Illinois Fertilizer
Conference Proceedings
January 27-29, 1997
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Susanne Aref, David Bullock, & Donald Bullock1
In the not-too-distant past, the American public viewed U.S. farmers as playing
a positive and constructive role in the conservation of natural resources and
the environment. But over the past two decades, the effects of agriculture on
the environment, both real and perceived, have become a matter of increased
public concern. The use of modern agricultural pesticides and fertilizers have
come under increased public scrutiny. At the same time, changes in technology
and increased international competition have continued to alter the economic
structure of U.S. farms: bigger farms are more viable today than in the past.
This structural change has squeezed some producers out of farming, and ultimately
led to the depopulation of many rural communities. This, then, is the setting
of the tremendous political debate being waged between environmental and agricultural
activists over the past decade. Little doubt exists that modern agriculture
practices can lead to environmental damage, but it also seems that few in the
non-farming public recognize that farming can take place with minimum or no
damage to the environment. This lack of understanding has resulted in many calls
from the general public and policy makers for mandatory and across-the-board
restrictions on modern production agriculture. There seems little recognition
that restriction of agricultural practices without consideration of the farm
enterprise itself could lead to large decreases in farm profit and further reductions
in farm numbers. It seems that policy makers face a trade-off. often there simply
is no easy way to improve both environmental quality and the financial position
of farmers. Improvement of one often damages the other.
For one important agricultural practice, however, recent research suggests that
there may be a way of making both farmers and the environment better off. This
agricultural practice is the application of N fertilizer to corn. Application
of N fertilizer to corn can have negative environmental effects; the N fertilizer
can leach and/or wash into groundwater and surface waters. High levels of nitrate-N
have been found in the drinking supplies of numerous U.S. communities. Concerns
about the health effects of contaminated drinking water have led to calls for
farmers to use less N fertilizer on corn. But following past fertilizer application
recommendations of the University of Illinois and other land grant universities,
many farmers have been reluctant to lower N application rates, for fear of lowering
yields and income. However, farmer reluctance to lower N fertilizer application
rates may be based on inferior information provided by land grant universities.
Recent studies based on short-term experimental data suggest that currently
recommended rates are too general and that in some specific situations the current
recommendations are far too high, and thus are neither economically optimal
nor socially optimal when environmental effects are considered.
Weather is very difficult to predict accurately more than a few days in advance,
and therefore stochasticity is a prevalent and important aspect of agricultural
production and decision making. It is this stochasticity due to weather that
makes risk and uncertainty important aspects of farmer decision making and optimal
fertilizer application rate recommendations. Due to the uncertainties of weather,
farmers cannot be sure at the time of fertilizer application exactly what the
effects of the application on crop yields will be. Rather, in making input decisions
farmers deal in probabilities--they must think about what the probabilities
are that increased or decreased input use will raise or lower yields, and by
how much. In this way, farmers conceptualize agricultural output as having a
probability distribution, and it is this probability distribution of output
which farmers try to affect when they choose inputs such as N.
Early studies in the agricultural economics literature of the effects of N fertilizer
on the probability distribution of agricultural output examined only one of
its characteristics, its mean (i.e. average). That is, early research attempted
to answer how application of N fertilizer would affect mean crop yields (e.
g. Heady and Dillon 1961). Such studies continue to be conducted by agronomists
and appear regularly in the agronomy literature. The basic methodology often
used in these studies is to assume that mean yield response to N takes on a
quadratic functional form, which implies that yield increases with increasing
N rate to some point and then declines with further increases in N rate. A more
realistic and intuitively appealing response model would have yield increasing
with increasing N rate and then leveling off. In the past, the quadratic function
has been used because it is much easier to work with than models which level
of.
Once a functional form of mean yield response is selected, statistical procedures
are conducted using that form, and the results are used in combination with
economic theory to predict a level of N fertilizer application which maximizes
average farm profits. These profit maximizing application rates are then recommended
to farmers. Recent research by Cerrato and Blackmer (1990) using two-year experimental
data from six Iowa sites suggests that a spline function (a functional form
which does level oft) is superior to the quadratic function for several reasons.
Chief among that list is that the quadratic function leads to an overestimation
of the mean profit maximizing level of N fertilizer application. In other words,
the quadratic results in more N being recommended than is really necessary.
In a similar study Bullock and Bullock (1994) confirmed the superiority of the
spline function methodology over the quadratic function methodology using longterm
experimental data from two Illinois sites. For one of their two sites, Bullock
and Bullock found that assuming a quadratic functional form led to substantial
overestimation of the economically optimal N fertilizer application rate and
consequently a reduction in expected profits.
In the agricultural economics literature, a few researchers have attempted to
estimate the effects of fertilizer on the variance of the probability distribution
of output (Colyer 1969; Doll 1972; Fuller 1965; McArthur and Dillon 1971), and
Day (1965) attempted to characterize the effects of fertilizer on the skewness
and kurtosis (i.e., third and fourth moments) of the probability distribution
of output . Each of these studies of the response of the output probability
distribution to fertilizer employed what Just and Pope (1979) called the "traditional
approach" of using experimental data to conduct econometric estimations
of the impact of fertilizer on output. Just and Pope (1979) showed that virtually
all of these traditional studies made implicit assumptions that predetermined
their results and led to (possibly erroneous) conclusions that ~increased fertilizer
application rates increased the variance of output. Thus, recommended N fertilizer
application rates from traditional studies were based on flawed methodology.
Just and Pope (1979) offered a "more general stochastic specification"
of output response to inputs in an attempt to avoid the problems of the traditional
approach. But Antle (1983) showed that Just and Pope's (1979) method suffered
from the same types of limitations as affected the traditional approach: whereas
the traditional approach restricted the elasticities of the higher moments of
output with respect to an input to be proportional to the elasticity of mean
output with respect to the input, Just and Pope's (1979) approach restricted
the elasticities of the higher moments to be proportional to the variance with
respect to the input. Antle (1983) introduced a "flexible moment-based
approach" to estimate characteristics of the output probability distribution.
Antle (1983) used a version of Anderson, Dillon, and Hardaker's (1977) "gross
approach," in which instead of parameterizing and directly estimating a
production function, he started with a general parameterization of the moments
of the output probability distribution. Antle's (1983) method basically was
to assume the moments of the output probability distribution to be linear (in
the parameters) functions of inputs, and to use residuals from lower moment
estimations to obtain parameter estimates for higher moment functions.
Antle (1983) states as a potential limitation of his approach is that a "good
estimation" of the effects of inputs on the mean of the probability distribution
of output was vital, lest substantial bias in the parameter estimates of the
other moment functions be introduced (p. 195). But a good estimation is especially
difficult to obtain for nonirrigated field crops, such as is almost all Illinois
corn. For in the "gross approach" the sources of output variation
(such as rainfall and temperature) on yield are not identified, which has led
Roumasset and Rosegrant (1985) to conclude that "in the gross approach,
production risk is treated as a black box." Without the use of rainfall
and temperature variables in the estimation of the mean function, standard errors
can be very large, causing difficulty in obtaining a good estimation of the
effects of inputs on the mean. (This was a problem in Bullock and Bullock (1994),
and in Cerrato and Blackmer (1990).) Thus, Antle's (1983) "gross approach"
is unlikely to be useful in the study of the effects of N fertilizer on Illinois
corn yield. (This conclusion has been verified in preliminary research.)
In their study of the effects of fertilizer on Filipino rice yield, Roumasset
and Rosegrant (1985) offer a useful alternative to Antle's (1983) approach,
for cases in which measurable stochastic variables (such as rain and temperature)
are important to the production process. Roumasset and Rosegrant's (1985) empirical
results emphasize that Antle's (1983) approach of estimating optimal inputs
without environment-specific information about the sources of risk can lead
to large errors. As an alternative to Antle's (1983) approach, Roumasset and
Rosegrant (1985) estimate the joint probability density function of the measurable
stochastic variables, and then use Monte Carlo methods to draw randomly from
this estimated distribution, place the results of their random draws into an
econometrically estimated response function, and thereby obtain an empirical
distribution of the probability distribution of output. Then by assuming various
levels of risk aversion and various levels of input and output prices, the authors
calculate optimal N estimation difficulties of the Antle approach, and avoids
the difficulty in analytical approaches of predetermining results.
The finding of Cerrato and Blackmer (1990) and Bullock and Bullock (1994) that assuming splined functional forms can lead to better, and more realistic information, is important. But these papers have shortcomings which will be addressed in the propsed research. The first shortcoming of Cerrato and Blackmer (1990) is that the authors use very short-term (one or two years) data sets from agronomic experiments to draw their conclusions. Because agronomic experiments are expensive, this practice of using short-term data to derive economic conclusions is common in the agronomic literature. But because weather can vary greatly from year to year, using short-term data to draw conclusions about the effects of N on corn yields may be misleading. The response of corn yield to N during wet years is not likely to be the same as during dry years. Nor is the response of corn yield to N during cool years likely to be the same as during hot years. Much useful information is lost unless experimental data is gathered over enough years at a given location to constitute a reasonable sample from the population of weather conditions farmers will face.
A second major shortcoming of Cerrato and Blackmer (1990), Bullock and Bullock
(1994), and many other previous studies is that they only look at the effects
of N fertilizer on average (mean) corn yields and do not consifer the effect
of farmer attitude toward risk when making N fertilizer decisions. These studies
give as their recommended N fertilizer application rates those rates which maximize
farm profits on average. But considerable evidence exists that it is not the
objective of most farmers to maximize average profits, rather farmers are also
concerned about the variance of their yield and profit. For instance, farmers
may be willing to trade off lower mean profits. A story sometimes told is that
while "a little extra" fertilizer applied will not on average raise
their yields, it may be beneficial in case of excessive rainfall or other bad
weather. Often a farmer's objective in choosing fertilizer quantities would
not be to maximize expected profits, but perhaps rather to maximize some function
of the mean and variance of the profit distribution (Meyer 1987). With this
view a farmer would rather have consistent yields than large swings from year
to year. For example, many farmers have indicated that for a given two year
period they would prefer two 160 bu/acre crops over 0 bu/acre and 320 bu/acre
crops. This view of risk is apparently common among farmers and indicates that
farmers are not "risk neutral" (Antle 1987; Binswanger 1980). Farmer
decision making is more complicated than agronomist have recognized in the past.
Therefore, it is important that the proposed research will examine the effects
of N fertilizer on higher moments (e.g. variance, skewness, kurtosis) of the
probability distribution of yield.
In the research we are conducting here a longer-term data set from on-going
agronomic experiments at two Illinois sites (Monmouth, 13-years; and Perry,
15-years), which contains information on N fertilizer application rates and
corn yield is being used. Most experimental data used to study the effects of
N fertilizer on corn is from only one or two years of experiments. We also possess
a 94-year set of climatic data for the experimental sites. In this research,
the impact of weather on corn yield and the effect of N on corn yield are being
measured and accounted for using long-term experimental and weather data and
Monte Carlo methods (a type of computer simulation) following the methods of
Rosegrant and Roumasset (1985). The inclusion of weather data into the response
model will reduce the standard errors of the data and improve substantially
the confidence in the derived optimum N application rate.
Field plots were established at Perry, IL in 1980 and at Monmouth, IL in 1982.
All plots are still in existence. N fertilizer was applied to all plots as urea
broadcast and pre-plant incorporated into the soil at 0, 60, 120, 180, 2401b/acre.
At Perry, wheat in a given plot was fertilized with urea as a broadcast application
at one-half the rate given to corn for that plot. Plot treatments were maintained
in place, thus, a given plot received the same N rate each year corn was grown.
Individual plots were 30 ft by 45 ft (twelve 30 inch rows).
At each location the experiment was arranged as a split-plot in a randomized
complete block with three replications. Cropping sequence was whole plots. Crop
species was the split-plot. Nitrogen fertilizer rate was randomized within split-plots.
All crop species were present each year.
The large number of years and the presence of the rotations makes the data set
unusual and particularly useful for this research. Crop rotation will be included
into the regression analysis. The weather data from each location has been obtained
from the Illinois State Water Survey. The weather data spans the period from
1901- 1994 and includes daily rainfall; minimum, maximum, and mean temperatures;
and modified growing degree days.
Corn yield for each plot was measured. The ninety-four year weather data are
being used to estimate a joint probability distribution of the important weather
variables such as rainfall and temperature during corn pollination and grainfill
period. Climatic conditions during such periods are known to have a huge effect
on corn yield and are assumed to affect the effect of N fertilizer on corn yield.
Multivariate regression analysis assuming a splined functional form will be
used to estimate the effects of N fertilizer application rates and weather variables
on corn yield. Following Rosegrant and Roumasset's (1985) study of Filipino
rice, Monte Carlo methods will be used in many times randomly drawing weather
"shocks" from this estimated joint probability distribution, and then
inserted into the estimated corn response function to obtain an estimated probability
distribution of output. Bootstrap procedures will be employed (Noreen et al.
1989) to obtain statistical confidence intervals around various optimal N fertilizer
application rates. Sensitivity analysis will be conducted to examine how N fertilizer
application rate recommendations change with changes in assumptions about producer
risk preferences.
The preliminary results of this work support the argument and conventional
wisdom that climate is extremely important in predicting yield. We have found
that nitrogen rate alone accounts for only about 40% of the variation in yield.
When climatic factors are taken into consideration approximately 91% of the
variation is accounted for. It is particularly important to note the presence
of significant and substantial interactions terms between environment and nitrogen
rate. This indicates that the optimum amount of nitrogen will depend upon climate
encountered. At the time of this writing our results are not complete, but it
is clear that of the climatic variables considered, the mean high temperature
in August is perhaps the most important. We would have thought that a precipitation
variable would have been most important, but that does not appear to be the
case. We suspect that in general Illinois soils and climate provides reasonable
water supply to crops although exceptions such as 1988 do occur. It appears,
though, that the effects of high temperatures during the August grainfill period
and the subsequent increase in respiratory destruction of carbohydrates has
been underestimated. The effect of these interactions on optimal nitrogen rates
will be estimated from simulation runs. We shall elaborate on these biological,
climatic, and economic points during the talk.
1 Susanne Aref is Assistant Professor, Department of Crop Sciences;
David Bullock is Associate Professor, Department of Agriculture and Consumer
Economics; and Donald Bullock is Associate Professor, Department of Crop Sciences,
University of Illinois.
