Land Quality, Irrigation Development,and Cropping Patterns in theNorthern High Plains

Erik Lichtenberg

This article examines the interactions between land quality, crop choice, andtechnological change using a framework that integrates cross-sectional and intertemporalaspects of diffusion. The empirical results indicate that (a) the acreages allocated todifferent crops vary significantly over land quality, (h) crops tend to be grown on specificranges of land quality, (c) the introduction of center pivot technology induced significantchanges in cropping patterns, (d) land quality-augmenting technologies tend to beutilized primarily on lower qualities of land, and (e) irrigation development has beenquite sensitive to tax policies.

Key words: center pivot, cropping patterns, irrigation systems, land quality, land use,technological change.

This article develops a framework for incor­porating land quality into empirical studies ofcropping patterns and technology choice. Theframework is applied in a study of the changesin cropping patterns associated with thespread of center pivot irrigation technology inthe northern High Plains. The empiricalframework is notable in that it (a) integratesthe cross-sectional and intertemporal elementsimportant in the diffusion of new technologiesand (h) integrates technology choice withshifts in cropping patterns, a phenomenonwhich has been largely ignored in the empiri­cal literature . The first section presents a theo­retical model of crop and technology choicewith differential land quality. Subsequent sec­tions draw out and test the implications of thismodel for the diffusion of center pivot irriga­tion technology in the northern High Plains.

Theoretical Model

Suppose that land quality can be representedby a scalar measure q. For convenience let q

be normalized such that minimal land qualityis zero and maximal land quality is one, i.e.,0:$ q :$ 1. Let G(q) represent the total acreagehaving quality at most q and g(q) = G' (q) bethe amount of acreage having quality q. Foranalytical convenience, assume that g(q) iscontinuous. Assume that production exhibitsconstant returns to land of any given qualitybut that production is neoclassical in all inputsand land quality and can therefore be rep­resented by a restricted profit function. De­note the per acre production function for theith cropfi(xi , q), where Xi is a vector of inputsused to produce crop i and the restricted profitfunction r'(p., w, q), where Pi is the price ofcrop i and tV is a vector of input prices.

For simplicity, consider the problem of al­locating land between two technology combi­nations. (Extending the results to multiplecrops is straightforward, as Lichtenbergshows.) Let L] (q) be the proportion of land ofquality q allocated to crop 1. If the farmermaximizes profits, the relevant decision prob­lem is to choose

L 1(q) to max It {r1(pl' w, q)Lt(q) + r2(p2' w, q)[l - L](q)]}g(q)dq for all 0 :$ q < 1..0

Erik Lichtenberg is an assistant professor, Department of Agricul­tural and Resource Economics, University of Maryland.

Scientific Article No. A-4782. Contribution No. 7821 from theMaryland Agricultural Experiment Station.

The author thanks Richard Just, David Zilberman, MargrietCaswell, Peter Berek, Leslie Sheffield, and the./ollrnal reviewersfor their advice and assistance.

The necessary conditions

r1(pl' w, q) - r2(p2' w, q) :$ 0

imply that L] (q) = 1 if r1(q) > r2(q) and L 1(q)= 0 otherwise; that is, that all land of quality q

Copyright 1989 American Agricultural Economics Association

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should be allocated to the most profitablecrop. Thus, if it is profitable to grow bothcrops and if the production functions of bothcrops are concave in land quality, each cropwill be grown on a unique, compact range ofland qualities. If crop 1 is grown on lowerquality land, acreage planted to crop 1 will be

Al = fl g(q)dq = G(qJ,

where ql is defined by

rt»; W, ql) = r(P2' W, ql),

and acreage allocated to crop 2, will be A 2 =

G(1) - G(ql)'The introduction of a land quality­

augmenting technology can be incorporatedinto this model as an exogenous shift in theprofitability of the crop grown on lower qualityland, a shift that is smaller for higher qualityland. This effect can be represented by a shift­er z which increases the profitability of crop 1(r~ > 0) and does not affect the profitability ofcrop 2 (r~ = 0). Differentiating the acreageequations and the equation defining ql yields

aA I/az = - g(ql)rl!D > 0 andaA2/az = -aAI/az < 0,

where

D = Plfd(ql) - P2f;;(ql) < 0

because r' > r for q < ql and r1 < r2 for q >q.. The introduction of the technology wouldthus be expected to result in an expansion ofacreage allocated to crop 1 and a simultaneousreduction in the acreage allocated to crop 2.

The impacts of changes in crop prices,found by differentiating the acreage equationsand the equation defining ql' are

aA I/ap = - g(ql)fl(ql)/D > 0 and

aA2/apl = -aA I/apl < 0,

that is, an increase in the price of crop 1 willincrease acreage allocated to crop 1 and de­crease acreage allocated to crop 2. Similarly,

aA 1/ap2 = g(ql)f2(ql)/D < 0 andaA2/ap2 = -aAl/ap2 < 0,

that is, an increase in the price of crop 2 willlead to an increase in acreage allocated to crop2 and a decrease in acreage allocated to crop 1.

In many cases crop prices are correlatedand will therefore change simultaneously. Forexample, com, sorghum, and small grains areclose substitutes for use as feed grains; thus,

Amer. J. Agr. Econ.

markets for these crops are often modeled as asingle market for feed grains. An exogenousincrease in the demand for feed grains (e.g.,because of bad harvest in the Soviet Union)would increase the expected prices of all feedgrain crops. This effect can be captured in themodel by writing p, as a(Pl), a function ofPI' Ifthe two prices are positively (negatively) cor­related, a'(Pl) > 0 « 0). (If the two are uncor­related, a' (PI) = 0.) Substituting this functioninto the equation defining ql and differentiat­ing yields

aAl/ap = [(a' (Pl)/(ql) - f(ql)]g(ql)/D > 0

whenever

P!j1(ql) > [a' (Pl)Pl/a(pl)]pJl!(ql),

that is, whenever the revenue per acre earnedby crop 1 exceeds that earned by crop 2 by atleast a factor equal to the elasticity of P2 withrespect to Pl'

Consider next the impact of changes in inputprices. Differentiating the acreage equationand equation (3) yields

aAl/awj = [Xli(ql) - X2j(Ql)]g(Ql)/ D < 0,

whenever factor j is used more intensively inproducing crop 1 than crop 2 (and vice versa).Intuitively, an increase in the price will givefarmers an incentive to cut back on its use andto substitute other less costly inputs. Onemechanism for doing so is to shift land intocrops which use it less intensively. For thisreason, changes in factor prices may lead tochanges in cropping patterns.

Irrigation Development in theNorthern High Plains

Land quality must be understood as a vectorof attributes affecting productivity. Among themost important of these attributes are fertility,water-holding capacity, topography, and depthof topsoil. The relative importance of theseand other attributes varies from region to re­gion. In the northern High Plains, two ofthese, attributes-water-holding capacity andtopography-have historically played a majorrole in determining cropping patterns andtechnology choice. Low late-season rainfallhas meant that, under dry land management,yields have depended heavily on the water­holding capacity of the soil. Crops whoseyields are quite sensitive to water (com, soy-

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beans) have thus been grown only on veryhigh qualities of land, while those whoseyields are less sensitive to water (oats, barley,rye, and hay) have tended to predominate onlow qualities of land.

Until fairly recently, the spread of irrigatedfarming was also limited largely by water-hold­ing capacity and topography. Flood irrigationmethods were not viable on land with sandysoils (low water-holding capacity) or rollingterrain so long as labor requirements ofhand-move sprinkler systems rendered themuneconomical for most situations. As a result,irrigated agriculture was restricted to areaswith relatively flat topography and good soils.

Center pivot irrigation technology, whichbegan to gain widespread acceptance in themid-1960s, obviated these obstacles. Essen­tially a self-propelled sprinkler system, it hasthe capacity to adjust delivery volumes to ac­commodate sandy soils and rolling terrain, itcan navigate rolling hills, and it requires lesslabor than conventional sprinkler systems. Inshort, center pivot technology is essentially aland quality-augmenting technology in thesense defined by Caswell and Zilberman: Bysubstituting capital and energy for the waterabsorption capabilities and the water-holdingcapacity of the soil, it enhances the ability oflower quality land to provide water and nutri­ents for crops, thereby reducing the productiv­ity differentials between lower and higherqualities of land.

Under conditions like those in the northernHigh Plains the principal attraction of centerpivot technology appears to lie in the produc­tion of water sensitive crops, especially corn,on lower quality land. The theoretical analysisof the preceding section suggests that a majoreffect of the spread of this technology wouldbe a pronounced shift in cropping patterns,specifically, increases in irrigated corn acreageand decreases in the acreages allocated to sor­ghum, small grains, and hay, the crops pre­dominant on lower qualities of land under dryland management.

Corn, sorghum, and small grains are all feedgrains with highly correlated prices so thatsimultaneous variations occur in all cropprices. For example, real corn and sorghumprices received by Nebraska farmers between1966 and 1980 had a correlation of 0.95, andreal corn and oat prices had a correlation of0.92. The average revenue per acre earned byirrigated corn was 1.21 times that of sorghumand 4.34 times that of oats, and log-log regres-

Land Quality and Irrigation 189

sions of real sorghum and oats prices receivedby Nebraska farmers 1966-80 on the real priceof corn yielded estimated elasticities of 0.96and 0.89, respectively. Combining these em­pirical findings with the results obtained in thepreceding section suggests that aA/ap shouldbe positive for irrigated corn and negative forcrops like sorghum and small grains on thequalities of land on which they compete. Thus,sorghum and small grains should exhibit nega­tive own-price responses on lower qualities ofland and positive own-price responses onhigher qualities of land, which implies thattheir own-price acreage responses should beincreasing in land quality.

Finally, because center pivot technology ismore capital intensive than dry farming meth­ods, increases in the cost of capital (and espe­cially the cost of center pivot systems) shouldresult in decreases in irrigated com acreageand increases in the acreages allocated to sor­ghum, small grains, and hay on lower qualitiesof land. This effect should be manifested em­pirically in (a) a negative correlation betweencapital cost and irrigated com acreage and (b)a positive correlation between capital cost andsorghum and small grains acreages on thequalities of land on which they compete withirrigated com. Because sorghum and smallgrains compete with irrigated com on lowerqualities of land but not higher ones, theircapital cost acreage responses should be de­creasing in land quality.

Data and Estimation

The factors influencing the diffusion of centerpivot technology in the northern High Plainswere examined empirically using a multino­mial logit regression model of county-levelcrop land allocations of the seven major cropsgrown in western Nebraska during the years1966-80, the period of rapid diffusion of thistechnology. A probabilistic regression modelis implied by the assumption that availablecrop land is fully utilized; the multinomiallogitspecification is presently the only one compu­tationally feasible for a data set of this typeand size. This approach (application of a prob­abilistic model to panel data) allows simulta­neous examination of the cross-sectional (dif­ferences among farmers and farms) and inter­temporal (differences due to price trends andchanges in information and learning) compo­nents of the adoption process. It thus permits

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a unified appraisal of the factors affectingtechnological change. Previous work (for asurvey see Feder, Just, and Zilberman) hasaddressed these two classes of componentsonly separately.

For each of six crops (irrigated com, dryfarmed com, wheat, sorghum, small grain,soybeans) the log of the ratio of the acreage ofthe crop harvested in each county relativeto dry farmed hay acreage (In AdAo) was re­gressed on a quadratic function of expectedown-crop price, expected hay price, estimatedcenter pivot system cost, and average landquality in the county using weighted leastsquares. Computational difficulties associatedwith the size of the problem prevented the useof simultaneous equations or maximum likeli­hood methods. The quadratic representationallowed investigation of changes in averageland allocated and in price and cost responsesacross land quality. Only one grain price wasincluded in each regression because of thehigh correlation among grain prices. Thus, the"own-price" coefficient reflects the influenceof an increase in all grain prices. Because thedependent variable in each regression includestwo crops, only the coefficients of outputprices are fully identified: The coefficients ofland quality and center pivot cost reflect thesimultaneous influence of these variables onboth crops. However, as long as the co­efficients relating to the effects of the othervariables on hay acreages have the expectedsigns, it is possible to ascertain the qualitativeeffects of these variables on the acreages ofother crops.

The data used in the regression analysiswere as follows. The sample consisted oftwenty-two counties in western Nebraska(Adams, Arthur, Boyd, Buffalo, Chase, Cus­ter, Dawes, Dawson, Franklin, Frontier, Fur­nas, Gosper, Grant, Harlan, Hayes, Holt,Howard, Keya Paha, Lincoln, Logan, Phelps,Webster) for which recent, mutually compar­able soil surveys were available. Data on har­vested acreages of each crop in each countywere taken from the Nebraska Department ofAgriculture. Expected prices of com, wheat,oats, and soybeans were estimated as theaverage price of a harvest time futures con­tract at planting time. The futures price of cornwas used to represent the expected price ofsorghum because of the high correlation be­tween the two. The expected price of hay wasestimated using regressions of actual hayprices on the size of cattle herds, range condi-

Amer. J. Agr. Econ.

tions, and, for 1973-80, the expected price ofcom. The coefficients of the model were esti­mated separately for each year beginning with1966, using only observations from that yearand the years preceding it back to 1960. Theprice predicted by each year's model wastaken as the estimated expected hay price.

The cost of installing a center pivot systemwas measured by the estimated annualizedcost per acre of a standard system, assumed toconsist of a well 250 feet deep, a pump andgearhead, a fuel tank and diesel power unit,and a ten-tower sprinkler system designed toirrigate one quarter section (effectively, 130acres) of land. The cost of each componentwas annualized using straight line depreciationof each item over the lifetimes used by Bitneyet al. The cost series was constructed on thebasis of a number of budget estimates, notablySheffield (1970, 1975, 1977), Henderson, andBitney et al. and from information provided byLeslie Sheffield of the University of Nebraska.Cost estimates for the two years for whichother estimates were unavailable were esti­mated using straight line interpolation be­tween the estimates for the preceding and suc­ceeding years. Following Bitney et aI., aninterest cost equal to the cost of the systemtimes half the prevailing interest rate (esti­mated as the midpoint of the rates charged bybanks for cooperatives as reported by the U.S.Department of Agriculture [USDA], p. 450)was added to the cost of the system. The pro­ducer price index for farm products (USDA,p. 419) was used to deflate these nominalprices and costs.

Land quality in each county was measuredas the countywide average available watercapacity in the top six feet of soil. For soilswhich are predominantly sandy like those inwestern Nebraska, available water capacity isthe best scalar measure of soil productivityavailable. It is determined principally by soilorganic matter content (which in tum is theprincipal determinant of intrinsic soil fertilityand good soil structure for plant growth) and isthus a monotonically increasing indicator ofthe three most important components of soilproductivity: ability to hold water and nutri­ents, fertility, and tilth (Thomson and Troeh).A soil depth of six feet reflects the rootingzone of corn, the crop most limited by wateravailability. This depth allows a more accurateappraisal of the productivity of soils underlainby rock, clay, or other impervious materialthrough which crop roots cannot penetrate.

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For each county the average available watercapacity in the top six feet of soil was calcu­lated as a weighted average of the averageavailable water capacity of each soil type,where the weights equaled each soil type'sshare of total available land in the county.Excluded were all soils unusable for crop pro­duction, such as land with a slope exceeding10% (steepness prevents its use for anythingbut grazing), soils with severe salinity or alka­linity problems, streambeds, and gravel de­posits.

Estimation Results

The results of the estimation procedure areshown in table 1. Overall, the model fit thedata extremely well. The model accounted fora large proportion of the variation in almostevery case, and almost all of the estimatedcoefficients were statistically significantly dif­ferent from zero at the 1% level.

It is evident that land quality exerts amarked influence on cropping patterns. Forevery crop except irrigated corn, the landquality coefficients have the highest sig­nificance levels of any coefficient except theconstant term. The finding that land qualitydoes not affect irrigated corn acreage is con­sistent with the depiction of center pivot irri­gation as a land-augmenting technology thatreduces soil productivity differentials. In addi­tion, the land quality coefficients are amongthe largest in absolute value for all dry farmedcrops, a finding that supports the hypothesisthat land quality is one of the principal deter­minants of cropping patterns in the absence ofirrigation.

The log odds of each crop but one are con­cave in land quality, suggesting that, as hy­pothesized, a distinct range of land qualitycontains the maximum acreage of each crop.The log odds of the apparent exception,wheat, are convex in land quality; but sincewheat acreage is essentially zero on qualitieson land as high as about 5.0, wheat storagealso effectively has a unique maximum at thehighest quality of land available. While theexact range of land quality on which each cropis concentrated cannot be estimated (becausethe effect of land quality on each crop cannotbe identified), the qualitative evidence sug­gests a strong tendency toward specializationof land use according to land quality, confirm-

Land Quality and Irrigation 191

ing the validity of the classical Ricardianmodel of land allocation.

The coefficients expressing the impacts ofchanges in crop prices also behaved as ex­pected. The price response of sorghum isnegative on land having an average water-hold­ing capacity less than 6.82 inches. Sorghumacreage is quite price sensitive on these lowerqualities of land: A 1% price increase leads toreductions in sorghum acreage ranging fromover 3% (when average available water capac­ity is about 6 inches) to almost 20% (whenaverage available water capacity is under 2inches). It thus appears that large proportionsof land with low available water capacity allo­cated to sorghum are subject to substitutionfor irrigated corn. The coefficient expressingthe impact of land quality on price response ispositive as expected: As land quality in­creases, the profitability of irrigated corn rela­tive to sorghum decreases until, on high qual­ities of land, sorghum becomes the moreprofitable crop. Small grains acreage, interest­ingly, exhibits a negative price response on allqualities of land. The coefficient describing theimpact of land quality on price response isnegative but quite small and statistically insig­nificant, suggesting that price response ofacreage of this crop varies little over land qual­ity. Irrigated corn acreage has a price elastic­ity greater than one on all qualities of land,which indicates that land subject to shifts fromother crops into irrigated corn make up a siza­ble proportion of irrigated corn acreage. Theprice response of soybeans (which is grownonly as an irrigated crop in this region) de­creases markedly as land quality increases,further confirming the characterization ofcenter pivot as a land-augmenting technology.

The coefficients expressing the impacts ofchanges in center pivot system costs also be­haved as expected. The impact of center pivotcost on irrigated corn and soybeans acreagesis negative on all qualities of land. The respon­siveness of irrigated corn acreage to centerpivot cost decreases as land quality increases,and the responsiveness of soybean acreageincreases as land quality increases, both asexpected. Sorghum and wheat acreages varieddirectly with center pivot cost on lower qual­ities of land (for sorghum, land with availablewater capacity less than 6.7 inches; for wheat,land with available water capacity under 5.9inches), where competition with irrigated cornwas expected. Surprisingly, they varied in­versely with center pivot system costs on

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higher qualities of land where substitutions be­tween these crops and irrigated crops wereexpected to be negligible; this negative elastic­ity probably reflects the greater capital inten­sity of those crops relative to small grains,which had a very high (and positive) centerpivot cost acreage elasticity on these highqualities of land.

Finally, consider the estimated own-price/center pivot cost interaction terms. One wouldexpect this coefficient to be negative for irri­gated crops. As the cost of a center pivotsystem grows larger, increases in the expectedprice of the crop should offer less of an in­ducement to farmers to shift acreage from dryfarmed crops, so that the price response ofirrigated crop acreages should grow smaller.The same logic suggests that this coefficientshould be positive for nonirrigated cropsplanted on qualities of land which are shiftedto irrigated crops, since increases in centerpivot costs make the former more attractiverelative to the latter, and vice versa. Fornon irrigated crops planted on qualities of landwhich are not shifted to irrigated crops, onewould expect this coefficient to be zero be­cause increases in center pivot costs shouldhave no effect on the relative profitability ofthese crops.

These predictions are borne out by the esti­mated coefficients. The interaction terms forirrigated corn and soybeans are negative andsignificantly so. The interaction terms for sor­ghum and small grains, the crops hypothesizedas the main competitors of irrigated corn, werepositive; the coefficient for irrigated com wassignificant as the 5% level. The estimated in­teraction coefficients were not different fromzero at the 5% level for wheat and dry farmedcom, the crops grown predominantly on qual­ities of land not subject to irrigation develop­ment.

Implications

Overall, these empirical results indicate thatthe acreages allocated to different crops varysignificantly over land quality and, indeed,that crops tend to be grown on specific rangesof land quality. The adoption of center pivottechnology is shown to have induced sig­nificant changes in cropping patterns, spe­cifically, substitution of irrigated corn for sor­ghum and small grains. This evidence alsosuggests that land quality-augmenting tech-

Land Quality and Irrigation 193

nologies like center pivot irrigation will tend tobe adopted especially rapidly on lower quali­ties of land.

The use of center pivot irrigation technologyin the northern High Plains has been a topic offierce debate. Opponents have expressedalarm over conversion of lower quality landsto irrigated farming, arguing that this will re­sult in greater erosion hazard and groundwatercontamination by agricultural chemicals.Many have argued that tax breaks have beenlargely responsible for the pace of irrigationdevelopment and the enhanced threat of envi­ronmental damage because they make invest­ment in center pivot-irrigated farming attrac­tive to absentee investors lacking deep con­cern for the land (see, for example, Center forRural Affairs). This study supports some oftheir arguments. The spread of center pivottechnology was shown to be the most rapid onsandy soils that are more erosion-prone andmore vulnerable to groundwater contamina­tion. In addition, the rate of adoption of centerpivot technology was shown to be quite sensi­tive to the cost of capital, which is determinedin part by tax policies. During 1966-80, in­vestment tax credits, interest deductibility,and accelerated depreciation reduced the realuser cost of capital by 10% to 20% (Hrubovcakand LeBlanc). The results of this study sug­gest that reductions of this size in the cost ofcapital would accelerate irrigation develop­ment on sandy land between 13% and 40%,implying that tax policies could be held ac­countable for a significant fraction of invest­ment in center pivot systems. More broadly,this implies that the environmental spilloversof agriculture may be as sensitive to mac­roeconomic policies as agriculture in generalhas been recognized to be, so that greatercoordination is needed among a broad array ofpolicies.

[Received December 1985; final revisionreceived June 1988.]

References

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Caswell, Margriet, and David Zilberman. "The Effects ofWell Depth and Land Quality on the Choice of Irriga­tion Technology." Amer. J. Agr. Econ. 68(1986):798-811.

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