20. Finally, by changing the price assumption, the impact of price changes on the preference for new technology adoption has been explored. The results of the simulations carried out for the maize technology are shown in Figure 6 and 7 (section 5).
21. Maize. Maize is by far the most important crop, grown over about 70% of the cropped area in the District. The 15 year AVG maize yield (0.563 tons/ha) falls between a MIN of 0.222 of and a MAX of 0.913 9.
22. The maize crop budgets compare two farms equipped with their own oxen, plough and harrow. The annual cost of the equipment is estimated by applying a capital recovery factor at 10% interest over the expected life of the equipment and amortized over the number of hectares tilled (either farmers' own, or through contract work). The comparison involves essentially the use of hybrid seeds and fertilizers in the improved technology. In a first scenario, the price of maize is assumed to be M1,000/ton. This price reflects market conditions in the area at the time of the SEPSS, and compares with a Government support price of M 610/ton (Maseru), and with a price prevailing in RSA of M 400/ton. In a first approximation, the latter would represent the border value to be used for economic evaluation.10
Figure 2 (maize price = M 1,000/t, yield increase factor 1.66)
23. Figure 2 shows that, with the expectation of a price of M1,000/ton and of a yield increase of 66% the improved technology, the traditional and the improved technologies are on an
Figure 2 bis (maize price = M 610/t, yield increase factor 1.66)
indifference position if total expected returns are compared. However, the sum of probable negative returns is much less with the traditional technology, which suggests that the improved package would not be adopted.
24. The results are much worse if the GOL support price for maize (M 610/ton) is applied to calculate returns to labour (Figure 2 bis). In this case the traditional technology shows a stochastic dominance of first degree: no rational farmer would adopt the improved technology with such a price expectation. It is interesting to explore the effect of price liberalization. If the RSA border equivalent price is expected, improved technology has even less chance, and the probability of traditional technology showing positive returns to labour is only 25%. The implications are that there is no comparative advantage for the production of maize in the area, no matter which technology is selected, and that the relative advantage of traditional technologies increases as output prices fall.
25. The conclusion that a package involving use of fertilizers, chemicals and hybrid seeds would not be viable if a highly variable climate prevents the attainment of expected yield increases commensurate with the genetic potential of the material planted can of course be reached intuitively. What cannot be intuitively arrived at is the relationship between the expectation of an average yield increase, the price of the crop, and the likelihood of adoption of a technology which implies a given increase in cash costs. This matter will be further discussed in Section 5.
26. Conclusion on maize: Farmers may well continue to grow maize in the Mountain Areas of Lesotho, but they would be ill-advised to try and improve their technology by the route suggested (hybrid seeds and fertilizers). While emphasis on hybrid varieties seems clearly ill placed, there may be a market for composite seeds, which would tilt the scale with the expectation of high prices. Such an expectation could indeed reflect the farmers' preference for "their own maize", and may explain the persistence of the crop in an unsuitable area. The situation calls for launching a programme of applied research aimed at reducing the sensitivity of crop yields to climatic conditions rather than at increasing the crop yield potential.
27. Wheat. Wheat is the second most important crop in the area, being grown over 15-20% of the area cropped. (Sorghum, the other main cereal grown, accounts for 5-10%). The 15 year AVG yield of wheat (0.624 tons/ha) falls between a MIN of 0.210 and a MAX of 1.075 11.
28. A similar analysis applied to the case of wheat demonstrates the sensitivity of the stochastic efficiency of improved low input technology to the price of the wheat crop. Given a yield increase expectation of 50%, and the high price prevailing at the time of the SEPSS in the area (M 1250/ton), the improved technology essentially shows a stochastic dominance of the first degree, i.e. preferable in (almost) all points of the CDF.
29. Applying the GOL support price of wheat (M 650/ton) a situation of stochastic dominance of second degree prevails. A 50% yield increase would result in the two curves showing an apparent indifference between the two technologies, except that negative returns from the traditional technologies are less than with the improved technology.
30. Conclusion on wheat. Wheat yields seem to be declining marginally in Thaba T'seka. Despite the agronomic advantage that the crop ought to have in the climatic conditions of the area, wheat is not a preferred crop in Thaba T'seka. Farmers are unlikely to be enthusiastic about the improved package, unless it can be shown that yield would increase significantly more than 50%. Spending public money to extend the present improved wheat technology is hard to justify. Research efforts should concentrate on both higher yield potential and better resistance to adverse local conditions.
31. Beans. Pulses are grown over 5-10% of the area cropped. The 15 year AVG bean yield (0.35 tons/ha) falls between a MIN of 0 and a MAX of 0.788 12.
32. The case of beans, selected as a proxy for a number of pulses, shows a definite stochastic dominance of the improved technology package at the market price of M3,150/ton and a yield increase expectation of 66%. However the high risk of switching to the new technology, indicated by the size of possible negative results (twice that of traditional technology) is clearly evidenced.
33. Conclusions on beans. The improved technology is likely to be of interest, particularly if the yield increase expectation is more than 66%, which is possible with legumes (sensitivity to fertilizers and, above all, pest control applications).
34. The same analysis has been carried out for a variety of crops from data relating to six other Districts of Lesotho 13. Similar results have been obtained in most cases. Only in Leribe, where natural conditions are distinctly better, the recommended improved technologies show stochastic efficiency dominance over traditional practices. This confirms the conclusion that conventional technological solutions, often imported from other areas in which different agro-ecological conditions and different farming systems prevail, do not provide adequate responses to the deep routed problems of agricultural production in the country.
Figure 3: Summary of farming risk in six Lesotho Districts
Only Leribe District offers reasonable chances of farmers adopting improved technologies based on chemical inputs and high yield crop varieties. Quting, though a lowland District, offers worse opportunities that in the Mountains: it is one of the driest areas of the country. Of the three mountain Districts, Mokhotlong seem to offer less risky farming opportunities, particularly to maize growers.
35. Figure 3 shows a summary of the farming risk in the six Districts, measured by the probability of crop yields being less than the average yield of the 15 years time series, and less than 50% of that average. Figure 4 relates the stochastic dominance profiles of traditional vs. "improved" practices for different crops to the farmgate price of the crop.
Figure 4: Adoptability of "low input" improved technology at different crop prices
Note: in Figure 4, the expression "trad" refers to the curve representing the stochastic efficiency profile of traditional technologies, the expression "imp" refers to improved technologies.
36. Cropping in the mountain areas of Lesotho is to a fairly large extent on terraced land: some terraces, however, show signs of degradation. Ox drawn equipment is almost universally used for ploughing, harrowing and, in the case of maize sorghum and pulses, seeding as well.
37. Small farmer households face a situation of very high risk, with almost 50% chance that their crop yield will turn out below average. The chances of total crop failure are between 25% of the sown area for wheat and sorghum and 31% for maize. Correcting the situation by way of investment in irrigation is out of the question for food crops (topography involves prohibitive costs for other than micro-schemes). There may be some scope for high value crop production (fruits, flowers). These crops require high technical standards, good quality control, sophisticated packing, and ready access to transport infrastructure, to ensure successful marketing: the comparative advantage in these lines would almost certainly be in the lower land areas of the country.
38. In Lesotho, at the moment, the achievement of economic returns from agricultural development in the mountain areas, adequate to justify the cost of externally financed projects appraised in accordance with established procedures, cannot be expected. A preliminary estimate shows DRCs well above parity of international market prices when improved agricultural practices are simulated, and for traditional technologies as well. This confirms the generally held view that the resources of the mountain areas are inadequate to support the population presently settled there, and that long term solutions have to be found outside the agricultural sector, possibly involving substantial out-migration.
39. Until the economy of Lesotho has developed sufficient job opportunities to absorb a large share of the mountain area population in non-agricultural activities, food security will remain the main priority of the people settled in those areas, and a priority objective of Government policy, with a view to holding people there at an acceptable standard of survival. Farmers will aim to reduce the cash cost of cropping as much as possible, and therefore are likely to adopt technologies which minimize external input requirements, maximize in situ capture of moisture, and increase crop resilience to moisture stress and to other climatic hazards.
40. Several considerations relevant to the design of agricultural development policy for the Mountain Areas of Lesotho can be derived from the analysis:
1. In terms of the value of crop produced for human nutrition, there is a 47% chance that the average farm land available per caput (0.3 ha) will supply less than 2,500 calories per day with the traditional technology. Available improved technologies for cereals which could obtain a 50% yield increase would reduce that probability to about 15%, but the financial risk involved for the farmers prevents this solution from being widely accepted. Potatoes, a crop recently introduced in the area, appear to offer the potential to bridge the gap. The nutritional production implications of farming this crop over 10% of the land cropped with traditional technologies, at the expense of maize, wheat and sorghum, have been simulated, applying to potatoes the frequency distribution of wheat yields (annual yield data for potatoes are not available). This scenario would reduce the probability of inadequate calorie production to 20%, and increase overall food availability to a significant extent.
The situation is illustrated in Figure 5.
2. Agronomic research ought to concentrate on crop varieties which would be more resilient to the climatic hazards of the zone. A thorough review of the work done so far for the area, and of the potential offered by research in similar areas all over the world must be undertaken. While basic research is out of the question in Lesotho for financial and other reasons, contracting out research programs to institutions abroad is advisable, and applied research in the area on possible promising improved varieties must be part of the development measures proposed on a priority basis.
3. While most crops in the area are grown as pure stands in the farming system, the Machobane developed technique 14for continuous intercropping of several crops offers interesting advantages, particularly with respect to the risk reduction objective. This technology is beginning to spread in the area, but is not yet the object of official support. Lesotho research organizations ought to monitor solutions found by Machobane farmers in adapting the technology to local conditions, as well as the constraints faced. Providing the link between research and Machobane farmers is a GOL function which deserves top priority.
4. Investing public money on extension of presently available technical solutions by expanding the Village Level Workers network is not justified, except possibly for potatoes. Efforts should be concentrated on providing an adequate linkage between research and farmer innovators by improving the professional capacity for understanding local production problems at the Subject Matter Specialist level, provided that a close dialogue with the research stations can be effectively established.
5. Promoting private sector investment in seed multiplication (co-operatives, groups, or individuals) may be justified in the case of composite maize seeds, as well as potatoes.
Figure 5
41. Let us go back to the analysis of the case of maize and explore the possibility of establishing an empirically derived relationship between the yield variance due to non-predictable factors, the level of the crop price, and the stochastic efficiency of a new technology relative to that of the traditional technology. This would enable the analyst to respond to the following question: what is the level of productivity increase that a farmer would consider sufficient to induce him to adopt a new technology, given the incremental cost to be incurred, the crop prices that may confront him, and the fluctuations in yields which he is accustomed to experience in his area?
42. To explore that relationship it is assumed that a reasonably prudent innovative farmer would adopt a new technology if the chances of negative returns to labour were no greater than those from currently applied technology. This is a stringent condition, near to stochastic dominance of first degree, but one that would correspond reasonably well to what is known about the "risk aversion" of agricultural producers, particularly those who have a high liquidity preference (fear to lose money) as most small farmers do. The stochastic efficiency frontiers elaborated for maize in section 3 have been further analyzed to construct such relationship.
43. The results are illustrated in Figure 6. This compares the average yield increase factor expected from the recommended improved maize technology which brings about (i) a target 50% increase of returns to labour, and (ii) the stochastic dominance of the improved technology over the traditional one. In Figure 6, the stochastic dominance condition of the improved technology is defined as in the previous paragraph.
44. With a price of M1,000/ton, an average yield increase of about 90% (yield up to 1.14 t/ha) would generate 50% higher returns to labour; but the technology would have stochastic dominance (i.e. would be accepted) only if the expectation was to achieve an average yield 160% higher than with traditional technology (1.9 t). With a lower price (M 600/ton) the corresponding values are 116% (1.3 t) and 260% (about 2.1 t), respectively. The lower the price the larger the spread: with the price prevailing in the RSA (M 400/t) the graph is meaningless since both technologies show negative returns.
Figure 6
45. The two curves have a different shape, the higher one reflecting the shape of the CDFs from which it is derived 15. The spread between the two curves depends on the yield fluctuation data upon which the stochastic efficiency curve is built. The less acute the fluctuations, the more the two curves will tend to coincide, and viceversa. This result has wider implications. In the Lesotho context, it suggests that it may be more important to develop technologies which would tend to reduce yield fluctuations, rather than increase the absolute productive potential.
46. From the above data, the graph in Figure 7 has been constructed. The simplest way to grasp the meaning of Figure 7 is to think of the sight of a gun, which must be raised higher, the further away is the target, and the less powerful is the charge in the cartridge. As in a ballistic table, the graph shows how much higher one needs to set the sight in order to hit the target. Naturally, as with all guns, the sight cannot be raised to hit beyond the range of the gun.
47. Figure 7 shows, for example, that, in the context of the Thaba T'seka experience, with an expected maize price of M 800/ton, a dominant (acceptable) technology ought to obtain 45% better yields than the one which would obtain, on average, 50% more returns to labour than the traditional technology. If the higher target is technically not feasible, the technology would be rejected.
Figure 7
48. When embarking on a new venture, a reasonably prudent decision maker would attach more weight to the risk of obtaining larger negative results than to the opportunity of reaching larger positive results. This can intuitively be accepted as a feature of the basic psychology of most decision makers. Most agricultural producers operating under conditions of fluctuating outcomes, to be persuaded to change from a well known technology to an expected superior one, would require the expectation of obtaining average returns larger than those which they would accept in the absence of fluctuations, with a view to offsetting the larger losses expected to be incurred when adverse circumstances prevail.
49. Can a practical method be devised to assess how much larger that expectation would be? Let us go back to Figure 6 and 7. A closer look would suggest that a general rule might be at work, applicable not only in the extreme circumstances of Lesotho's mountain areas, but in all situations in which fluctuating economic results have been usually experienced in farming, and would be expected from adopting a new technology as well. The rule can be formulated as follows:
Whenever the returns of a technology innovation are expected to fluctuate as a result of fluctuations of independent variables affecting those results:
(i) the wider the fluctuations of the independent variables, the larger would be the difference between the expected average result which would induce the technology change, and the expected average result set as a target, and
(ii) the lower the expected price of the product, the larger would be the difference between the expected average result which will induce the technology change, and the one expected to achieve the target on average.
50. The rule would apply to all technology changes which require an increase in cash costs per unit of land, and would operate more forcefully, the more the risk aversion of the producers would be close to the criterion set in paragraphs 8 and 41.
Figure 8: maize yields distributed triangularly, maize price fixed.
51. In many countries, the actual production performance of many Agriculture and Rural Development Projects has fallen short of expectations. It is suggested that some of the disappointing results might have been predicted if the rules stated above had been taken into account in project evaluation. The graphs of Figure 6 and 7 suggest a method to measure the spread between the expected incremental results required to achieve project targets on average, and those required to induce the technology switch.
52. In many countries/project areas, however, sufficient data to perform the full analysis might not be available. A short-cut method has accordingly been explored, with a view to providing a "rough and ready" indicator of the requirements for technological innovations to be accepted in a small farmer environment.
53. The analysis has been repeated for the maize crop, based on a value for the expected most likely yield, and for the minimum and maximum yield. The values used are the same as in the previous analysis, i.e. the actual minimum and maximum yields recorded, and the yield increase factor of the improved technology. The three yield points have been used to estimate the probability frequencies distribution of a series of equally spaced yield data, comprised between the minimum and the maximum, assuming such distribution to be triangular. The results (compare Figure 8 with Figure 2) are remarkably similar to those obtained using the full 15 years yield statistics 16. In Figure 8 and Figure 9, the curve A represents the traditional technology, the curve B represents the improved technology.
54. The triangular distribution method can be used equally well in cases when the yields fluctuations are not very important, but significant price fluctuations may occur. Figure 9 shows the simulation of the maize technology analysis obtained by assuming a fixed yield increase factor of 1.9 and fluctuating price distribution with MIN=400 M/ton, Mode=610 and MAX=1000 spread over 15 intervals.
Figure 9: price fluctuations distributed triangularly, maize yield fixed.
55. The analysis of the Lesotho case confirms Anderson and Dillon's suggestion that the triangular distribution assumption17 can be used to construct the CDF of the frequencies of an independent variable in the absence of adequate time series of actual data which are acceptable approximations for the purposes of risk analysis. The basic parameters can be "guesstimated" by experienced agronomists, if actual observations are not available from the field, or of very limited coverage. These can be inferred from climatic data and/or other agronomic considerations, and by asking farmers about their past experience with crop yields and price fluctuations in the context of RRA/PRA investigations. The CDFs calculated on the basis of the triangular distribution assumption can be used construct graphs similar to Figure 6 and 7.
56. The application of the methodology will save time spent at project appraisal on performing cumbersome hypothetical "sensitivity analyses", while providing a logical framework for simulating farmers' likely reactions, and avoiding over-optimistic assumptions about technology adoption rates.
57. Simulations derived from triangular distributions of the frequencies of the main variables which determine the selected index of profitability would give us an idea of the extent to which the performance of a new technology should exceed the performance of an established technology, for the former to be worth placing in an extension package. The analysis presented in this note suggests, for example, that, for a technological package to be accepted by small producers, if price and yields fluctuate between two extremes, one being about 2 times higher than the other, and those fluctuations are not correlated with one another, the expected average yield ought to be some 30% to 40% higher than the target yield which would in theory obtain adequate incremental returns to labour. Expected fluctuations of only one of the variables would obviously have much less, but always a noticeable impact.
1 LESOTHO: A Note on the Machobane System, TCI Occasional Paper Series no.7. The methodology used in both notes has been developed by Romano Pantanali, Senior Advisor, Economics, FAO Investment Centre, with the assistance and advice of Alice Carloni, Rural Sociologist of the FAO Investment Centre, who led the two FAO missions to Lesotho, and carried out the statistical analysis for all Lesotho Districts, except Thaba T'seka. Professional review by several staff members of the FAO Investment Centre provided useful comments and suggestions for improvement of earlier drafts of both papers.
2 The study was undertaken by a team which included GOL officials from the District Agricultural Offices and staff from Sechaba Consultants, a Lesotho firm. The team operated under the leadership Sechaba's partner, Thuso Green. Alice Carloni designed the SEPSS, joined in the participative discussion of the SEPSS findings in Lesotho, and supervised closely the elaboration of data and the final SEPSS text.
3 The methodology is suggested by J.R. Anderson and J.L. Dillon in Risk Analysis in Dryland Farming Systems, FAO 1992, Chapter 3.
4 Ministry of Agriculture, Department of Economics and Marketing, and Ministry of Planning, Bureau of Statistics: Lesotho Agriculture Situation Report, 1994 (mimeograph). Similar fluctuations are recorded for all Districts of Lesotho, and with regard to total production of major crops as well. No statistically significant trend can be estimated from the available data. The linear regression trendline of total crop production data from 1977 to 1994 does show an apparently negative slope (-2% per annum), but the standard error of the regression coefficient is equivalent to almost 60% of the coefficient itself. The data of the series range between a MIN and a MAX value in the ratio of 1 to 4.3. Adding the 1995 and 1996 data when they become available (1996 was an exceptional bumper crop year like 1978) would perhaps reduce the negative coefficient substantially. Data on area planted seem to show a slightly upward trend but the linear regression coefficient of the series is even less significant than for total crop production. The conventional view that land productivity and crop production in Lesotho are on a downward trend cannot be confirmed. From available data it can only be said that production per capita is generally declining.
5 Correlation is high between maize and sorghum yields (0.89), much less between wheat and maize and sorghum. Bean yields show the least correlation with those of the other crops.
6 Farmers cultivating maize are faced with a probability of 31% that they would not harvest more that 1/5 of the area sown; that probability is 25% in the case of wheat and sorghum.
7 p values are plotted on the x axis for convenience in using the EXCEL graph wizard
8 The model can be made more sophisticated by assuming a non-linear relationship between the two curves, and/or elaborating more complex crop budgets, which may represent reality better. However, such a procedure would be generally not advisable: it requires making a complex set of assumptions, difficult to verify and/or to derive from statistics often of doubtful quantitative value. By increasing the sophistication of the model, the relative position of the two curves may change to some extent, but this is not likely to cause substantially different conclusions. In decision making, we will argue later on, it is the left hand side of the curves which matters most: here the constant costs and yield increase factor assumptions may result in overestimating the advantages of the improved technology to some extent, a factor which ought to be taken into account on a case by case basis.
9 The SD of the AVG is 0.242. The trend shows a decline of 0.25% per annum, with a SE of 0.015 (not significant). The probability of exceeding the AVG is 53%, thus the probability of worse results is 47%.
10 Cereal prices (maize and wheat) have been much higher in Lesotho than in neighbouring RSA, as a result of the monopoly granted by GOL to Lesotho Flour Mills, a State enterprise. In turn, prices in the RSA are above import parity as a result of the protectionist policy of the RSA Government. Liberalization of trade in cereals has recently been announced by the GOL.
11 The SD of the AVG is 0.284. The trend shows a decline of 1.28% per annum, with a SE of 0.017. The probability of exceeding the AVG yield is 53%, thus the probability of worse results is 47%.
12 The SD of the AVG is 0.278. The trend shows an increase of 2.3% per annum, with a SE of 0.016. The probability of exceeding the AVG is 47%.
13 All districts data have been analysed: the tables summarize the results for the three mountain districts (Thaba T'seka, Qacha's Nek, and Mokhtlong), and the best (Leribe) and worse (Quting) district of the country.
14 LESOTHO: A Note on the Machobane System, TCI Occasional Paper Series no.7.
15 In Figure 6 and 7 two lines represent each curve: the thick continuos line is obtained by running a regression on the data represented by the broken line. As the graph shows, the CDF-derived scatter regression is represented by a polynomial equation of the 3rd order, while an exponential equation fits the lower scatter. The equations are presented for illustrative purposes only, given the small number of observations from which they are derived.
16 The order of magnitude of the sums of returns calculated from the CDFs is similar because the MIN and MAX points of the triangular distribution are the same as those of the statistical series. Accordingly, the general applicability of the methodology depends on how good the guess of these values would be in the absence of data. Although setting different MIN and MAX values would increase the difference of the sums derived from the triangular distribution assumptions and those derived from actual data, the general indications would not change unless the guessed MIN and MAX values are considerably different of the actual values.
17 The formula written in an array of a LOTUS or EXCEL spreadsheet to obtain the CDF derived from the triangular distribution of a series of frequencies (Anderson and Dillon, cit., page 47) is:
=IF(x<m,((x-a)^2)/((b-a)*(m-a)),(1-(b-x)^2)/((b-a)*(b-m)))
with: a =MIN; b=MAX; m =MODE