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Soil Conservation: An Assessment of the National Resources Inventory, Volume 2 (1986)

Chapter: 2. Assessing Soil Erosion Productivity Damage

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Suggested Citation:"2. Assessing Soil Erosion Productivity Damage." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
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Suggested Citation:"2. Assessing Soil Erosion Productivity Damage." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
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Suggested Citation:"2. Assessing Soil Erosion Productivity Damage." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
×
Page 23
Suggested Citation:"2. Assessing Soil Erosion Productivity Damage." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
×
Page 24
Suggested Citation:"2. Assessing Soil Erosion Productivity Damage." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
×
Page 25
Suggested Citation:"2. Assessing Soil Erosion Productivity Damage." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
×
Page 26
Suggested Citation:"2. Assessing Soil Erosion Productivity Damage." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
×
Page 27
Suggested Citation:"2. Assessing Soil Erosion Productivity Damage." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
×
Page 28
Suggested Citation:"2. Assessing Soil Erosion Productivity Damage." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
×
Page 29
Suggested Citation:"2. Assessing Soil Erosion Productivity Damage." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
×
Page 30
Suggested Citation:"2. Assessing Soil Erosion Productivity Damage." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
×
Page 31
Suggested Citation:"2. Assessing Soil Erosion Productivity Damage." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
×
Page 32
Suggested Citation:"2. Assessing Soil Erosion Productivity Damage." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
×
Page 33
Suggested Citation:"2. Assessing Soil Erosion Productivity Damage." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
×
Page 34
Suggested Citation:"2. Assessing Soil Erosion Productivity Damage." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
×
Page 35
Suggested Citation:"2. Assessing Soil Erosion Productivity Damage." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
×
Page 36
Suggested Citation:"2. Assessing Soil Erosion Productivity Damage." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
×
Page 37
Suggested Citation:"2. Assessing Soil Erosion Productivity Damage." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
×
Page 38
Suggested Citation:"2. Assessing Soil Erosion Productivity Damage." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
×
Page 39
Suggested Citation:"2. Assessing Soil Erosion Productivity Damage." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
×
Page 40
Suggested Citation:"2. Assessing Soil Erosion Productivity Damage." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
×
Page 41
Suggested Citation:"2. Assessing Soil Erosion Productivity Damage." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
×
Page 42
Suggested Citation:"2. Assessing Soil Erosion Productivity Damage." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
×
Page 43
Suggested Citation:"2. Assessing Soil Erosion Productivity Damage." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
×
Page 44
Suggested Citation:"2. Assessing Soil Erosion Productivity Damage." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
×
Page 45
Suggested Citation:"2. Assessing Soil Erosion Productivity Damage." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
×
Page 46
Suggested Citation:"2. Assessing Soil Erosion Productivity Damage." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
×
Page 47
Suggested Citation:"2. Assessing Soil Erosion Productivity Damage." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
×
Page 48
Suggested Citation:"2. Assessing Soil Erosion Productivity Damage." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
×
Page 49
Suggested Citation:"2. Assessing Soil Erosion Productivity Damage." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
×
Page 50
Suggested Citation:"2. Assessing Soil Erosion Productivity Damage." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
×
Page 51
Suggested Citation:"2. Assessing Soil Erosion Productivity Damage." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
×
Page 52
Suggested Citation:"2. Assessing Soil Erosion Productivity Damage." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
×
Page 53
Suggested Citation:"2. Assessing Soil Erosion Productivity Damage." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
×
Page 54
Suggested Citation:"2. Assessing Soil Erosion Productivity Damage." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
×
Page 55
Suggested Citation:"2. Assessing Soil Erosion Productivity Damage." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
×
Page 56
Suggested Citation:"2. Assessing Soil Erosion Productivity Damage." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
×
Page 57
Suggested Citation:"2. Assessing Soil Erosion Productivity Damage." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
×
Page 58
Suggested Citation:"2. Assessing Soil Erosion Productivity Damage." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
×
Page 59
Suggested Citation:"2. Assessing Soil Erosion Productivity Damage." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
×
Page 60
Suggested Citation:"2. Assessing Soil Erosion Productivity Damage." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
×
Page 61
Suggested Citation:"2. Assessing Soil Erosion Productivity Damage." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
×
Page 62

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2 Assessing Soil Erosion Productivity Damage DavidJ. Walker and Douglas ~ Young Scientists have long recognized in a general sense that erosion reduces crop yields; however, economic assessment of erosion damage has always been elusive. The erosion process is gradual, and annual yield variability from weather, disease, and pests obscures the inexorable reduction of crop yields from soil loss. In many regions, technical progress has boosted crop yields faster than erosion has reduced them, perhaps persuading some that erosion damage is of no consequence. Yet, technology may only be masking erosion damage in many instances. In fact, some types of technical progress can actually increase erosion damage. A correct assessment requires that the effects of erosion and technology on yields be disaggregated and that separate projections be made of their impacts. Accurate measures of erosion damage are important. Many farmers, while admitting that erosion may reduce crop yields and farm income in the future, may be unwilling to adopt conservation with only a vague notion of the long-term cost of erosion damage. The Soil Conservation Service's (SCS) recent targeting of con- servation efforts stresses the need for information on erosion damage. Rather than identifying areas for action on the basis of high erosion rates, target areas could be selected based on net economic benefit of conservation, including the erosion damage avoided. Simple physical criteria, such as soil loss, may be misleading because some areas with high erosion rates may not suffer reduced yields if subsoils are deep and suitable for cultivation. Even when yield loss is significant, if the crops have a low value, the economic loss may not be as great as in an area with moderate erosion but high-value crops. 21

22 OBJECTIVES AND SCOPE OF ANALYSIS Damage from soil erosion is generally divided into onsite productivity impacts and offsite environmental effects. Although both components are necessary to compute aggregate economic damage of soil erosion, thi paper focuses exclusively on the measurement of onsite productivity effects, in light of the authors' conceptual and empirical research specialization. This focus does not reflect a belief that economic measurements of offsite environmental impacts are not equally important. The objectives of this paper are to: (1) develop and explain fundamental concepts for the correct assessment of productivity damage from soil erosion, (2) present empirical evidence from the Pacific Northwest Palouse region on the historical nature of technical progress and its interaction with erosion as both processes have influenced winter wheat yields through time, (3) discuss an explicit wheat yield projection model for the Palouse based on historical patterns and rates of technical progress and erosion interactions, (4) present an operational computerized erosion damage assessment model that incorporates the Palouse wheat yield projection model, (5) discuss possible uses of the National Resources Inventory (NRI) data for regional and national erosion damage assessments, and (6) summarize the research and policy implications of the analysis. s CONCEPTS FOR MEASURING EROS ION DAMAGE There are four concepts involved in the assessment] of erosion damage: (1) a basic comparison of yields with and without conservation (or with and without erosion), (2) an awareness that the yield penalty from using con- servation tillage should not confound the assessment of erosion damage, (3) the identification of residual and reparable yield damage, and (4) the need to separate the effects of technological change from those of erosion. The first three concepts apply to erosion damage measurement either with or without technical progress, whereas the fourth concept explicitly considers the influence of concurrent technical progress on erosion damage measurement. A physical measure of erosion damage--yield damage--is used in this section to illustrate the concepts for measuring erosion damage, and then an economic measure of erosion damage is presented based on those concepts.

23 Wheat yield (bu/ac) 70 68 / / l l l 5.2 - F ~B ! 15.4 18 Topsoil depth (inches) FIGURE l Yield damage with zero-erosion basis and conservation basis. Compare With Versus Without The basic idea underlying the measurement of erosion damage is the "with versus without" comparison so common in economic analysis. Two possible comparisons are relevant. In a comparison of yield with erosion versus yield without, the basis for comparison is yield after zero erosion, i.e., with unchanged topsoil depth. Erosion damage is the lost Yield from gross erosion with conven t~onal tillage. Alternatively, the erosion damage comparison could be yield with conservation versus yield without. Here, the basis for comparison is dynamic or changing over time, yield with topsoil depth conserved using the most cost-effective conservation tillage system available. Erosion damage is the lost yield from the additional erosion under the conventional (erosive) tillage system compared to conservation tillage erosion. These two bases for measuring erosion damage can be illustrated graphically (see Figure l). Consider, first, erosion damage with a zero erosion basis for comparison The yield with a current topsoil depth of 18 inches is 70 bushels/acre. After 64 years of erosion erosive tillage, topsoil declines to 5.2 with conventional inches and yield

24 declines to 51 bushels/acre. Erosion damage with this measure is 19 bushels/acre, the difference between yield with eroded soil and yield without erosion. With the best conservation alternative as the basis for comparison, topsoil depth and yield after 64 years is 15.4 inches and 68 bushels/acre, respectively. Erosion damage with this measure is 17 bushels/acre, the difference between yield with eroded soil and yield with conserved soil. There are instances when either measure may be more appropriate. The measure derived from the zero erosion basis may be more useful for evaluating alternative con- servation practices in a region, while that derived from the dynamic basis, or comparison with the best conserva- tion alternative, might be more useful for selecting target areas for conservation emphasis. Avoid Confounding Tillage Yield Penalty and Damage Even with a dynamic basis for comparison, where two different relevant tillage systems generate the two topsoil depths used for the yield damage assessment, one yield-topsoil depth response function must be used to measure yield at both the conserved and eroded topsoil depths. The conservation tillage response function should be used on the premise that ultimately conser- vation will be required to protect the soil. It would be a mistake to use separate yield-topsoil depth response functions for conservation and conven- tional tillage to estimate yields at the conserved and eroded topsoil depths, respectively. Often the con- servation tillage system will yield less at the same topsoil depth than the conventional system, causing its response function to lie below that for the conventional system (see Figure 2). If the yield at the eroded soil depth (5.2 inches) is measured with the conventional yield function Lye) but the yield at the conserved topsoil depth (15.4 inches) is measured with the conservation yield function (Yc), erosion damage would be confounded with the tillage yield penalty. In cases where yields are lower with conservation tillage, using both yield functions would underestimate the damage attributable to erosion (10 bushels/acre versus 17).

25 Wheat yield (bu/ac) 68 58 FIGURE 2 penalty. Conventional Tillage Yield Function Conservation Tillage Yleld Function _,Ye l I 17 ll l 5.2 15.4 Topsoil depth (inches) Avoid confounding erosion damage with tillage Distinguish Between Reparable and Residual Yield Damage It is useful to partition yield decline from soil erosion into two components, reparable damage and residual damage. Reparable damage is usually associated with loss of soil fertility from erosion and is that portion of the yield decline from erosion that can be restored by increasing organic matter, fertilizer, or other inputs. After economically optimal input adjustments, there will usually be residual yield damage due to deterioration in the soil environment. Reduced moisture infiltration and retention capacity, diminished rooting zone, and impaired soil structure cause residual damage to yields that cannot be remedied economically. To distinguish between reparable and residual yield damage, consider Figure 3. The restored-yield curve incorporates the yield impact of making economic adjust- ments in inputs as erosion proceeds, but the constant- input curve reflects yields if no such adjustments are

26 restored-yield curve Yield -,, - , - ,, - , - a- constant-input yield curve hi?; an', /,' C,_,''_ F Residual Damage ~ is' ~ Reparable / B ~H ~ Damage D E Topsoil Depth A FIGURE 3 Residual and reparable erosion damage. made. From initial topsoil depth A, using the conser- vation practice for a number of years would reduce topsoil depth to E and yield to G--providing the basis for comparison with the erosion alternative. If an erosive practice were used for the same number of years, topsoil depth would be reduced further, to D. Yield WOUld Recline with erosion, whether economic input adjustments are made (GC) or not (GB). damage is given by GH. Some of this yield damage might be restored, depending on subsoil and climatic factors. By increasing fertilizer or other soil-substituting inputs, yield could be restored to point C. The yield decline that can be restored is the reparable component of erosion damage, BC in Figure 3. The remedy must cost less than the value of the yield damage restored. Total yield . the economic cost of erosion damage. This cost would be included as part of The restored-yield curve reflects the relationship between yield and topsoil depth after profit-maximizing input adjustments to erosion have been made. Although topsoil depth is the only explanatory variable illustrated in Figure 3, other inputs also vary in the restored-yield

27 function. The extent of the input adjustment process is limited by yield response to increased inputs, by the cost of those inputs, and by output value. The restored- yield curve indicates residual damage to yields. OF in Figure 3 is the difference between yields with conserved soil and yields with eroded soil after profit-maximizing Throughout this paper, reference to yield damage always means this residual yield damage, and yield damage is always measured along the restored-yield curve. input adjustments have been made. Separate the Effects of Erosion and Technology Erosion damage assessment is considerably complicated by the impact of technical progress on crop yields. This _ section first considers technological change that is exogenous with respect to erosion--that is, the rate of technical progress is independent of the rate of erosion. Later, technology that is induced by erosion is con- sidered. Yield observations over time are confounded by the joint influence of erosion that reduces yield and tech- nology that increases it. In regions where the latter of f "~b Norm; no t-=c, . =~ an, failure to disaggregate this joint influence could lead to the erroneous conclusion that erosion damage does not exist. With exogenous technical progress, erosion damage should not be measured as an absolute decline in historical yield but as the decrease in potential yield with technology and conservation. This requires establishing how much higher yields would be with new technology if soil is conserved. It is necessary to separate the projected effects of erosion and technology. Simply ignoring technology could result In overestimates or underestimates of erosion damage, depending on the interaction between technical progress and topsoil depth. The effect of exogenous technical progress on erosion damage can be illustrated beginning with Figure 4. Curve Yo illustrates the yield damage from the additional erosion with conventional tillage compared to conservation tillage over a 64-year period with static technology; that is, no technical progress in yields. In this example (identical to Figure 1), erosion with conventional tillage over 64 years would reduce topsoil depth to 5.2 inches and yield to 51 bushels/acre. Using conservation tillage over the same period would reduce topsoil and yield by

28 Wheat yield (bu/ac) 117 100 68 _ I_ ~i; F i I ! 5.2 15.4 18 Topsoil depth (inches) FIGURE 4 Residual yield damage with land-neutral technical change. less, to 15.4 inches and 68 bushels/acre. The differ- ence, yield with conservation versus yield without conservation, is 17 bushels/acre and measures yield damage in the absence of technical progress. Land-Neutral Technology Land-neutral technical progress is illustrated in Figure 4. Technology shifts the yield function upward from Yo to Yn, increasing yield by an equal absolute amount at each topsoil depth. Land-neutral technical progress is most likely on cropland with deep, friable subsoils. In the absence of technology, yield would have declined from G to C. Because technology boosts yield from G to C' in spite of erosion, one might conclude that technology had eliminated erosion demean That faulty conclusion, however, is based on a "before versus after" erosion comparison which confounds exogenous technology and erosion damage. A correct measure of erosion damage is based on a with conservation versus without conservation comparison

29 of yield along the technology-augmented yield function, Yn. This measure of erosion damage is the difference between potential yield with conservation and exogenous technology versus realized yield with erosion and the same technology. Potential yield declines from G' at the conserved soil depth to C' at the eroded soil depth giving a yield damage measure of 17 bushels/acre after 64 years of erosion. Ignoring technology by measuring yield damage along Yo, which assumes static technology, produces an identical measure of yield damage, 17 bushels/acre. Even though there has been an upward yield trend over time in this example, exogenous technology has not reduced erosion damage. Land-Complementary Technology Land-complementary technical progress boosts yields more at deeper topsoil depths as illustrated by the shift from Yo to Yn in Figure 5. Improved crop cultivars might be an example of land-complementary technical change. Improved crop varieties usually realize their greatest genetic yield potential in a soil environment with nonrestrictive moisture and nutrient supplies. These conditions are more often found on less eroded sites. Because land complementary technical change increases the slope of Yn relative to Yo in Figure 5, the appro- priate measure of erosion damage, lost potential yield of G'F', is greater than the erosion damage, OF, which would be measured if technology were ignored. Land- complementary technology actually increases erosion damage (32 bushels/acre versus 17 bushels/acre) when damage is measured appropriately.2 Land-Substituting Technology Land-substituting -technology boosts the yield function more at shallower topsoil depths as shown in Figure 6. An example might be tillage improvements that conserve soil moisture. Because topsoil serves as a moisture reservoir, moisture deficiency is more likely at eroded sites with shallow topsoil. Thus, technical advances that conserve soil moisture are likely to boost yields more for shallower topsoils. Compared with no technology, yield damage decreases with land-substituting

30 Wheat yield (bu/ac) 132 100 G,/n / ~ 32 Cal ~ ~ ._. IF' / ' 1 I / / - - 17 Fl 1 1 5.2 15.4 18 Topsoil depth (inches) FIGURE 5 Residual yield damage with land-complementary technical change. technology (11 bushels/acre versus 17 bushels/acre) because the technology-shifted yield function (Yn in Figure 6) becomes less steep. Because erosion damage with exogenous technology i s measured along a single technology-augmented yield function, only the case of land-substituting exogenous technology mitigates erosion damage. This reduction in yield damage is due solely to reduced slope of the yield function and occurs regardless of whether or not there is an upward yield trend over time. It is important to incorporate technology projections in erosion damage assessment. Ignoring technical progress will result in unbiased damage estimates only with land- neutral technical progress. Ignoring land-complementary technology will underestimate erosion damage. Ignoring land-substituting technical progress will overestimate erosion damage.

moo W heat yield (bu/ac) / Yn ~ ! ~yO IF . ~ . 5.2 15.4 18 Topsoil depth (inches) FIGURE 6 Residual yield damage with land-substituting technical change. Induced Technology The discussion thus far has assumed that any tech- nical advance would occur independently of farmer decisions about conservation and the resulting rate of erosion. There is a possibility, however, of induced technical progress. Concern over the rate of erosion might encourage research and development that results in yield enhancing technical advances. Induced technology alters the damage assessment procedure. Recall that the relevant comparison (dynamic basis) for damage assessment with exogenous technology is yield with technology on conserved soil versus yield with the same exogenous technology on eroded soil. Yield damage is measured along the single technology-augmented yield function. Only one yield function is needed because the same level of technology would apply independently of erosion scenario. But if all technical advance is induced, two yield functions are needed to reflect the different levels of technology in the with conservation and without conservation scenarios.

32 Wheat yield (bu/ac) Ye 1 1 5.2 15.4 18 Topsoil depth (inches) FIGURE 7 Residual yield damage with induced technology. Damage assessment should be based on yield with conservation and unchanged technology versus yield with erosion and induced technology. Because two yield func- tions reflecting different levels of technology are involved, induced technology always offsets some erosion damage. With induced technology, as illustrated by the shift from Yo to Yn in Figure 7, yield damage is the difference between yield at G. conserved topsoil and unchanged technology, versus Field at C', eroded topsoil and induced technology. In the absence of technology, yield damage would have been the difference in yield between G and C in Figure 7. But technology induced by concern over erosion boosts yield from C to C' at the eroded topsoil depth, offseting some erosion damage. Exogenous and Induced Technology To exhaust all the possibilities, consider the case with both exogenous and induced technology. Exogenous technology shifts the yield function from Yo to Y1 in Figure 8. This technical advance would occur even in the absence of heavy erosion, so Y1 is the correct curve for measuring yield at the conserved topsoil depth. With

33 Wheat yield (bu/ac) ~1 ~ 15.4 Topsoil depth (inches) FIGURE 8 Residual yield damage with exogenous and induced technology. heavy erosion over time, topsoil may be eroded to, say 5.2 inches. Figure 8 incorporates an additional shift in the yield function to Yn from technology induced by con- cern over heavy erosion. Yield with eroded topsoil is thus measured along curve Yn. The correct damage measure with induced and exogenous technology combined would be yield with conserved soil and exogenous technology at G versus yield with eroded soil and induced technology at C' . NATURE OF PAST TECHN ICAL PROGRESS: EMPIRICAL EVIDENCE FOR WINTER MEAT YIELDS IN THE PALOUSE REGION The discussion in the preceding section established the importance of projecting technology trends as well as erosion rates to assess erosion damage accurately. While there is no foolproof method for projecting whether future advances in agricultural technology are likely to be land- neutral, -complementary, or -substituting, and exogenous or induced, a logical first step is to examine how recent technical advances have influenced yields.

34 Winter wheat yield (bulac) 80 70 60 50 40 30 '/ 20 _ 0 5 / un~ction for 1970-1974 / / ~ Function for 1952-1953 10 15 20 25 Topsoil depth (inches) FIGURE 9 Comparison of winter wheat yield-topsoil depth relationships from the 1950s and the 1970s, eastern Whitman County, Washington. SOURCE: Young et al., 1985. Young et al. (1985) conducted a statistical evaluation of the impact of technical progress on winter wheat yields in the eastern Palouse region of southeastern Washington between the 1950s and the 1970s. This 2-decade interval witnessed several notable advances in wheat production technology in the region, including introduction of higher yielding semidwarf varieties, greater use of commercial nitrogen fertilizer, more effective chemical weed control, and improved tillage techniques. Figure 9 summarizes the statistical functions that describe the response of winter wheat yields to topsoil depth in the eastern Palouse during the early 195Os and the early 1970s. The 1950s function was derived by Young et al. (1985) from statistical relationships estimated by Pawson et al. (1961) using over 800 observations from farmers' fields collected during 1952 and 1953. The 1970s function was estimated by Taylor (1982) from 89 observa

35 Lions, also from farmers' fields, collected by Wetter (1977) in the same region during 1970-1974. Equations 1 and 2 describe the statistical relation- ships underlying the response functions in Figure 9: 1952-1953 function Y = 24.96 + 31.64(1-0.9OD) (1) 1970-1974 function Y = 38.92 + 40.50(1-0.900), (2) R2= 0.45, (3.40) (~.79), where Y and D represent winter wheat yield in bushels per acre and topsoil depth in inches, respectively. R2 is the proportion of wheat yield variation in the data set explained by the 1970-1974 curve in Figure 9. The figures in parentheses under the coefficients of Equation 2 are standard errors. Pawson et al. did not report these for their equation but Young et al. hypothe- sized standard errors of equal magnitude for the two functions to test statistically the nature of the tech- nology shift between them. The results of this test rejected at the 10 percent significance level the hypothesis of a land-neutral or land-substituting technology shift and supported the alternative of land-complementary technical change over the 2 decades. Indeed, point estimates of yield projections from the two functions reveal that technology over the 2 decades boosted average wheat yields by 22.9 bushels/acre on a deep 30-inch topsoil, but only by 14.4 bushels/acre on subsoil (O inches topsoil). This represents a 59 percent greater yield increase due to technology on the deeper topsoil. Kaiser (1967) provides similar evidence of greater wheat yield growth in the Palouse on deeper topsoils based on unpublished data from the 1950s and 1960s. The land-complementary technical shift evidenced in Figure 9 is consistent with agronomic principles. Among other properties, the new semidwarf wheat cultivars have Greater genetic Potential for converting moisture and nutrients Lo narvestan~e grain. However, these cultivars are likely to come closest to achieving their higher genetic yield potential in an uneroded soil environment where moisture, nutrients, and rooting zone are usually more suitable for crop growth. Furthermore, the higher yield potential with new cultivars or improved cultural practices will be restricted at the outset if soil _ _ . . . . . .

36 structure problems on clay subsoils exposed by erosion impede germination and establishment of the stand. Support for the view that future technical progress in the region also is likely to be land-complementary comes from one other important qroup--the farmers in the region. that on average the farmers expected wheat yield growth over the next 50 vears to be three times hither on typical A survey of 272 Palouse farmers in 1980 revealed hillslopes than on hilltops, which are more eroded and have much shallower topsoils (STEEP Project, 1980). The empirical yield response functions in Figure 9 should also permit conclusions concerning residual yield damage, as described in the previous section. Farmers, whose fields were included in the sample used to estimate the 1970's function, have presumably adjusted inputs in a profit-maximizing manner in response to erosion and other changes over the 2 decades. Consequently, the 1970's response function should represent the conceptual restored yield function described in Figure 3, as required to measure residual damage. Finally, it seems that most, if not all, of the technical progress in wheat production that occurred in the Palouse between the early 1950s and early 1970s was exogenous, not induced specifically by concern over erosion. Topsoil depletion was apparently much less important than other factors in determining agricultural technology in this period. ~. . For example, concerns about lodging and disease resistance were major factors in development of the short-strawed semidwarf wheat vari- eties. The development of inexpensive procedures for producing inorganic nitrogen fertilizers and effective herbicides grew out of pervasive exogenous breakthroughs in chemical technology during and after World War II. Furthermore, the development of improved crop cultivars is not an advance applicable only to eroded fields. In fact, as mentioned, uneroded soils are a more suitable environment. Fertilizer application is also widely practiced and is not used solely on eroded sites Because of impairment in soil structure or moisture limitations with erosion on some soils, fertilizer tech- nology would boost yields more on uneroded sites with these soils. It is not likely that technologies with a . greater payoff potentially on uneroded sites would be induced by concern over erosion. It is more likely that these technologies are the result of a desire to enhance agricultural productivity in general and therefore must be considered exogenous.

37 A final reason for believing that much of the tech- nical progress in yields has been exogenous is the difficulty in applying embodied technologies differ- entially to eroded and uneroded parts of a field. It would not be practical for farmers to plant a special hybrid variety on eroded sites in a field and a standard variety in the balance of the field. often not feasible to vary fertilizer application on . . . Similarly, it is eroded sites within a field. Given the difficulty in treating eroded parts of fields differently with these techniques and since these technologies increase yield ~. . - more on deeper, uneroded soils in many cases, it seems fair to conclude that much of the yield-enhancing technology in agriculture during this century has been exogenous rather than induced by erosion. Hayami and Ruttan (1971), who are noted for their studies of technical progress in agriculture, reach similar conclusions for U.S. agriculture in general. They ascribe much of the yield progress in agriculture becinnina with the 1930s to hither vieldino varieties ~, _ , Such as byDrld corn and to the development or commercial nitrogen fertilizers. They present evidence to support the claim that the development and improvement of these yield-enhancing technologies was stimulated by general fertility limitations of the land as reflected in the stagnant yield trend from the 1870s to the 1920s. If the concern that motivated scientific and commercial interest in developing these technologies was concern about general fertility limitations in the agricultural land base, these technical advances must be considered exogenous, not induced by concern over soil erosion. The consequences for erosion damage assessment are significant. Much of the yield-enhancing technical prog- ress in agriculture has not been the type that offsets erosion damage. As shown earlier in this paper, exoge- nous, land-complementary technical progress increases erosion damage. Thus, technology in the Palouse, and perhaps in the rest of the nation, rather than mitigating the problem of erosion and yield damage, has actually intensified it. Appendix B develops and examines an empirical Palouse wheat yield projection function incorporating the dual influences of erosion and technology consistent with the data and principles reviewed in this section.

38 COMPUTERIZED DAMAGE ASSESSMENT MODEL A computerized model has been developed for assessing the economic cost of erosion damage incorporating the principles outlined thus far (see Appendix C). The earlier discussion of physical yield damage used an erosion period of many years to illustrate damage graphi- cally. The economic erosion damage model is programmed to assess the incremental damage from one more year of erosion, where the consequences of that erosion are measured over a future damage horizon. The model contains two main components--a time-driven erosion productivity simulator and an economic assessment module. The erosion productivity simulator models the physical relationship between erosion and soil properties and then models the impact of those changed soil proper- ties on crop yields. The current version of the erosion productivity simulator (for analysis in the Palouse) uses topsoil depth (depth of the mollic epipedon4) as a proxy for soil properties such as organic matter content and bulk density that are affected by erosion and are cor- related with topsoil depth. In addition to modeling the negative impact of erosion on crop yields, this simulator also projects the positive impact of technical progress on yields. The economic assessment module evaluates the long-run and short-run economics of erosion control. Long-run economics encompass the cost in the future of damage from current erosion. One such cost is the present value of lost future income over a relevant damage horizon from reduced yields due to erosion in the current year. In the past, a damage horizon of 75 years has been used for evaluating the future consequences on yield and income of current-year erosion. This time horizon is long enough to incorporate the management periods of current operators, their children, and their grandchildren. With family farms, it is reason- able to assume that an operator would be concerned about those future consequences of his management decisions. Also, with a 4 percent real private rate of discount, a 75-year time horizon captures 95 percent of the present value of erosion damage into perpetuity. Another com- ponent of long-run damage is the present value of the cost of any soil-substituting inputs, such as fertilizer, that are increased in the future to offset the effect of current erosion on future crop yields. These two cost

39 streams constitute the residual and reparable erosion damage components, respectively. A short-run economic evaluation can be included if the erosion damage assessment employs the best conserve- tion alternative as the basis for comparison. It compares the current income of the erosive practice with that of the conservation practice. The value of any yield dif- ferential with the conservation practice (due to a tillage yield penalty, for example) is captured here as well as any cost difference between the practices. The damage model was used to make an empirical estimate of the cost of erosion damage for wheat produc- tion with conventional tillage in the Palouse. Annual soil loss with this practice on typical slopes averages 10.4 tons/acre. The damage estimate presented here is based on a comparison of "with versus without" erosion (as explained in the first section of this paper) and measures the present value of the lost income over 75 years from reduced future yields due to 1 year of erosion with con- ventional tillage in wheat. The price of wheat was $3.60/bushel and the initial topsoil depth was assumed to be 10 inches, a moderately to severely eroded soil in the Palouse. The empirically estimated wheat yield projection function (see Appendix B), incorporating exogenous land-complementary technology observed in the Palouse, was used in the damage model. The cost of erosion damage under the assumed con- ditions is $12.78 per acre. This is the present value of the lost income from 1 year of erosion with conventional tillage in wheat. The cost of erosion damage would be less with deeper topsoil and greater with shallower topsoil. USE OF NRI DATA FOR REGIONAL AND NATIONAL EROSION DAMAGE ASSESSMENT Applications to date of the economic damage model described in the previous section and in Appendix C have been exclusively at the farm level (Walker, 1982; Walker and Young, 1986). These have generated results on the optimal point in time for farmers to adopt specified conservation practices. These results could be useful in SCS conservation education programs with farmers when private onsite benefits from avoiding erosion damage justify immediate adoption of conservation practices.

40 Results have also been generated for policymakers on the required conservation subsidy (or erosion penalty) neces- sary to encourage farmers to adopt conservation practices when social criteria warrant adoption earlier than would be optimal from a strictly private evaluation of onsite effects. While development of region-specific conservation education and incentive programs is likely to remain a major use of these damage assessment techniques, the general concepts also have relevance for national or regional assessments of onsite productivity damage from erosion. Walker (1983) has proposed a net benefit func- tion for use in selecting target areas for conservation emphasis. Such areas could be identified based on the economic cost of erosion damage and the potential for avoiding that damage with appropriate conservation prac- tices that are available for the area. This section evaluates the possible use of information from the 1982 NRI for national economic damage assessment and identifies other data requirements and possible sources. NRI DATA RELEVANT FOR DAMAGE ASSESSMENT The 1982 NRI, like its predecessors, focused primarily on describing current use, annual erosion rates, conserva- tion treatment needs, and cropland conversion potential of all private land in the United States.5 Given its primary emphasis on these land characteristics, the NRI would not be expected to contain much of the detailed information on crop productivity relationships required to assess economic erosion damage. As described earlier, measuring erosion damage requires detailed information on crop yields by erosion status le.g., remaining topsoil depth) for different tillage systems. Furthermore, to make inferences about the interaction of erosion and technology over time, time-series observations are needed on site-specific crop yields. However, no crop yield information was collected for the 1982 (or earlier) NRI sample sites. The NRI data base does contain four other information components required for national erosion damage assessment: Estimates of erosion rates by region and site for prevailing management systems. Both the site character- istics and management practices are described in con

41 siderable detail. These include explicit values for all the variables of the Universal Soil Loss Equation (USLE). Management data collected include land use, irrigation status, cropping history for the past 3 years, conserva- tion practices used, and value of the USLE crop manage- ment factor. Degree of past erosion. Information was collected on "degree of erosion, whether the site was "nonarable because of past erosion," "soil loss tolerance limit" or T value, and "land capability subclass." Possibly this information, plus supplementary data from local soil surveys, could be used to estimate current topsoil depths for different soils in a region. o Information on existing and needed conservation treatments. As noted earlier in this paper, measurement of damage averted by conservation requires identification of the optimal (most cost-effective) conservation farming system for a particular area. Data on existing and needed conservation treatment for each site might help identify the optimal conservation system for different areas. · Topographic features and cropping patterns. The very detailed information on distribution of cropland by topographic features and cropping patterns throughout the nation would be useful for aggregating the cost of erosion damage. ADDITIONAL DATA NEEDS FOR DAMAGE ASSESSMENT Along with the technical information available from the NRI data base, regional or national erosion damage assessments will require assembling data (or assumptions) on: Static technology yield relationships --Yield penalties for alternative management systems --Crop yield impacts of erosion within a given technological era · Technical progress relationships --Whether technical progress for various regions and crops is induced or exogenous with respect to erosion --Whether technical progress for various regions and crops is land-substituting, -neutral, or -complementary --Projected rates of technical progress, for various regions and crops

42 · Cost and returns information --Crop prices through time --Current production costs for different management systems --Changes in production costs as optimal input adjustments are made in response to reparable erosion damage · Present value analysis parameters --Discount rates --Planning horizon lengths The yield relationships can empirically (as exemplified by functions depicted in Figure 9) general simulation models such Impact Calculator (EPIC) model Research Service scientists at al., 1983). Yield relationships must be derived by uniform pro- cedures for all crops and regions to obtain consistent national erosion damage estimates. This means that synthetic yield projections as generated by the Yield- Soil Loss Simulator fused for the 1980 Resource Conserva- tion Act (RCA) Appraisal] or the EPIC model (used for the 1985 RCA Appraisal) will orobablv be necessary. either be estimated the Palouse wheat yield or synthesized using as the Erosion Productivity developed by Agricultural Temple, Texas (Williams et , _ ~ ~ Appro- pr~ate data sets for estimating empirical topsoil depth- yield relationships are unlikely to be available or affordable for all major crops and production regions. Where appropriate data are available, these relationships should be estimated to validate and calibrate the general simulation models. Looking ahead, incorporating soil depth and yield measurements into future NRIs would provide a consistent national data base for estimating yield relationships. Although most previous analyses have used topsoil death - ~,& ~_ l ~_ d~ alone as a proxy for the set of soil Properties altered Fir comic: i ^^ IV^'lr`^ 1 ~ Q'1 ~ ~'~-~&' "My -ace' r other soil properties like organic matter content may also be measured if necessary to make accurate yield projections. As indicated earlier, forecasts of the rates and nature of future technical oroaress for var ions crane and _ _ , _ , regions are necessarily subjective, but evaluation of historical trends as exemplified by this analysis of winter wheat yields in the Palouse can provide some guidance. As noted in a recent review by Young (1984) of crop yield projection models employed in 15 long-run soil

43 conservation benefit evaluations, there has been little or no investigation outside the work reported here from the Palouse on technical progress-topsoil depth inter- actions or on whether technoloov was induced rev erosion or exogenous. _ , ~ . _ ~ Given its importance for damage assessment, high priority should be given to searching for data sets to examine technical progress patterns for other major crops and production regions. Assessment of erosion damage in the 1980 RCA appraisal incorporated crop- and region-specific rates of technical , progress (USDA, 1981), but assumed uniformly multiplica- tive technology--a form of land-complementary technology-- throughout, as shown by Young (1984) based on documenta- tion in Benbrook (1980). Also, the 1980 RCA appraisal implicitly assumed exogenous technology, as evidenced by the use of a single technology-augmented yield function for measuring erosion damage with a crop in a production region. Although the crop- and region-specific technology rates were modeled with some detail, little or no judgment was made on whether technical progress was (1) exogenous or induced or (2) land-complementary, -substituting or . . . -neutral across crops and regions. If technology differs from this assumed uniform pattern for some crops and regions, substantial bias in damage projections could result. In future RCA appraisals, it would be desirable to elicit forecasts of technical progress patterns from agricultural scientists who are familiar with past technical advances in crop yields for major production regions and are knowledgeable about likely developments in the foreseeable future. Information on base-period crop prices can be obtained from statistical reporting services in the states. Supply and demand projections would be required to model endoge- nous changes in crop prices through time in response to erosion impacts. Base-period crop production costs for different management systems can be obtained from budgets prepared by extension economists and others. The EPIC model contains a submodel option that computes required fertilizer adjustments to compensate for fertility losses due to erosion. This might provide a basis for estimating reparable erosion damage. Discount rates and planning horizons should be elicited from the appropriate decision-making clientele-- farmers for studies providing private managerial recommen- dations and policymakers for social evaluations.

44 SUMMARY AND CONCLUSIONS Four important concepts were developed and presented for correctly assessing erosion damage to crop productiv- ity: (1) use a "with versus without" comparison in mea- suring erosion damage to yields (yield with conservation versus without, or yield with erosion versus without); (2) avoid confounding conservation tillage yield penalty and erosion damage; (3) distinguish between reparable and residual yield damage, and include both components in the cost of erosion damage; and (4) project the separate effects of erosion and technology to avoid errors in erosion damage assessment caused by confounding erosion and technical progress. A computerized erosion damage model was described that incorporates these concepts. Ignoring technical progress in erosion damage assess- ment can lead to serious bias. Concluding categorically that technology offsets erosion damage because of a positive yield trend over time is a naive view based on an assumption that yield enhancement is due to techno- logical change induced by concerns over erosion. Exogenous technology can mitigate erosion damage only if it is land-substituting. Economists at Resources for the Future, citing Hayami and Ruttan (1971), have concluded that little agricultural technology has been induced nationwide by concern about the effect of erosion on productivity (Crosson and Stout, 1983). If yield-enhancing technical progress in major producing areas has indeed been exogenous and continues to be, then technogical progress has not erased erosion damage and is not likely to do so in the future. Thus, technology must not be seen generally as a substitute for soil conservation. In fact, if the exogenous land- complementary technology observed over the past 30 years in the Palouse continues and is typical of the situation across the country, technology--by boosting yields more on deeper topsoils--will increase the payoff from soil conservation. Another way of viewing this conclusion is that the cost of erosion damage is likely to increase in the future. Even without technical advance, the nonlinear yield response curve gets steeper as cumulative erosion reduces topsoil depth. If land-complementary technology continues, the yield curve will become steeper everywhere. A given amount of erosion reduces yield more if the yield response function is steeper, leading to a greater cost

45 of erosion damage. Thus, soil conservation may become even more important in the future. The evidence on the exogenous, land-complementary technical progress affecting winter wheat yields in the Palouse confirms that technology has complemented, not substituted for, soil conservation. A prudent strategy for ensuring future productivity includes continued support both for basic research to promote future technical progress and for vigorous soil conservation programs. Improved soil conservation enhances the payoff on research and development and vice versa. With the prospect of increased erosion damage costs in the future, an accurate assessment of erosion damage and using that information to target conservation efforts become all the more important. It may be sufficiently important to justify including additional data items in future NRI surveys to measure productivity impacts from erosion and to infer yield-enhancing technology trends for correct damage assessment. NOTES 1. These concepts for measuring erosion damage were originally presented in a paper by Walker (1983). The implications of induced technology for erosion damage, which were not discussed in that paper, are developed fully in this paper. 2. For a general mathematical proof of these conclusions that does not rely on specific graphical examples, see Young et al. (1985). 3. With induced technology, the generally improper comparison for assessing damage (yield before erosion versus yield after) coincides with the proper comparison (yield with erosion versus yield without). With exogenous technology, the two measures do not coincide. To assess damage correctly in all cases, use the "with versus without" comparison. 4. The mollic epipedon refers to the darkened upper layer of soil material with high concentration of organic matter. This layer includes the A horizon and may include a transitional B horizon. 5. The 1982 NRI is described in various USDA and National Research Council publications (National Research Council, 1982; USDA, n.d., 1983, 1984). Burns and Dunford (1985) also provide a concise description of the content and procedures of the 1982 NRI, including a copy of the questionnaire completed for each sample point.

46 REFERENCES Benbrook, C. 1980. Review of the yield-soil loss simulator. Council on Environmental Quality, Washington, D.C. Memorandum. Burns, S. H., and R. W. Dunford. 1985. An Overview of the 1982 National Resources Inventory. A. E. Series 85-2. Department of Agricultural Economics. Pullman: Washington State University. Crosson, P. R., with A. T. Stout. 1983. Productivity Effects of Cropland Erosion in the United States. Baltimore, Md.: Johns Hopkins University Press. Hayami, Y., and V. Ruttan. 1971. Agricultural Development: An International Perspective. Baltimore, Md.: Johns Hopkins University Press. Kaiser, V. G. 1967. Soil erosion and wheat yields in Whitman County, Washington. Northwest Science 41(2):86-91. National Research Council. 1982. Review of the National Resources Inventory Methods and Procedures. A report prepared by the Task Force on the National Resource Inventory, Board on Agriculture and Renewable Resources. Washington, D.C.: National Academy Press. Pawson, W. W., O. L. Brough, Jr., J. P. Swanson, and G. M. Homer. 1961. Economics of Cropping Systems and Soil Conservation in the Palouse. Agricultural Experimental Station Bulletin 2. Pullman: Washington State University. STEEP Project. 1980. A Survey on Crop Production in the Palouse. Washington State University and University of Idaho, Departments of Agricultural Economics and Rural Sociology. Unpublished. Taylor, D. B. 1982. Evaluating the Long Run Impacts of Soil Erosion on Crop Yields and Net Farm Income in th Palouse Annual Cropping Region of the Pacific Northwest. Ph.D. dissertation. Washington State University, Pullman. USDA (U.S. Department of Agriculture). 1981. Soil and Water and Related Resources in the United States: Analysis of Resource Trends. 1980 RCA Appraisal, Part II. Washington, D.C.: U.S. Government Printing Office. USDA. 1983. Release of 1982 National Resources Inventory Preliminary Data: Executive Summary. Washington, D.C. U.S. Government Printing Office. USDA. 1984. National Resources Inventory: A Guide for Users of 1982 NRI Data Files. (Draft.) Washington, D.C.: U.S. Government Printing Office. e

47 USDA. n.d. SCS. Inventory and Monitoring National Resources Inventory: Sampling Design. Washington, D.C.: U.S. Government Printing Office. Walker, D. J. 1982. A damage function to evaluate erosion control economics. Am. J. Ag. Econ. 64(4):690-698. Walker, D. J. 1983. Targeting soil conservation with a net benefit function incorporating erosion damage and technology. Paper presented at Symposium in Honor of John F. Timmons, Iowa State University, October 28, 1983. A. E. Series 396, Department of Agricultural Economics, University of Idaho, Moscow. Walker, D. J., and D. L. Young. 1986. The effect of technical progress on erosion damage and economic incentives for soil conservation. Land Economics. In press. Wetter, F. 1977. The Influence of Topsoil Depth on Yields. Tech. Note AGRO-10, and unpublished data underlying report. Soil Conservation Service, Colfax, Wash. Williams, J. R., K. G. Renard, and P. T. Dyke. 1983. EPIC: A new method for assessing erosion's effect on soil productivity. J. Soil Water Conserv. 38(5):381-383. Young, D. L. 1984. Modeling agricultural productivity impacts of soil erosion and future technology. Pp. 60-85 in Future Agricultural Technology and Resource Conservation, B. B. English, J. A. Maetzold, B. R. Holding, and E. O. Heady, eds. Ames: Iowa State University Press. Young, D . L ., D . B. . Taylor, and R. I. Papendick. 1985. Separating erosion and technology impacts on winter wheat yields in the Palouse: A statistical approach. In Erosion and Soil Productivity. St. Joseph, Mich.: American Society of Agricultural Engineers.

48 APPEND I X A: EROS ION-COMPENSATING TECHNOLOGY A special case of land-substituting technology enhances the capacity to repair erosion damage. This special case involves a new or improved input that is applied in increasing quantities on eroded soil. Because this type of technology specifically remedies a deficiency in a soil attribute caused by erosion, it is called erosion-compensating technology. This technology, by its nature, increases reparable damage. But it reduces residual damage by more, so that overall yield damage is reduced, as will be illustrated. Because this technology reduces residual yield damage, it is considered to be a special case of land-substituting technology. In the general case of land-substituting technology, the new or improved input is applied at a uniform rate for all topsoil depths. The entire yield function shifts upward but in a fashion that reduces the slope of the restored-yield curve. Because technology interacts with topsoil depth to boost yields more on shallow eroded soils (even though the application is uniform across topsoil depths), this general case was classified as land-substituting. ~ In the pure erosion- compensating special case, none of the new or improved input would be used on deep soils but increasing quantities would be used on eroded soils.* In this pure special case, technology rotates the restored-yield function through point A (deep topsoil) in Figure A-1. Suppose initially that this technology is exogenous, not induced by erosion. The upper terminus of the relevant constant-input yield curve shifts from G to G'. The relevant curve is the one associated with the conserved topsoil depth, D, which is the basis for *It is also possible that some of the new or improved input might be used on the deepest soil with application increasing at shallower depths. This technology would shift the yield function upward, as in Figure 6 in the text, but unlike the pure general case of land- substituting technology, this mixed case would involve increased application at shallower depths. The analysis of residual and reparable damage would proceed exactly as in the pure special case of erosion-compensating technology presented here.

49 Yield 1 1 , D Topsoil Depth p FIGURE A-1 Erosion-compensating technical progress . comparison in estimating erosion damage. Potential yield on conserved soil shifts with improved technology from G to G' because of the new or improved input associated with the technical advance. That same input level is applied for all topsoil depths along the constant-input yield curve, shifting it from GH to G'H'. The comparison of the shift from H to H' at the eroded topsoil depth E to the shift from G to G' depends on the change in the marginal product of that new or improved input with top- soil depth. The change in marginal product with respect to topsoil depth is given by: a2y/(aXsaxi) < o, (A-1) where y equals f(xl,...,xs), crop yield is a function of a vector of inputs; xi equals the input associated with the technical advance; and XS equals topsoil depth. The marginal product of the new or improved input increases with decreased topsoil depth because the input is a substitute for topsoil depth. The input is applied in the same quantity at eroded and conserved topsoil

50 depths along the constant-input yield curve, yet because marginal product increases with shallower topsoil, the constant-input yield curve shifts upward slightly more at the eroded depth than at the conserved depth, HH' ~ . as a result, one overall yiela damage decreases slightly with exogenous erosion-compensating technology, G' - H' < G - H. The decrease in overall yield damage is the result of two other changes--an increase in reparable damage but a decrease in residual damage of a larger magnitude. The increase in reparable damage, AB = II' - HH' > O. and the decrease in residual damage, AD = -II' + GG' ~ O. are illustrated in Figure A-1. Reparable damage increases with erosion-compensating technology because the upper curve shifts more than the lower curve, II' > HH'. None of the new or improved input associated with erosion-compensating technology is used at I or H (before technology). With technical advance, the amount of the input used at I' on the restored-yield curve is greater than the amount used at H' on the constant-input yield curve. Because of the greater application of the new or improved input, the shift II' exceeds the shift HH' and reparable damage increases with erosion-compensating technology, I' - H' I - H. Residual damage decreases with erosion-compensating technology because the restored-yield curve shifts upward _ more at shallow topsoil depths, II' > GUI'. More of the erosion-compensating input is used for the shift II' and its marginal product is higher than at GUI'. Therefore, residual damage decreases, G' - I' < G - I. Comparing absolute values shows that the decrease in residual damage is greater than the increase in reparable damage: EBB ADD ~ ~DI III' - HH' I = II' - HH' I-II' + GG' I = II' - GG' Idol because HH' > GUI'. To recapitulate, exogenous erosion-compensating technology increases reparable damage, but reduces residual damage more; as a result, overall yield damage decreases. If the shift in yield functions illustrated in Figure A-1 were due to induced technology, residual damage would decrease even more. Using the appropriate

51 "with versus without" conservation comparison, residual yield damage would be the difference between yield with conservation versus yield with erosion and induced technology, G - I'. With induced erosion-compensating technology, residual damage is less than with exogenous technology, G - I' < G' - I'. Reparable damage is the same as with exogenous technology because reparable damage is measured at the eroded topsoil depth, where the yield function shift from technology is the same whether it is induced by erosion or exogenous. Because induced technology reduces residual damage more than exogenous technology does while the effect on reparable damage is the same, induced erosion-compensating tech- nology reduces overall yield damage more than exogenous technology does, G - H' < G' - H'. Erosion- compensating technology may often be induced rather than exogenous because it specifically remedies a soil property altered by erosion. Even though reparable damage increases, the cost of erosion damage decreases for two reasons. First, an outright decrease in residual yield damage equal to I~Dl - Idol reduces the cost of erosion damage by the value of that yield. Second, residual damage is replaced by reparable damage in the amount I~Bl. This, too, reduces the cost of erosion damage because the cost of the remedy must be less than the value of the residual yield damage that is restored or repaired.

52 APPENDIX B: WHEAT YIELD PROJECTION FUNCTION This appendix discusses a wheat yield projection function for the Palouse that exhibits the historical pattern of interaction between technology and topsoil depth described in the text. This function was intro- duced initially by Papendick et al. (1985), but it is developed more fully here. The projection function is then incorporated into a computerized erosion damage assessment model. Algebraically, response functions such as those illustrated in Figure 9 in the text can be expressed as: Ye = a + b(1 - RD) for the base period (B-1) YD = A + B(1 - RD) for T years later, (B-2) where YD equals wheat yield in bushels per acre; (a, b, A, B. R) are estimated parameters with (a, A) > 0; (b, B) > 0, and 0 < R ~ 1; and D equals topsoil depth in inches. Taking advantage of the common functional form of (B-1) and (B-2), the two equations can be combined into a single yield projection function by including a time variable, t: Yt = (a + a t) + (b + b't)(1 - RD), (B-3) where Yt is projected yield in year t, t = 0 represents the base period characterized by Equation B-1, (a, b, R. and D) are as defined above, and a' = (A - a)/T, and (B-4) b' = (B - b)/T. (B-5) Equations B-4 and B-5 preserve the exact historical pattern and rate of technical progress on the "intercept" and "slope" coefficients of the response functions illus- trated in Figure 9 in the text. For simplicity, a' and b' incorporate the average annual rate of adjustment in the two coefficients that was observed during the T years separating the two functions. Both a' and b' are posi- tive, assuming technical progress. Taking the time derivatives of Equation B-3 as topsoil depth approaches 0 and infinity, a' and (a' + b'), respectively, can be interpreted as the annual rates of change in wheat yields

53 due to technology on subsoils and very deep topsoils. Topsoil depth, D in Equation B-3, can also be expressed as a function of time: D = D - A t, (B-6) where Do is the original topsoil depth in the base year, when t = 0, and As is the erosion rate expressed in inches per year. Substituting Equation B-6 into Equation B-3 provides the final yield projection function: Yt = (a + a't) + (b + b't)[1 - Rt O - s )] . (B-7) Equation B-7 describes the combined impact of technical progress and erosion on wheat yields given the pattern of recent technical progress for winter wheat in the Palouse. PROPERTIES OF THE PROJECTION FUNCTION Before using a mathematical projection function such as B-7 for long-term simulations, it is important to examine the plausibility of its mathematical behavior. Extremum and Slope Conditions Will yields continue growing for a period, reach a peak, and then begin declining eventually as a result of the joint influence of erosion and technical progress incorporated in Equation B-7? To answer this question, differential calculus is used to examine the annual growth (or decay) rate for yield: dYt/dt = = d[a + aft + b - bR(D° - d[(a + a't) + (b + b~t)(1 - R(D° ~ Ast))]/dt ASt) ~ bat - b'tR( ° As )]/dt

54 = a' + bR ° s )(lnR)As + b' - b'[R(D° ~ Ast) R( o s )(lnR) (-A )t] O <I) <0 <0 = (a'+ b') + R(DO - Ant) -- - >o ~ lo~lnx~As - ~ + b'(lnR)Ast].(B-8) Given the presence of technical progress, continuing soil erosion, and the restrictions on parameters imposed at the outset, the definitive sign determinations noted in Equation B-8 can be made. Note that (lnR) < 0 because O < R < 1. Clearly, the yield trajectory can either be rising or declining depending upon the value of t and the parameters. Whenever (a' + b') in Equation B-8 is greater in absolute value than the following negative term, yields will be rising over time. When this inequality is reversed, yield decline will occur over time. The point in time at which yields peak out (if such a point exists) might be identified by evaluating.the first-order conditions for a local extremum. dyt/dt = (a' + b') + R( O s )[b(lnR)As - b' + b'(lnR)A t] - O which implies , (B-9) R o s ) - (a' + b')/[-b(lnR)As + b' - b'(lnR)Ast], which implies - (Do ~ Ast)lnR = ln(a' + b') ln[-b(lnR)As + b' - b'(lnR)Ast]. (B-10)

55 Although Equation B-10 implicitly defines a function of t, the expression cannot be explicitly solved for t by algebraic procedures. However, unreported numerical analyses of the yield-projection function with parameters typical of those for winter wheat grown on eastern Palouse sites showed the yield trajectory to peak out. For dif- ferent response parameters, technical progress rates, or erosion rates, the results could be quite different. Concavity It is also of interest to evaluate the concavity of the yield projection function. Taking the second time derivative of Equation B-7 yields: d2yt/dt2 = d{(a' + b') + R( ° S [b(lnR)As - b' ~ b' (lnR)~ t]}/dt = b(lnR)AsR( ° Ast) (-As)lnR - b'R(D° ~ ASt)( A )1 R (Do ~ Ast) Rt o s lnR(-A lb'(lnR)Ast (D - A t) = (lnR)A R s [b(-As)lnR + b' + b' - b' (lnR)Ast] = (lnR)AsR ° s ){[As(lnR)](-b - b't) + 2b'} < 0. (B-ll) Given the presence of technical progress, continuing erosion, and the restrictions on the parameters imposed at the outset, we can make the definitive sign determina- tions noted in Equation Bell. Because this second derivative is negative, the yield projection equation proposed in this paper will always generate strictly concave yield trajectories as illustrated in Figure B-1. It must again be noted that this functional form is based on limited data on one crop, winter wheat, grown in one region, the relatively high-rainfall eastern Palouse

56 Wheat yield Time FIGURE B-1 General shape of yield trajectory generated by purposed functional form. of southeastern Washington. Furthermore, no empirical validation exists for this function in the subsoil (zero topsoil) zone. Under many situations, projected yields could still be rising at the point subsoil is reached. Additional detail on the data sources and statistical analysis techniques underlying the development of this function is provided in Pawson et al. (1961), Wetter (1977), Hoag and Young (1983), and Young et al. (1985). In general, this examination of Equation B-7 revealed plausible yield trajectories that are concave with respect to time and that can peak and eventually decline if the impacts of erosion outweigh those of technical progress. EMPIRICAL YIELD PROJECTION MODEL In specifying the values of a' and b' of Equation B-7, it was decided to use the average wheat yield growth rate for the longer period 1950-1980 instead of that for 1953-1973 (the interval bracketed by the empirical func- tions in Figure 9 in the text). The period 1953-1913 happened to bracket a period of atypically rapid tech- nical progress in wheat yields in the Palouse. Conse- quently, use of the shorter period to estimate a' and b' in accordance with Equations B-4 and B-5 was judged likely to overestimate longer-term rates of future technical progress .

57 The technical progress parameters (a' and b') were calculated as described below to reflect the long-term (1950-1980) effective rate of wheat yield growth in the Palouse. Recall that the yield projection function is: Yt = (a + a't) + (b + b~t)(l_R(Do ~ Ast)` ,. (B-12) Let a' equal 1.632 b', because this is the ratio exhibited by a' and b' derived by comparing the 1952-1953 response function of Pawson et al. (1961) with the 1970-1974 response function of Taylor (1982) (see Figure 9 and Equations 1 and 2 in the text). Differential calculus is used to solve algebraically in Equation B-13 for the effective rate of yield growth exhibited by Equation B-12 considering both technical progress and erosion: dYt/dt = (a' + b') + R = (B-13) (Do ~ A t) s [b(lnR)As - b' + b'(lnR)Ast] (2 632b.) + R(Do ~ Ast)[b(lnR)As _ b' + b'(lnR)Ast] The effective yield growth rate in Whitman County has been 0.56 bushels/acre/year over the 1950-1980 period (Homayoun-Mehr, 1982). The rate was faster early in the period and slower later, but this is the long-term average. By inserting the Pawson et al. and Taylor estimated parameters into the yield projection function and setting dyt/dt = 0.56 for the midpoint year (1965) of the 1950-1980 period, the values of a' and b' can be solved for to yield this long-term historical, and assumed future, rate of yield growth due to technology. First, set t = 0 at 1952, so t = 13 at 1965. Based on Pawson et al., set Do = 18 inches as the area- weighted average Palouse topsoil depth in 1952. Following Krauss and Allmaras (1982), 0.059 inches/year is used as the long-term regionwide average soil loss rate in the Palouse. Then, solve algebraically for b' from:

58 dYt/dt se=t 0 56 2 632 b' + R(Do ~ Ast)[b(1 R)A - which implies b' + b'(lnR)A t] - 0.56, (B-14) b' = [0 56 _ R(D° ~ ASt)b(lnR)A ]/{2 632 + R(Do ~ Ast)[-1 + (lnR)Ast]}. (B-15) Solved at estimated values gives: b' = [0 56 0 9(18 - (.o59)13)31 64(1n 0 9)0 059] - 0 9(18 - (.059)13)(_1 + (ln 0.9)(0.059)13)] = (0.56 + 0.032)/(2.632 - 0.176) = 0.592/2.456 = 0.241 (B-16) for the 1950-1980 period as opposed to b' = 0.443, when b' is derived solely from the 1952-1972 period using Equation B-5. ~ ~ So the final function, reflecting 1950-1980 long-term technology rates, Yt = [24.46 + 1.632(0.241)t] + (31.64 + 0.241t)tl-o.90(l8 ~ Ast)) (B-17) where t = -2 at 1950, -1 at 1951, 0 at 1952,..., n at (1952 + n). As an example, projecting eastern Palouse regional average winter wheat yield for 1982: Y1982 = [24~46 + 0.393(30)] + (31.64 + 0.241(30))(1-0.90[18 0-059(30)]' = 68.34 bushels/acre. (B-18)

59 In fact, 65 to 75 bushels/acre is a widely accepted current average winter wheat yield range for the eastern Palouse. REFERENCES Hoag, D. L., and D. L. Young. 1983. Yield-topsoil depth response functions: Linear versus Mitscherlich- Spillman. STEEP Agric. Econ. Working Paper 82-2. Department of Agricultural Economics, Pullman: Washington State University. Homayoun-Mehr, F. 1982. Analysis of yield trends for Washington pulse and grain crops. Unpublished MA special project paper. Washington State University, Pullman. Krauss, H., and R. Allmaras. 1982. Technology masks the effects of soil erosion on wheat yields--a case study in Whitman County, Washington. In Determinants of Soil Loss Tolerance, E. L. Schmidt et al., eds. Madison, Wis.: American Society of Agronomy. Papendick, R. I., D. L. Young, D. K. McCool, and H. A. Krauss. 1985. Regional effects of soil erosion on crop productivity--the Palouse area of the Pacific Northwest. In Soil Erosion and Crop Productivity, R. F. Follet and B. E. Stewart, eds. Pawson, W. W., O. L. Brough, Jr., J. P. Swanson, and G. M. Homer. 1961. Economics of Cropping Systems and Soil Conservation in the Palouse. Agricultural Experimental Station Bulletin 2. Pullman: Washington State University. Taylor, D. B. 1982. Evaluating the Long Run Impacts of Soil Erosion on Crop Yields and Net Farm Income in the Palouse Annual Cropping Region of the Pacifi Northwest. Ph.D. dissertation. Washington State University, Pullman. Wetter, F. 1977. The Influence of Topsoil Depth on .c Yields. Tech. Note AGRO-10, and unpublished data underlying report. Soil Conservation Service, Colfax, Wash. Young, D. L., D. B. Taylor, and R. I. Papendick. 1985 Separating erosion and technology impacts on winter wheat yields in the Palouse: A statistical approach. In Erosion and Soil Productivity. St. Joseph, Mich: American Society of Agricultural Engineers.

60 APPENDIX C: COMPUTERI ZED EROSION DAMAGE ASSESSMENT FUNCTION it The computerized erosion damage model discussed in this paper is presented mathematically in Equation C-1. The model calculates the present value of the future consequences of choosing the erosive practice for one more year. t-1 c( 'Dt-l)] ~ [Ce(t,Dt 1) ~ C (t D )] T c t-l) c( ~ t)] =1 (C-1 ) + [Cc(t + i,Dt) - Cc(t + i,Dt 1)]}/(l + r) , where P equals crop price; Dt equals topsoil depth at the end of year t*; Ye,YC equals crop yield with erosive conventional practice and conservation practice, respectively; Ce,Cc equals production costs of the respective practices (includes variable costs and annualized equipment ownership costs); t equals time variable, which serves as proxy for technology, T equals number of years in damage horizon, and r equals real rate of discount. This equation is derived in Walker (1982). Time (t) and topsoil depth at the end of period t (Dt) are included as arguments in the yield function to allow projection of yields as a function of the separable effects of erosion and technology. The explicit form of the yield function was developed in Equation B-17. For notational simplicity in Equation C-1, it is assumed that erosion with the conservation practice is negligible so that topsoil depth and yield can be maintained indefinitely with the conservation practice. Walker (1982) also presents a more general formulation of the *An end-of-year convention is used so that topsoil depth and technology at the end of year t-1 are assumed to influence yield and cost in year t.

61 model where the conservation practice slows but does not eliminate erosion. Time and topsoil depth are also included as arguments in the cost functions to allow inputs and thus costs to vary over time with declining topsoil depth and technology. Price is treated as an exogenous variable in this formulation. In applying the damage model for regional or national erosion damage assessments, it would be desirable to allow for endogenous changes in equilibrium crop prices with cumulative erosion over time. The terms in Equation C-1 account for the private costs and benefits of choosing the erosive practice one more year and are explained below. The first two groupings of terms capture the effect of tillage choice on current-year income. P. [Ye (t,Dt_l) - YC (t,Dt-l) ] Expression C-a reflects any yield differential between the erosive and conservation practices in the current year. If the erosive practice is higher yielding, this term is positive, representing a benefit in the current year of choosing the conventional practice. If the conservation practice is higher yielding, this term is negative, representing a cost of choosing the conventional practice. ~ [Ce (t,Dt_l) - CC (t~Dt-l) ] Expression C-b captures any difference in cost between the two practices in the current year. If the conserva- tion practice saves labor or equipment, this component might be negative--a cost of choosing the erosive practice. If the conservation practice requires more costly chemical weed control, this component might be positive--a benefit from choosing the erosive practice. The final group of terms captures the impact of tillage choice in the current year on future income. T ~ {P.[Y (t + i,Dt 1) ~ Y (t + i,Dt)] - (C-a) (C-b) ~ [Cc(t + i,Dt) - Cc(t + i,Dt_l)]}/(l + r) (C-c)

62 Expression C-c measures the future cost of erosion damage incurred in the current year or, in the parlance of resource economics, the user cost of exploiting the soil. The first bracketed term is the residual damage from current-year erosion--the present value of lost income in the future from reduced yield due to post- poning the adoption of conservation another year. There- fore, yield damage is computed using the conservation yield function. The second bracketed term is the reparable damage due to current-year erosion. It reflects the cost of additional inputs in the future like fertilizer to substitute for topsoil lost in the current year. The sum of these cost/benefit components represents the net present value to the farmer of choosing the conventional practice for another year. If it ~ 0, the current profit advantage with conventional tillage outweighs the present value of long-run erosion damage, and the economic incentive is to exploit the soil at least one more year. If it < 0, the cost of long-run erosion damage exceeds the current profit advantage with conventional tillage, and the immediate adoption of conservation is profitable. Expression C-c can be calculated separately in the damage model to estimate the cost of erosion damage as reported for a Palouse site in the main text. REFERENCE Walker, D. J. 1982. A damage function to evaluate erosion control economics. Am. J. Ag. Econ. 64(4):690-698.

Next: 3. Field Estimates of C Factors: How Good Are They and How Do They Affect Calculations of Erosion »
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Written by the foremost authorities in the field, this volume brings together the technical papers from which Volume 1 is drawn. The 10 papers and discussion from a National Research Council symposium cover such topics as soil erosion classification, evaluating how soil erosion damages productivity, calculating soil erosion, understanding ephemeral gully erosion, wind erosion, and the impact of range erosion on land use.

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