Environmental and Resource Economics 9: 323-340, 1997. (~) 1997 Kluwer Academic Publishers. Printed in the Netherlands. 323 Do Farmers Overuse Nitrogen Fertilizer to the Detriment of the Environment? SATYA N. YADAV l , W I L L I S P E T E R S O N 2 and K. W I L L I A M E A S T E R 2 i Department of Agricultural Economics & Rural Sociology, 221, Agricultural Building, University of Arkansas, Fayetteville, AR 72701, USA; 2 Department of Applied Economics, University of Minnesota, St. Paul, MN 55108, USA Accepted 9 July 1996 Abstract. Increasing use of nitrogen fertilizer in U.S. agriculture has led to nitrate contamination of water resources. The main objective of the study is to determine if the current use of nitrogen exceeds the profit-maximizing level, since reducing such discrepancy, if any, could raise farmers' profitability and enhance water quality making it a win-win situation. Specific objectives of the study, however, are two-fold. First, develop an appropriate methodology for estimation of an agronomic production function utilizing panel data with several treatments from experimental plots. Second, using experimental data from 1987 through 1990 for three farm sites in southeastern Minnesota, empirically estimate the production function and profit maximizing level of nitrogen application. Our results show that both the current recommended rate, 150 lb/acre, and farmers' use, 176 lb/acre, of nitrogen exceed the profit maximizing level of nitrogen in the region. It is shown that the recommended rate needs to be revised and made more site or area specific rather than a general figure for the entire region. The study shows considerable residual nitrogen build-up in the soil profile, implying that farmers have been applying more nitrogen than could be utilized by corn plants. The later finding highlights the importance of soil testing for plant nutrients when making decisions on fertilizer application. Key words: ground water contamination, nitrate contamination, nitrogen overuse, profit maximization 1. I n t r o d u c t i o n The d e v e l o p m e n t o f high-yielding crop varieties and a reduction in chemical and fertilizer prices h a v e greatly increased the use o f these inputs in U.S. agriculture. C o n s u m p t i o n o f primary nutrients (nitrogen, phosphorus, and potash) has increased b y m o r e than threefold, and that o f nitrogen m o r e than fourfold between 1960 and 1990 (Vroomen 1989). Increased fertilizer use, however, has not c o m e without costs or externalities to society (Johnson et al. 1989)J Besides soil erosion and surface water pollution, the p r o b l e m o f ground water contamination b y nitratenitrogen is b e c o m i n g a serious and ubiquitous environmental concern (Pye 1983). Indeed, such contamination m a y result from several sources, including industrial wastes, municipal landfills, mining activities, septic systems, and agricultural activities. However, evidence suggests that agriculture, through the usage o f inorganic fertilizers, is a m a j o r contributor (Hallberg et al. 1985). 324 SATYA N. YADAV ET AL. Ground water contamination by nitrate-nitrogen has been confirmed in 31 states and is suspected in 6 others (Lee and Nielsen 1987). In Minnesota, the percentage of wells exceeding EPA's standard varies from 1% to 44% across data sets, for the period between 1978 and 1990. 2 Nevertheless, EPA analysis found that 7.3% of wells exceeded 10 mg/1 of NO3-N. This figure can be regarded as a good approximation of the incidence of ground water contamination problems in Minnesota (Wall 1991). Concerns over the pollution of ground water and/or surface water arise because of their expected adverse effects on human and livestock health as well as on the environment, including methemoglobinemia or 'blue baby' syndrome. Throughout the state of Minnesota, 75% of the population depends on ground water sources for their drinking water supply. Moreover, ground water is used by 93% the state's municipal water supply systems. In addition to these vital uses, ground water is essential in industrial usages, including food and beverage processing, and livestock production (MPCA 1989). Given the dependence on ground water, nitrate contamination of ground water is causing growing anxiety at both the state and federal levels. The main objective of the study is to determine if farmers' use of nitrogen in southeastern Minnesota exceeds that of the profit-maximization level. If it can be shown that the current nitrogen application rate is higher than the optimal level in a (non-environmental) profit-maximizing context, the reduction in fertilizer use would increase farm profitability and enhance water quality. This is a win-win situation. Specific objectives of the study, however, are twofold. First, we develop an appropriate methodology for estimation of an agronomic production function utilizing panel data with several treatments from experimental plots. Second, using experimental data from 1987 through 1990 for three farm sites in southeastern Minnesota, we empirically estimate the production function and profit-maximizing level of nitrogen application. This is then compared with the current level of nitrogen usage in the region. 2. Experimental Design and Data Collection The data for this study are from experimental sites on three farms: Site 1 (in Olmsted county), Site 2 (in Winona county), and Site 3 (in Goodhue county). All lie in southeastern Minnesota where nitrate contamination of ground water is a growing concern. Well samples taken in the mid-1980s by the Minnesota Department of Health and the Minnesota Department of Agriculture indicated that 39% of the rural private wells in this area exceeded the U.S. public health drinking water standard of 10 mg NO3-N/1 (Randall et al. 1990). There could be a couple of reasons for such an increased level of contamination in this part of the state. First, the intensive agricultural production system in the region uses a considerable amount of chemical fertilizers and manures. Second, soils in southeastern Minnesota are rather shallow over a fractured limestone and sandstone bedrock, called Karst. Mature Karst structure is characterized by sink- DO FARMERSOVERUSENITROGENFERTILIZER? 325 Table I. Description of nitrogen and tillage managements at three experimental sites Treatments type Applications of nitrogen (lb/acre) Site 1 (Olmsted Co.) Site 2 (Winona Co.) Site 3 (Goodhue Co.) No. 1 No. 2 No. 3 No. 4 No. 5 No. 6 No. 7 No. 8 No. 9 No. 10 No. I 1 No. 12 No. 13 No. 14 No. 15 No. 16 0 (CP) 75 (CP, spring) 150 (CP, spring) 255 (CP, spring) t50 (CP, fall) 150 (CP, fall, NH) 150 (CP, spring, SD) 150 (NT, spring) 175 (CP, spring, manure) a 310 (CP, spring, manure) a 0 (CP) 50 (CP, PP) 100 (CP, PP) 150 (CP, PP) 200 (CP, PP) 0 (NT) 100 (NT, PP) 150 (NT, PP) 200 (NT, PP) 100 (CP, PP + SD)b 150 (CE PP + SD)c 150 (CE SD 4-1F) 0 (CP) 50 (CP, PP) 100 (CP, PP) 150 (CP, PP) 200 (CP, PP) 0 (NT) 100 (NT, PP) 150 (NT, PP) 200 (NT, PP) 100 (CP, PP + SD)b 150 (CE PP + SD)c 150 (CE PP + SD)a 100 (CP, SD 4-1F) 150 (CE SD 4-1F) 150 (CE PP, NH) 150 (CE SD41E NH) a Liquid hog manure applied only in 1987 and 1988. No manure or fertilizer was applied in 1989 or 1990. b p p + SD: 50 lb nitrogen before planting and 50 lb after planting. c p p + SD: 50 lb nitrogen before planting and 100 lb after planting. d p p + SD: 100 lb nitrogen before planting and 50 lb after planting. CP: Tillage with chisel plow; NT: no tillage; spring/fall: nitrogen applied in spring/fall; SD: nitrogen applied in split dose; SD 4-1F: nitrogen applied at 4-leaf stage; PP: nitrogen applied before planting; NH: use of nitrogen inhibitor. f Unless stated, source of nitrogen is anhydrous ammonia, split dose implied half before and half after planting at knee high stage of plant growth. holes, enlarged joints, n u m e r o u s springs, disappearing streams, c a v e systems, and dry valleys. Often, such t o p o g r a p h y has p o o r surface drainage, thereby allowing a quick m o v e m e n t o f water into the sub-soil through sinkholes and disappearing streams. Thus, ground water in Karst terrain is closely related to surface reservoirs (Jannik et al. 1991; Growl 1986). 2.1. EXPERIMENTAL DESIGN T h e data were collected by the D e p a r t m e n t o f Soil Science, University o f Minnesota. T h e experimental procedures for collecting data f r o m the three sites were initiated in 1986. However, actual data collection was started in 1987 and lasted through 1990. Altogether, there were 38 treatments, 10 at site 1, 12 at site 2, and 16 at site 3, each planted with continuous corn (see Table I for details). Continuous corn was selected as the cropping pattern because it is a c o m m o n practice in 326 SATYAN. YADAVET AL. Table II. Distribution of residual nitrogen (lb/acre) in the soil profile across the three sites Depth (feet) Ammonium-nitrogen(NH4-N) Site 1 Site 2 Site 3 Nitrate-nitrogen (NO3-N) Site 1 Site 2 Site 3 0-1 1-2 2-3 3--4 4--5 5--6 6-7 7-8 16.7 5.7 5.3 3.3 2.8 3.3 3.8 2.2 18.7 8.2 3.9 2.7 2.4 2.4 3.6 4.1 18.4 8.7 10.8 9.9 8.7 7.6 7.7 6.6 21.5 15.4 10.5 8.7 4.6 4.5 5.7 4.4 76.4 61.9 66.4 52.7 32.9 24.8 18.6 17.4 23.1 17.3 14.8 14.5 23.2 22.3 23.1 18.7 Note: Figures are based on 1987 sampling. the region (MDA 1991). Moreover, corn utilizes a large share of the nitrogenous fertilizers applied in the region (USDA 1991). A randomized complete-block design with four replications was established at each site, for every treatment, every year.3 Accordingly, the data set consists of 608 (38 x 4 x 4) observations. Treatments among and within sites varied from each other only with respect to fertilization and tillage management practices. All other aspects of cultivation practices were controlled, except weather. Fertilizer and tillage management practices were varied in the experiment in order to see their impact on ground water pollution. Variations in fertilization included time of application (fall vs. spring; pre-plant vs. four-leaf stage), method of application (split vs. single dose), with and without use of nitrogen inhibitor, and source of nitrogen (anhydrous ammonia vs. manure). The variation in tillage practices included either deep tillage using chisel plow or no tillage. In addition, there were several treatments at each site with nitrogen rates of 150 lb/acre, the extension service recommended rate for corn in the region. Treatments involving this rate along with variations in cultivation practices were included in the experiment to examine their effects on yields and the residual nitrogen build-up in the soil profile. 2.2. RESIDUAL NITROGEN IN SOIL PROFILE The data set collected for the three sites includes information on corn yield (bu/acre), fertilizer use, and nitrate concentration in the soil profile associated with each replication as well as other factors. Nitrate-nitrogen concentrations in lb/acre were recorded for each 1 foot incremental depth of soil reaching down to 8 feet depth. Table II shows layer-wise average residual nitrogen measured in lb/acre, across the three sites. The data were collected in April, 1987 (i.e. prior to the start of the experiment) and can be regarded as an indication of nitrogen build-up in the soil profile of the respective areas. In general, site 2 has the highest DO FARMERSOVERUSENITROGENFERTILIZER? 327 Table IlL Residual nitrate-nitrogen (lb/acre) at 5 feet depth of soil profile under various nitrogen application levels Month and Surface applications ofnitrogen (lb/acre) year 0 50 75 100 150 200 225 Site 1 1987 Oct. 1988April 1988 Oct. 1989April 1989 Oct. 1990April 1990 Nov. 62 50 26 63 27 32 11 - 73 62 47 83 43 132 38 - 99 118 151 182 147 200 124 - 213 154 241 208 325 416 192 Site2 1987Oct. 1988April 1988 Oct. 1989April 1989 Oct. 1990April 1990Nov. 152 129 104 199 65 79 31 191 128 119 182 105 81 53 - 270 191 215 250 158 152 129 347 195 289 351 308 363 206 447 311 414 400 641 412 366 Site 3 1987 Oct. 1988 April 1988 Oct. 1989 April 1989 Nov. 1990 May 1990 Nov. 49 47 43 58 17 36 31 63 NA 218 NA 22 NA 46 - 80 NA 120 NA 68 NA 67 106 99 269 196 108 148 142 181 139 382 199 263 237 249 - D D D NA: not available. n i t r o g e n b u i l d - u p f o l l o w e d b y the sites 3 a n d 1, r e s p e c t i v e l y . A s e x p e c t e d , nitrog e n a c c u m u l a t i o n d e c r e a s e d w i t h i n c r e a s i n g d e p t h o f the soil profile. T a b l e III s h o w s y e a r - w i s e n i t r a t e - n i t r o g e n a c c u m u l a t i o n ( n o n - a c c u m u l a t i v e ) at 5 feet d e p t h o f the soil profile, a s s o c i a t e d w i t h v a r i o u s l e v e l s o f s u r f a c e n i t r o g e n a p p l i c a t i o n s . A g r o n o m i c studies r e v e a l that n i t r a t e - n i t r o g e n at o r b e l o w 5 feet d e p t h c a n n o t b e u s e d b y the c o r n p l a n t a n d thus is c o n s i d e r e d to b e a p o t e n t i a l s o u r c e o f g r o u n d w a t e r p o l l u t i o n . N i t r o g e n is m o s t r e a d i l y a v a i l a b l e to c o m p l a n t s in the 0 to 2 o r 3 feet depth, d e p e n d i n g u p o n m o i s t u r e c o n t e n t o f the soil profile. T h e data r e v e a l a n i n c r e a s e in nitrate a c c u m u l a t i o n in the soil profile with i n c r e a s i n g l e v e l s o f n i t r o g e n applications. 328 SATYA N. YADAV ET AL. 3. Agronomic Yield Functions: Previous Studies Output requires inputs. Inputs can be controllable, such as fertilizers, pesticides, labor, and machinery, or uncontrollable, including rainfall, soil type, and topography. Assuming that all inputs, except macronutrients, are held constant, a general form of the corn response function can be represented as: Y = f(P IX), (1) where Y is corn yield in bushels per acre, P is a vector of macronutrients, each measured in pounds per acre, and X is a vector of all other inputs that are held constant. It becomes a critical task to adopt the correct functional form which describes the production relationship. Notable early works on yield functions include those of Spillman (1923), Heady (1952), Johnson (1953), Heady and Dillon (1961), Perrin (1976), and Heady and Hexem (1978). These studies empirically investigated the characteristics imposed, a priori, by the chosen functional form. De Janvry (1972) presented a model for optimal fertilizer use that accounted for risk due to weather variability. Griffin et al. (1987) identified 20 traditional and popular functional forms, and discussed their intrinsic properties. In order to choose a best form for a given task, they proposed to choose one over the other based on maintained hypotheses (homogeneity, homotheticity, elasticity of substitution, and concavity), ease of estimation (availability and properties of data, the resources available for computation, etc.), availability of data (goodness of fit and general conformity to data), and/or expected application of the results. Judging from the recent literature, the most commonly used agronomic response functions appear to be: quadratic, von Liebig, and the Mitscherlich-Baule (Frank e t a . 1990). Their algebraic formulations and characteristics are discussed here briefly. 3.1. QUADRATICFUNCTION The quadratic function has been a popular form of estimating crop response to macronutrients. Possibly, because it is simple and has other attractive properties, as described below. Its algebraic formulation is Yi = ]~o q- /~l Ni -q- /~2 Pi q- /~3 N2 q- l~4 p2 -~ ~5 Ni Pi -q- ~i, =l,2,...,n, (2) where Yi is com yield (bushels per acre), Ni is applied nitrogen (pounds per acre), Pi, is applied phosphorus (pounds per acre), flj (j -- 1, 2 . . . . . 5) are the parameters to be estimated, and Ei are the unexplained errors. The quadratic form imposes the restriction of non-zero elasticity of substitution (cr ~ 0) and the absence of growth 329 DO FARMERS OVERUSE NITROGEN FERTILIZER? plateau. 4 That is, for/31,/32 > 0 and/33,/34 < 0, yield decreases as Ni, and Pi levels become large, ceteris paribus, so that the function exhibits diminishing marginal productivity and input substitution for all Ni and Pi > 0. 3.2. V O N LIEBIG FUNCTION (3) Y / = min(Y*,/31 +/32 Ni,/33 +/34 Pi), where Y* is maximum corn yield and all other notations are the same as above. The formulation is consistent with the view that nitrogen and phosphorous play different biochemical roles in plant growth (Wild and Jones 1988). Moreover, it implies that the plant responds in a linear fashion only to the most limiting nutrient. After some level of application (say, N* and P* ), the plant will no longer respond to the applied nutrients. At this point, the plant reaches maximum growth (yield) at Y*. Thus, the von Liebig function, a priori, imposes a zero substitution elasticity among inputs, and a growth plateau after N* and P*. Given a wide range of agronomic nutrients, it is possible that characteristics imposed by both the quadratic and von Liebig models are not appropriate under all plant growth situations. For example, contrary to the von Liebig function, macronutrients may not exhibit strictly fixed proportions for all data sets and plant growth situations. The possibility of a > 0 and a growth plateau has considerable intuitive appeal while modeling corn yield response to the use of nitrogen and phosphorus. 3.3. THE MITSCHERLICH-BAULEFUNCTION = / 3 0 [1 - + U,))] [1 - + P,))] (4) This function allows for plateau growth and convex, but not necessarily L-shaped, isoquants. There are good reasons why this function is appealing. First, it can accommodate the cases from near perfect factor substitution (a --4 cx~)to near zero factor substitution (a --+ 0). Thus, the function is quite flexible about the extent of isoquant convexity depending upon the data and production process. 5 Second, like von Liebig, Mitscherlich-Baule imposes plateau growth which has considerable appeal for many, though probably not all, plant nutrients response relationships. Thus, in terms of isoquant pattern and plateau versus yield decline, it allows an analyst a broader range of possibilities in model evaluation. As reported in section 4.3, a quadratic function modified to reflect MitscherlichBaule properties gave the most satisfactory results. 4. Empirical Results As explained above, a panel data set is used to estimate the corn response function. Experimental data with several treatments are spread over four years, 1987 through 330 SATYA N. YADAV ET AL. 1990. In order to estimate yield function, we followed a two-step procedure. First, possible effects o f treatment, year, and interaction between year and treatment were examined through analysis o f variance. Second, a yield function, consistent with the underlying theory o f an agronomic response function, was estimated based on the inference(s) obtained from the first step. 4.1. ANALYSIS OF VARIANCE (ANOVA) Corn yields for each site in a given year for a particular treatment, Yij, can be explained as a sum o f five components: A c o m m o n value (#), an effect due to year (r an effect due to a particular treatment (r an interaction effect o f year and treatment ( r 1 6 2 and a residual quantity (e). This can be represented as, i = 1, 2, 3 , . . . , r(years) and j = 1,2, 3 , . . . , t(treatments), where # = overall mean, a constant, r Cj = /~i. - - ~ ---- effect due to an h-th year, = #.j - # = effect due to j-th treatment, ((~r = (r162 - # effect due to an interaction o f an h-th year with j-th treatment, and ~ij = random c o m p o n e n t explaining all extraneous variation, and are assumed to be independently and identically distributed normal random variables [that is, e's are iidN (0, a~), for all ij]. From the observed data, following sum o f squares were calculated for each site. 6 C -- correction term -- Y2../rt SSTOT -- total sum o f squares r t r t i j i j SSYR -- sum o f squares o f years r = ~ i t 1@-, 2 ~ ( f . ~ _ f..)2 = ~ ,__, Y j - C j j SSTRT -- sum o f squares o f treatment r = E t E(g.{ j 1 r = -r E Y , . { - c 331 DO FARMERS OVERUSE NITROGEN FERTILIZER? Table IV. Basic ANOVA table for year, tratment, and interaction effects on yield Source of variation Degrees of Sum of freedom (DF) squares(SS) Mean square (MSE=SS/DF) Expected mean square (EMS) Years Treaments Interaction Exp. error r-1 t-1 1 (r-1)(t-l)-I SSYR SSTRT SSINTER SSE SSYR/(r-1) SSTRT/(t-1) SSINTER/I SSE/(r-I) (t-1)-I MSE/MSE for error MSE/MSE for error MSE/MSE for error Total (rt- 1) SSTOT S S I N T E R = sum o f squares o f interaction r t = rt[~-~ ~ i YG(~.- ?.)(?J - ?.)]2/(SSYR)(SSTRT) j SSE -- sum o f squares o f experimental error r = ~ t ~-'~ (Y/j - l ? / . - l?.j + l~..) 2 - S S I N T E R i j = S S T O T - SSYR - S S T R T - S S I N T E R A relationship o f the sum o f squares formulations is summarized in Table IV. The following null hypotheses are tested with the aid o f ANOVA tables. 7 - the year effects do not exist, there are no treatment effects, and the interaction effects among years and treatments are irrelevant. - - Table V shows ANOVA results, including inferences based on F-tests. for each site, the effects o f year and treatments using nitrogen fertilizers were found to be statistically significant at the 5% level, while the interaction effect o f year and treatment was not found to be significant. A couple o f implications can be drawn from these results. First, both years and treatments involving uses o f nitrogen fertilizers are important variables in explaining variations in corn yields at each site. Second, the interaction term does not have a significant effect in explaining corn yield at any o f the three sites. As shown by Lentner and Bishop (1986), the later finding, however, is not unexpected for this type o f experimental data. 4.2. MEAN DIFFERENCE TESTS Site specific annual corn yields, averaged over all treatments, are given in Table VI. At site 1, mean corn yield in 1987 was higher than in any other year. The possible 332 SATYAN. YADAVET AL. Table V. ANOVA of year, treatment, and interaction (between year and treatment) effects for sites 1, 2, and 3 Source DF SS MSE EMS Inferences 3 9 1 8 1 26 15760 25887 25166 721 407 3632 5253 25166 90 407 140 42.33 179.75 0.64 2.91 - Reject Ho Reject Ho Cannot reject Ho Cannot reject Ho - 39 45686 3 11 2 9 1 32 84234 5989 5534 455 110 4352 28078 2767 51 110 136 206.45 20.34 0.37 0.81 - Reject Ho Reject Ho Cannot reject Ho Cannot reject Ho - 47 94685 3 15 2 13 1 44 41921 27676 24936 2740 4 3605 13974 12468 211 4 82 170.41 152.05 2.57 0.05 - Reject Ho Reject Ho Cannot reject Ho cannot reject Ho - 63 73206 Site 1 Years Treatments No-N vs rest Among N levels Interaction Exp. error Toml Site 2 Years Treatments No-N vs rest Among N levels Interaction Exp. error Total Site 3 Years Treatments No-N vs rest Among N levels Interaction Exp. error Toml r e a s o n s f o r l o w e r y i e l d s (in a b s o l u t e t e r m s ) in 1988 a n d 1990 c o u l d b e b e l o w n o r m a l r a i n f a l l in 1988 a n d a b o v e n o r m a l r a i n f a l l in 1990. A d d i t i o n a l s t a t i s t i c a l t-tests, h o w e v e r , s h o w e d that m e a n c o r n y i e l d s a c r o s s y e a r s w e r e n o t s i g n i f i c a n t l y d i f f e r e n t f r o m e a c h Other. A t site 2, m e a n c o r n y i e l d in 1988 w a s f o u n d to b e s i g n i f i c a n t l y d i f f e r e n t a n d the l o w e s t a m o n g all y e a r s . T h e t-tests, n e v e r t h e l e s s , s h o w e d that m e a n c o r n y i e l d s f o r y e a r s 1987, 1989, a n d 1990 w e r e n o t s i g n i f i c a n t l y d i f f e r e n t f r o m e a c h other. F i n d i n g s o f m e a n c o r n y i e l d d i f f e r e n c e s f o r site 3 w e r e s i m i l a r to site 2. T h e y e a r 1988 h a d the l o w e s t y i e l d , w h i l e y e a r s 1987, 1989, a n d 1990 h a d similar corn yields. T r e a t m e n t - w i s e c o r n y i e l d s , a v e r a g e d o v e r all f o u r y e a r s , a r e p r e s e n t e d in T a b l e V I I . A s e x p e c t e d , m e a n c o r n y i e l d f o r z e r o l e v e l o f n i t r o g e n ( t r e a t m e n t 1) w a s f o u n d to b e s i g n i f i c a n t l y l o w e r t h a n all n o n - z e r o l e v e l s o f n i t r o g e n at site 1. H o w ever, m e a n c o r n y i e l d s a m o n g t r e a t m e n t s i n v o l v i n g n o n - z e r o l e v e l s o f n i t r o g e n 333 DO FARMERS OVERUSE NITROGEN FERTILIZER? Table VI. Annual mean corn yields (bu/acre) for the three sites by year Years 1987 1988 1989 1990 Average Site l Comyields (bu/acre) Site2 Site3 187.12 (29.1) 146.85 (25.2) 166.49 (35.2) 134.89 (26.5) 188.85 (8.07) 80.340 (14.5) 165.92 (16.7) 170.31 (26.0) 177.71 (22.5) 109.04 (18.7) 125.09 (32.2) 130.60 (20.7) 158.84 (35.15) 151.35 (45.46) 135.61 (35.05) Note: The computations are based on observations from replications. Sample sizes are Site 1 = 160 (each year 40), Site 2 = 192 (each year 48), and Site 3 = 256 (each year 64). Figures in parentheses are standard deviations of the means. applications, surprisingly, were not statistically different from each other at 1% significance level (Table V). A considerable amount of residual nitrogen build-up (over several years) in the soil profile could be one possible reason. If so, such accumulated nitrogen should be considered as a valuable source of nitrogen supply for the plant. Also, corn yields among treatments involving the recommended dose of nitrogen, 150 lb/acre, were not statistically different from each other, irrespective of variations in source, time, season, use of nitrogen inhibitor, method of fertilizer application, and tillage practices used. These later findings have important implications. More environmentally favorable cultural practices could be chosen for nitrogen application without sacrificing profits. Results for site 2 and site 3 were similar to site 1. Mean corn yields for zero levels of nitrogen were significantly (at 1% level) lower than the non-zero levels at both sites 2 and 3. However, mean yields did not differ significantly among treatments using non-zero levels of nitrogen. 4.3. YIELD RESPONSE FUNCTION Characteristics of agronomic response functions, discussed above, prompted us to select the Mitscherlich-Baule functional form. Several attempts were made to estimate the Mitscherlich-Baule function using non-linear estimation packages. However, the direct estimation of this function did not provide a good fit. In contrast, the quadratic form gave a good fit to the data and a separate function was estimated for each site. 8 However, the estimated quadratic function was modified to reflect the properties of the Mitscherlich-Baule function. The values of N* were obtained by maximizing the respective function to serve as plateau for N in the 334 SATYA N. YADAV ET AL. Table VII. Treatment-wise mean corn yields at the three sites Treatments Site 1 No. 1 Corn yields (bu/acre) Site 2 No. 11 83.58 (24.5) 155.50 (19.0) 172.56 (23.0) 167.36 (13.8) 169.45 (22.3) 169.13 (19.9) 168.47 (19.1) 167.96 (24.2) 165.92 (38.5) 168.44 (34.5) - No. 12 - No. 13 - 126.72 (43.8) 153.10 (48.1) 155.76 (45.1) 157.75 (45.1) 163.03 (40.4) 127.97 (46.5) 155.32 (46.0) 151.86 (50.1) 155.84 (42.8) 156.67 (43.2) 160.24 (45.4) 151.99 (47.2) - No. 14 - - No. 15 - - No. 16 - - Average 158.84 (35.15) 151.35 (45.46) No. 2 No. 3 No. 4 No. 5 No. 6 No. 7 No. 8 No. 9 No. 10 Site 3 89.42 (27.5) 126.61 (27.5) 143.40 (28.3) 146.87 (27.4) 147.53 (28.5) 77.35 (31.8) 137.21 (31.5) 141.46 (33.5) 139.97 (32.6) 142.33 (26.2) 145.57 (26.4) 148.18 (26.1) 140.06 (30.9) 146.17 (27.7) 150.30 (29.8) 145.36 (24.3) 135.61 (35.05) estimated functions (Table VII). Each function is concave and increasing in nitrogen before the plateau is reached. Inferences obtained from the mean difference tests were used to formulate appropriate dummies. As far as we know, this is the first time such a modification of the quadratic form has been used. DO FARMERSOVERUSENITROGENFERTILIZER? 335 Table VIII. Corn response functions for sites 1, 2, and 3 Site Estimated corn response function Site 1 Y = 111.87 + 0.467 N* - 0.00128 N2. - 40.28 YEAR88 - 20.63 YEAR89 (27.88) (3.14) (-2.79) (-12.80) (-6.55) -52.23 YEAR90 + 44.07 FERT (-16.59) (3.61) where: N* =N, ifN <__182 N* = 182, if N > 182 Site 2 Adjusted R 2 = 0,82 Sample size = 160 Y = 167.12 + 0.368 N* - 0.00117 N 2. - 108.5 Y E A R 8 8 - 22.92 Y E A R 8 9 (56.62) (7.20) (-4.67) (-37.56) (-7.94) -18.54 YEAR90 (--6.42) where: N* =N, ifN _< 157 N* = 157, if N > 157 Site 3 Adjusted R 2 = 0.90 Sample size = 192 Y = 125.49 + 0.476 N* - 0.00149 N2. - 68.67 YEAR88 - 52.62 YEAR89 (46.95) (4.21) (-3.48) (-30.13) (-23.08) -47.11 YEAR90 + 24.85 FERT (-20.67) (3.29) where: N* =N, ifN _< 160 N* = 160, if N > 160 Adjusted R 2 = 0.86 Sample size = 256 Note: Figures in parentheses are t-values of the corresponding estimates. Where, Y = corn yield (bu/acre), N = nitrogen (lb/acre), YEAR.. = corresponding year dummies (1 for given year; otherwise 0), FERT = fertilizer dummy (1 if any amount of nitrogen applied; otherwise 0). Table I X s h o w s the p r o f i t - m a x i m i z i n g levels o f nitrogen use, m e a s u r e d in p o u n d s per acre. U s i n g the results o f estimated corn r e s p o n s e functions f r o m Table VIII, p r o f i t - m a x i m i z i n g levels o f nitrogen w e r e d e t e r m i n e d f o r e a c h site (by e q u a t i n g the c o r r e s p o n d i n g v a l u e o f marginal p r o d u c t to the price o f nitrogen) and are s h o w n in the s e c o n d c o l u m n o f Table IX. 9 A corn price o f $ 2 . 4 0 / b u and nitrogen price o f $0.15/lb w e r e used in the c o m p u t a t i o n . N o t e that these r e c o m m e n d e d values do not take into a c c o u n t o f the residual nitrogen in the soil profile. In the a b s e n c e o f further information, these are the values that w o u l d be r e c o m m e n d e d b y e c o n o m i s t s . H o w e v e r , o u r results s h o w that such a r e c o m m e n d a t i o n w o u l d not o n l y be m i s l e a d i n g but also detrimental to the e n v i r o n m e n t . T h e third and the fourth c o l u m n s o f Table I X s h o w r e c o m m e n d e d levels o f nitrogen for each site w h e n residual nitrogen available in the soil profile is taken 336 SATYAN. YADAVET AL. Table IX. Profit-maximizing levels of nitrogen (lb/acre) for sites 1, 2, and 3a Site No consideration of Consideration of residual nitrate at residual nitrogen 0-2 feet depth 0-3 feet depth Si~ 1 S i ~ 2b 158 131 131 00 127 00 Si~ 3 139 99 84 a Based on our conversations with the agronomists, corn roots can go down to 4 feet depth. However, most of the roots are distributed in the upper 2 feet depth of the soil profile. b No additional nitrogen is recommended for site 2 for the first year because of the residual nitrogen. into account, l~ We have considered two possible scenarios of root zone depths, 0-2 and 0-3 feet depth. In each case, recommended nitrogen application is much lower than the case involving no consideration of residual nitrogen. When nitrogen available in the upper 2 feet depth of the soil profile is included, the recommended rate (column 2) can be reduced by 17% (site 1) to 100% (site 2). 11 Such a reduction does not seem to reduce the corn yield and is supported by our findings in the earlier section. As shown in the fourth column, reductions in nitrogen would be still higher if the upper 3 feet depth of the soil profile is considered. Site 2 has the highest level of stored nitrogen in the soil profile. This finding is consistent with our previous findings of statistically no mean yield differences across zero and non-zero level of nitrogen applications. Of course, as the residual nitrogen is depleted, the recommended levels would increase over time, although not to the point where there is a residual build-up in the soil. The results also indicate that the profit-maximizing level of nitrogen use is not same for all sites. The implication is that nitrogen recommendation should be site specific rather than a general figure for the region as a whole. Moreover, considering residual nitrogen as a potential source of nutrient supply for the plant, the recommended rate should not be independent of existing nitrogen supply from the soil profile. The current recommended rate of nitrogen application for southeastern Minnesota is 150 lb/acre. However, farmers have been applying about 176 lb of nitrogen per acre in this region (Wall et al. 1989). This is higher than both the recommended and profit-maximizing levels of use. 12 It appears from this study that farmers in southeastern Minnesota could decrease nitrogen use and increase their profits from savings in fertilizer use. 13 Since farmers in this area are not atypical of farmers throughout the country, one suspects a general overuse of nitrogen fertilizers. Decreasing the use of this input would also benefit society. Beside surface contamination of water resources, there is a positive relationship between surface applications of nitrogen and residual nitrogen build-up in the soil profile (Table III). The excess nitrogen has the potential of leaching into the ground water. Reduced DO FARMERS OVERUSE NITROGEN FERTILIZER? 337 nitrogen application by farmers thus would have a direct and positive impact on decreasing nitrogen loading to water resources as well, thereby improving water quality of the region. This is a win-win situation. This is not to say that the profit -maximizing rate is optimum for society; leaching can still occur. 5. Concluding Remarks In this study, we estimate agronomic corn response functions utilizing panel data from three experimental sites in southeastern Minnesota. The estimated quadratic functions are further modified to reflect the properties of concavity until the maximum is attained and a flat plateau thereafter. Optimal uses of nitrogen are derived in the static context based on these estimated functions. The following conclusions can be drawn from our results. First, both the current recommendation rate, 150 lb/acre, and farmers' use, 176 lb/acre, of nitrogen in the study areas exceed the profit maximizing level of nitrogen for the region. The current recommended rate needs to be revised downward. Moreover, the study shows that the recommendation should be made site or area specific rather than a general figure for the entire region. Second, the current study shows a considerable residual nitrogen build-up in the soil profile, implying that farmers have been applying more nitrogen than could be utilized by corn plants. Since such nitrogen, especially that available in the upper 2 or 3 feet of the root zone, can also be utilized by plants, appropriate credit should be given for this nitrogen (to avoid over application), when making nitrogen recommendations. This will not only reduce production costs of farmers but will also reduce further deterioration of water quality in the region. The results of this study should be taken as preliminary. Although the three sites are not atypical of southeastern Minnesota, variations within and among regions exist. Additional studies are needed to substantiate or refute the findings of the study. Moreover, it should be emphasized that negative externalities from fertilizer usage have not been considered in assessing its profitability. Once such social costs are included in the analysis, the socially optimum level of nitrogen use would still be lower. Our study has also identified several areas for further research. First, since residual nitrogen in the soil profile and the level of contamination vary across the state, it is essential to have similar studies done for the other parts of the state, especially where nitrate pollution is perceived to be a serious problem. Second, this study shows that farmers apply more nitrogen than required to attain the same level of corn yields. The study, however, does not explain the reason behind it. An extensive study of why farmers use too much nitrogen could provide invaluable insights into how nitrogen application rate can be reduced. Also, the study focus entirely on continuous corn. Thus similar studies should be done for the other common crop rotations in the state. 338 SATYAN. YADAVET AL. Third, this study deals with the continuous com where fertilization is primarily through chemical fertilizers. There are many corn farms, however, that use different combinations of chemical fertilizers and manure. A comprehensive study combining both sources of nitrogen appears to be important for making nitrogen recommendation for these farms. Fourth, as pointed out in the text, agriculture (though major) is one of the sources of nitrate pollution. An extensive study on contribution of various other sources of nitrate pollution could be helpful in further curtailing pollution. Moreover, such steps would help assure farmers that they are not the only ones reducing their nitrogen use. Notes 1. An externality is said to exist when individual X's utility or production function consists of nonmonetary variables, values of which are chosen by others without giving any regard to its effects on X's welfare. Moreover, the decision maker does not receive (or pay) in compensation for this activity an amount equal in value to the resulting benefits (or costs) to individual X (Baumol and Oates 1988). 2. EPA has set a maximum contamination level of 10 mg/l nitrate-nitrogen (NO3-N) or 45 mg/l of NO3, to be safe for drinking water. 3. Size of each plot was 65 feet long and 30 feet wide. 4. Elasticity of substitution ((r) of P for N is defined as, d(Pi/N~) / d(fN/fP) where the differentials are restricted to variations along an isoquant. Thus, # refers only to input substitutions associated with a constant level of output. An expression for a based upon the quadratic function is 0"~ --fN fp(N, fN + P~ fp) N, P,(f.N f~. -- 2 f . ~ fN fv + f l . . f~) which is non-zero (Ferguson 1975). 5. The elasticity of factor substitution at the h-th data point for the Mitscherlich-Baule function is Y~[fN Ni + fpP,] N~ P~[2fN fp + I~3Y~ f2v +/~1 ~ fP] where fN = ~o ~l [1--exp(--fla (/34+Pi))] exp(-~l (~2+Ni))] and fp =/~o/33 I1-exp(-fll (/~2+ Ni))] exp(-/~3(fl4 + PI))], are the first derivatives evaluated at Ni and Pi respectively. The above result is obtained by substituting the values of fray = -~1 fN, fro, = f13 fv, and fNP = f~v f p / Y into the usual formula for ~r. The isoquants approach the limiting case of no factor substitution (right angle isoquants) as Ni and Pi get arbitrarily large. In contrast, ai increases as N~ and Pi get smaller, thereby suggesting a greater factor substitution. 6. The approach followed is from Lentner and Bishop (1986). 7. The data set consist of observations on the dependent variable for all categories of the explanatory variables. Therefore, it satisfies the assumptions of a fixed effect model. Accordingly, inferences discussed here are for the fixed effects model. See Iversen and Norpoth (1987) and Lentuer and Bishop (1986) for detailed discussion on this issue. 8. Characteristics of treatments vary across sites. Therefore, a single response function from pooled data would not be an appropriate procedure. DO FARMERS OVERUSE NITROGEN FERTILIZER? 339 9. Note that negative externalities from fertilizer uses have not been considered in assessing its profitability. Once such social costs are included in the analysis, the socially optimum level of nitrogen use would be still lower. See Yadav (1994) for a detail treatment on this issue. 10. We believe that although left-over nitrogen (after plant uptake) cannot be removed from the soil profile, it can be utilized by the successive crops. Following the approach of Rehm and Schmitt (1990), we give full credit to residual nitrate-nitrogen in our analysis. 11. The recommended levels of nitrogen under the third and the fourth columns have been derived by subtracting the average residual nitrogen available in the corresponding soil profile depth from Table II. The residual nitrogen consisted of nitrogen available in nitrate form. We used the data collected in April, 1987 (i.e., prior to the start of experiment) so as to reflect the existing nitrogen build-up in the soil profile in southeastern Minnesota. 12. Possible explanations for the high application rates include: overestimation of yield goals, perceiving fertilizer as a cheap insurance against nitrogen losses in the root zone, and discounting of the nutrient content of manure. Also, farmers may treat fertilizer as a risk-reducing input (Olson 1986). 13. This is supported by the fact that farmers in one of the study areas were able to reduce nitrogen use in corn by 21%. 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Landher (1991), The Sinkhole Collapse of the Lewiston, Minnesota Waste Water Treatment Facility Lagoon, Presented at the Proceedings of the Third Conference on Hydrogeology, Ecology, Monitoring, and Management of Groundwater in Karst Terrains, Clarion, Nashville, Tennessee, December. Johnson, P. R. (1953), 'Alternative Functions for Analyzing a Fertilizer Yield Relationship', Journal of Farm Economics 35, 519-529. Johnson, S. L., G. M. Perry, and R. M. Adams (1989), Managing Groundwater Pollution From Agricultural Related Sources: An Economic Analysis, Final Technical Report Submitted to U.S. Geological Survey, Renton, VA by Dept. of Agricultural & Resource Economics, Oregon State University, Corvallis, OR. 340 SATYAN. YADAVET AL. Lee, L. K. and E. G. Nielsen (1987), 'The Extent and Costs of Ground Water Contamination by Agriculture', Journal of Soil and Water Conservation 42, 243-248. Lentner, M. and T. Bishop (1986), Experimental Design and Analysis. 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