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Proceedings del XXIV Encuentro Nacional de Facultades de Administración y Economía
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PAPER Nº4
IV. Impacts of weather events on Ontario crop yields
Juan Cabas
Universidad del Bio-Bio
Alfons Weersink
University of Guelph
1. Introduction
In order to determine how Ontario farmers can best adapt to any changes in climate, the first
stage is to estimate the impacts of climate variability on crop yields. Such predictions can be based
on crop biophysical simulation models, such as CERES or EPIC (see Rosenzweig et al.). An
alternative is to use regression models with actual crop yield or profit as the dependent variable and
climatic measures as explanatory variables (Newman 1978; Waggoner 1979; Granger 1980; Dixon
et al. 1994; Segerson and Dixon 1999). Regression models have the potential flexibility to integrate
both physiological determinants of yield, such as climate, but also socio-economic factors. For
example, Kaufmann and Snell (1997) estimated a hybrid regression model integrating physical and
social determinants of corn yield in a way that is consistent with crop physiology and economic
behaviour. They found that climatic variables account for 19% of the variation in corn yield for
counties in the US Midwest while social variables accounted for 74% of the variation.
The discussion and analysis on climate change effects on crop yield has tended to focus on the
effects of predicted increases in average values of climate variables on average crop yields (Adams
et al. 1999). Rather than focus on the mean, others have suggested that the greatest challenge
facing the agricultural industry will arise from an increase in the frequency and intensity of extreme
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events resulting from climate change (CCAF 2002). There are several important questions that the
agricultural industry will therefore have to answer: What is the relative influence of climatic and
non-climatic factors on crop yield? How sensitive is the inter-annual average crop yield to climate
variability? How sensitive is inter-annual crop yield variability to climate variability?
The purpose of this study is to estimate the effects of weather on average yield and the variance
of yield for corn, soybeans and winter wheat in Ontario. The first section of this study reviews the
applications of regression models to estimate the impact of climate variability on crop yields in
order to develop an appropriate model for Ontario. The empirical model is then presented along
with a description of the necessary data. The fourth section presents the regression results.
2. Regression Model of Mean and Variance of Yield
2.1.
Stochastic Production Function
In order to determine the effects of weather and socio-economic variables on both the average
and variability of crop yield, a stochastic production function approach of the type suggested by Just
and Pope (1978, 1979) is developed. This method isolates the impacts of changes in a climate
variable on expected yield and yield variance. The general form of the Just and Pope production
function is:
=
Yt f ( X t , β ) + h1/ 2 ( X t , α )ε t
(1)
where Yt is the crop yield in period t, Xt is a vector of explanatory variables, f(.) is a production
function relating X to average yield with β as the associated vector of estimated parameters, h1/ 2 (.)
is the yield standard deviation function that relates X to the standard deviation of yield with α as the
corresponding vector of estimated parameters, and ε is a random error with zero mean and variance
σ 2 , The yield function is expressed in an explicit form for heteroskedastic errors, that allows for
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the estimation of variance effects. A positive sign on the partial derivative of output variance with
respect to an explanatory variable (α >0) implies that the marginal risk increases with input use
(Just & Pope 1978,1979.
The stochastic production function given by equation (1) can be estimated using maximum
likelihood estimation (MLE) or a three-step estimation procedure involving feasible generalized
least squares (FGLS) under heterosckedastic disturbances. Most empirical studies have used the
FGLS approach but MLE is more efficient and unbiased than FLGS estimation in the case of small
samples (Saha et al. 1997). Given the large sample in this study, the three stage estimation
procedure as described in Judge et al. (1985) is used. The stochastic production function with
heteroskedastic errors can be expressed as
Yi =X i' β + ei
i =1, 2,..., N
2
2
E (ei=
) σ=
exp[ Z i'α ]
i
(2)
(3)
where Z i' = ( z1i , z2i ,..., zki ) is a vector of N observations on k independent variables,
α = (α1 , α 2 ,....α k )' is a (Kx1) vector of unknown coefficients, and e is the random error term with
=
E (ei ) 0, E=
(ei es ) 0 fo ri ≠ s . The same independent variables (X and Z) can be used for both
the mean and variance of yield.
The first stage of the estimation procedure is to estimate equation (2) by least squares.
Equation (3) can be rewritten as ln σ i2 = Z i'α . The σ i2 are not known, but the second stage uses
the least square residuals from (2) to estimate the marginal effects of explanatory variables on the
variance of production. Therefore
ln=
ei*2 Z i'α * + ui
(4)
where ui = ln(ei*2 / σ i2 ) . Although ui has a non-zero mean, the mean and the variance of the
limiting distribution of α * is known. Finally, the third stage uses the predicted values from
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equation (4.4) are as weights for generating GLS estimators for the equation (4.2) or the mean
output equation.
2.2.
Estimation Procedure
The first step in estimating the equations 2 and 3 for each crop is to ensure the times series data
is stationary.
Stationarity is tested using Dickey-Fuller panel unit root tests. Non-stationary
variables are differenced once and retested with the process repeated until the stationarity condition
is satisfied.
In addition to repeated observations over time for each variable, there are also observations for
each unit or county. The panel nature of the data can be estimated using either a fixed effects
model, which controls for omitted variables that differ between counties but are constant over time,
or a random effects model, which considers that some omitted variables may be constant over time
but vary between cases. Determination of the appropriate model involves the inclusion of two
additional variables to equations 5 and 6: 1) V which is a time-invariant, unobserved county specific
effect, and 2) U which is a county-invariant, unobserved time specific effect. The independent
variables included in the analysis do vary across states and time. However, there may be other
unobservable, therefore omitted, variables that may be county specific (V) or time specific (U),
which affect changes in crop yield and mask the true relationship between the dependent variable
and independent variables in the model. The fixed effects model, assumes that V and U are
constants and conditional on the sample not randomly distributed, while the random effects model
assumes that V and U are randomly distributed and not conditional on the sample. A Breusch and
Pagan test and a Hausman specification test is used to determine if the covariance between V and X
is zero as required producing consistent estimates with a random effects model.
If the null
hypothesis of no correlation between county specific effects (V) and independent variables is
rejected, then a fixed effects model will be used in the regression of the three crop yield equations.
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3. Data
3.1.
Dependent Variable
The base dependent variable for the analysis is yield in bushels per acre for corn, soybeans and
winter wheat. Yield data were collected from 1960 to 2004 for the Ontario counties of Essex, Kent,
Elgin, Huron, Perth, Haldimand-Norfolk, Middlesex and Lambton. The basis for the selection of
these counties is data availability and the importance of the field crops in Ontario over the period of
study.
While there are regional differences in yield for the three crops, county crop yield averages
tend to follow provincial trends, which are illustrated in Figure 4.1. Provincial average corn yield
has increased dramatically from less than 80 bushels per acre in 1960 to more than 125 bushels per
acre in 2004. Winter wheat yield also increased and doubled from less than 40 bushels per acre in
1960 to approximately 80 bushels per acre in 2004. Although there is a strong upward trend in both
corn and wheat yield, there are still significant year-to-year variations, especially in the latter half of
the study period. In contrast, average soybean yield in the province has remained relatively flat
with some significant decreases in the last few years.
20
40
Yield (bu/acres)
60
80
100
120
Figure 1: Yield of corn, soybean and winter wheat in Ontario (1960-2004)
1960
1970
1980
year
corn
wheat
1990
2000
soy
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3.2.
Explanatory Variables
The yield response models generally have three major categories of explanatory variables: 1)
economic variables, 2) site characteristics, and 3) climatic measures.
Output to input price ratios have been included in several studies as an economic variable to
explain yield including Fox and Rickard (1999), Segerson and Dixon (1999), and Dixon et al.
(1994). The inclusion of such a variable suggests a supply function is estimated rather than a
production function in which input levels would be included as explanatory variables. Actual input
levels by crop are difficult to determine so input use is measured here using the approach of
Kauffmann and Snell (1997). The change in input use can be determined by re-arranging the profit
maximizing input level condition which is where marginal value product is equal to the input price;
Pcrop ∆Qcrop
∆Qinput =
Pinput
(5)
where Qinput is the quantity of purchased inputs per acre, Pcrop is the price per bushel of crop
lagged one year, Pinput is the price index for inputs purchased in the current period, and Qcrop is crop
yield in the current period (bushel/acre). Crop price is proxied by actual prices in the previous year
at the provincial level and input prices are measured by the index of prices paid by Eastern
Canadian farmers (OMAFRA 2005). The change in the use of inputs is expected to have a positive
effect on average crop yield.
Site characteristics are captured by soil quality as measured by the weighted average of the soil
capability classes for agriculture in the region with the weights equal to the share of total acreage.
Farmland area by soil class within each county is reported for Ontario in Hoffman and Noble
(1975). Increases in soil quality are assumed to increase average crop yield and decrease its
variance, ceteris paribus. An additional site variable used is the percentage change in acres planted
from one period to the next. It is assumed that an increase in area will result a decrease in average
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yield and an increase in its variance since as more land is brought into production of a given crop,
the comparative advantages of that incremental land will decline and so will yield of the crop. The
lower-quality land will also be subject to greater yield variation. A final site variable included is
location as proxied by latitude and longitude. It is assumed that sites further south and west will
have higher yields than other locations if all else is held constant. A time-trend variable is also
added to represent the effect of technological progress, such as new crop varieties and improved
cropping practices, during the sample period.
The major climatic variables include in previous studies are average temperature and
precipitation for alternative periods of time ranging from a month to a year. For example, Granger
(1980) used total seasonal precipitation (April to November), total precipitation in four months
(May, June, July and August) and monthly mean daily maximum and minimum temperatures to
explain yield of several California crops. Adams et al. (2002) also used monthly average maximum
daily temperatures and monthly precipitation but in a quadratic functional form hereby permitting
climate changes to have a non-monotonic effect on crop yield (i.e., a potential increase in yields
under warming in cooler locations and a decrease in yields under warming in warmer locations as
temperatures increases). Hansen (1991) estimated a corn yield function by considering climate and
weather variables for July because growing conditions in this month are strategic due to corn
pollinization occurring during that month. Interactions between variables were included to account
for changes in the marginal impacts of weather with respect to climate. Rickard and Fox (1999)
found mean monthly precipitation from April to September was positively related to yields of corn,
barley, and winter wheat. Chen et al. (2004) also included monthly average temperature but annual
rainfall and found crop specific differences in the climatic impacts on yield level and variability.
For example, in the case of corn and sorghum, precipitation and temperature were found to have
opposite effects on yield levels and variability. Chang (2002) also included seasonal average
monthly temperature and the seasonal mean of monthly average precipitation but also added the
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variation of these measures from their 20-year seasonal average to capture the effect of an extreme
event on yield.
Dixon et al. (1994) and Kaufmann and Snell (1997) modified the traditional inclusion of
temperature and precipitation in the crop yield response functions and developed corn yield models
that included weather related factors by phenological stages of crop development instead of
monthly values 37. Dixon et al. explain that “because of the year-to-year variability of weather
events and planting dates, the development stage of a crop during a particular month varies by
location and year. As a result, the use of monthly data provides only a rough approximation of the
weather effects on yields, and suggests that weather related factors should be measured by growth
stage of the crop.” The weather variables used for each of the fourth growth stages considered were
the mean of daily high and daily low temperatures, accumulated solar radiation available for
interception, mean daily soil moisture measured as percentage of available water, and accumulated
precipitation.
Several studies using cross-sectional data to explain crop yield or land value have also used
climatic variables. Sergerson and Dixon (1999) included 30-year average monthly temperatures
and precipitation levels (January, April, July, and October) and not the levels of these variables that
are observed for the actual crop season as would be done with most conventional yield response
studies. Squared terms were included for the climatic variables. The precipitation variables were,
in general, significant with January and April precipitation having a negative effect on corn and
soybean yield and a positive effect on wheat yield. July precipitation was positively related to the
yield of corn and winter wheat. Reinsborough (2003) and Weber and Hauser (2003) examined the
relationship between climate and agricultural land value in Canada using data from the 1996 Census
of Canada. Their empirical cross-sectional Ricardian models included monthly temperature and
37
The phenological stages of development considered were sowing to germination, germination to seedling
emergence, seedling emergence to the end of the juvenile stage, end of the juvenile stage to tassel initiation,
tassel initiation to silking, silking to the beginning of the grain filling period, and effective grain filling period
to physiological maturity.
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precipitation for January, April, July and October, squared values for those climatic variables in the
case of Reinsborough’s research and interactions in the Weber and Hauser study.
All models explaining yield include the above site and economic variables, but two
specifications of climatic variables will be used. The first variation includes summary measures of
climate over the whole season. One is the length of the growing season (DGS) measured in days,
starting when the mean daily temperature is greater than or equal to 5oC for 5 consecutives days
beginning March 1. Mean temperature for the growing season (TGS) in Celsius degrees is expected
to have a positive effect on yields, as is precipitation for the growing season (PGS) measured in
mm. The variation in seasonal temperature is captured by the coefficient of variation (CV) for
temperature measured as is the standard deviation of the weekly mean temperatures expressed as a
percentage of the annual mean of those temperatures.
Similarly, the CV for precipitation is
measured as the standard deviation of the weekly precipitation estimates expressed as a percentage
of the annual mean of those estimates. These two variables have been included to capture the
effects of extreme events on average crop yield. An increase in the CV represents an increase in the
proportionate variability of these two weather variables and it is assumed to decrease the level of
crop yields and increase their variance.
An interaction variable between precipitation in the
growing season and mean temperature of the growing season is also included for all crops plus one
in the coldest quarter for winter wheat.
The second yield model uses monthly weather variables for the growing season (April to
October) instead of seasonal summary measures. The climatic variables for these months include
mean monthly minimum temperatures and total precipitation levels within the month. Squared
values for temperature and precipitation variables are included to allow for non-monotonicity. A
positive coefficient for the linear term and a negative coefficient for the quadratic term would
suggest that an intermediate value has the greatest positive effect on yield.
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Weather variables were obtained from Dr Dan McKenney of the Canadian Forest Service,
Great Lakes Forestry Centre. Base climatic data is obtained for meteorological stations from the
Canadian Atmospheric Environment Service in Downsview Ontario. (Mackey et al. 1995). Since
the weather stations are not located in each county or there may be several within a county, weather
variables for each county were estimated using a climate interpolation method named ANUSPLIN
(McKenney et al. 2001). McKenney et al. (2001) couple the climate surfaces determined by
ANUSPLIN with the longitude, latitude and altitude values from a digital elevation model (DEM)
to produce grids (maps) of the required climate variables for each period of time. Summary
statistics for all of the variables used in the function regressions are given in Table 1.
The behavior of major weather variables over time is illustrated for Perth county in Figures 3
and 4. Mean temperatures for April fluctuate significantly between periods with a slight increase in
the average over time (see Figure 3). Similarly, monthly precipitation levels vary widely between
years (see Figure 4) with an apparent increase in spring rainfall over time. The growing season also
fluctuates significantly over the period of study (see Figure 4).
Finally, variability of April
temperature and precipitation measured by the standard deviation of weather variables (see figures
5 and 6) appears to be fluctuating significantly over the period of study with a decreasing trend until
1990 for April temperature but not for April precipitation. The variability of these two variables
clearly present the arguments for the study of the effects of extreme events in agricultural
production as a result of climate change.
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-4
-2
Temperature (Celsius)
0
2
4
Figure 2: April mean minimum temperatures in Perth county
1960
1970
1980
Year
1990
2000
0
5000
Precipitation (mm)
10000
15000
20000
Figure 3: April precipitation in Perth county
1960
1970
1980
Year
1990
2000
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190
200
Days of Growing Season
210
220
230
240
Figure 4: Length of the Growing Season in Perth county
1960
1970
1980
year
2000
1990
.4
Standard Deviation April Temperature
.6
.8
1
1.2
1.4
Figure 5: April mean minimum temperature variability by year in Perth county
1960
1970
1980
Year
1990
2000
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0
Standard Deviation April Precipitation
10
20
30
Figure 6: April mean precipitation variability by year in Perth county
1960
1970
1980
Year
1990
2000
4. Results
On the basis of the multivariate augmented Dickey-Fuller panel unit root-test (Sarno and
Taylor 1998), the null hypothesis that all variables are I(1) processes was rejected. Therefore, the
data series are stationary. A random effects model was rejected as the appropriate means of
estimating the panel data on the basis of the Breusch and Pagan Lagrangian multiplier test (see
Appendix for the output of this and other tests). The Hausman test results indicated that a fixed
effects specification could not be rejected for the three crops so the crop yield functions were
estimated using a fixed panel model with dummy variables for the counties. This model assumes
that each unit or county has a unique but constant source of variation. The soil quality and location
variables were dropped because these variables were found to be perfectly collinear with the
dummy variables for the individual counties.
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The Breusch-Pagan/Cook-Weisberg test rejected the hypothesis that there are homoskedastic
errors for corn and winter wheat. The Wooldridge test for autocorrelation in panel data indicated
that the null hypothesis of no first-order autocorrelation could be rejected. On the basis of this test
result, I estimated the fixed effects models with a robust Cochrane-Orcutt AR(1) regression. The
models were estimated using STATA software.
4.1.
Average Yield
The regression coefficients for average yield are listed in Table 2 for corn, Table 3 for soybean,
and Table 4 for winter wheat. Regressions were estimated for each of the three crops without any
climatic variables, with seasonal climatic variables, and with monthly climatic variables. The
regressions fit the data well as indicated by the high adjusted R-squared values across all models for
all three crops. The lowest adjusted R-squared value is 0.77 for soybeans.
The non-climatic factors are all important in explaining average crop yield and have consistent
signs across the three crops. The change in input use determined from the profit-maximizing input
level condition (equation 5) had a statistically significant positive effect on average yield. The
impact is particularly evident for corn, which uses more inputs than the other two crops. The
positive correlation with input use and corn yield was also found by Kauffman and Snell (1977)
who suggested the proxy measure for input use.
Soil quality also had a statistically significant positive effect on average yield as expected with
the largest effect noted for wheat. Mean corn and soybean yield appear to respond to better quality
land when climatic variables are included in the regression, which is consistent with the impacts of
individual climatic variables noted below. Although soil quality had an important effect on mean
yield, location dummies were generally statistically insignificant for corn and soybeans.
Differences were noted for wheat with lower yields tending to occur in the counties in the southwestern portion of the region.
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Technological advances as captured by a time trend variable also increased average yield as
expected. The productivity increases have been largest for corn, followed by wheat and lowest for
soybeans, which is consistent with the trend in yields illustrated in Figure 1. Increases in area
significantly increase soybean and winter wheat yield. The effect was not significant for corn,
which may be due to the large base area of corn at the beginning of the estimation period in contrast
to the increasing area planted to soybean and wheat over time. It was hypothesized that increasing
crop area may mean bringing in more marginal land into production and thereby decreasing average
yield. However, the area considered is a relatively small region and most of the land well-suited to
producing all three crops so marginal productivity of the new land is unlikely to drop.
Given the high adjusted R-squared values in the mean crop yield models without climatic
variables, average yield in southern Ontario appears to be determined largely by input use, soil
quality and technological advances. However, weather variables do enhance the explanatory power
of the regression models of mean crop yield.
Length of the growing season has a statistically significant positive effect on average yield for
corn and soybeans as expected. It not significant for winter wheat, which is harvested much earlier
in the year than the other two crops so total growing season length is not as relevant. A related
variable is average temperature of the growing season and it has the expected positive effect on
mean yield across all three crops. The monthly climatic model indicates that the temperature effects
are important early in the growing season as average temperatures in the latter months are generally
statistically insignificant. In addition, there is no quadratic effect noted for the monthly temperature
variables suggesting that it cannot become too warm for crops at least within the observed
temperature range within the data set. Increasing the variability in temperature over the growing
season decreases average yield of corn and soybeans as expected but has no statistically significant
effect on mean winter wheat yield. The latter is not as dependent on warm temperatures as the
other two crops.
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Total precipitation in the growing season is positive and statistically significant for soybean and
winter wheat. Although total precipitation is not important in explaining average corn yield, the
levels of rainfall before planting begins in April and during the pollination period of June are
statistically significant as expected.
Similarly, the influence of rain within the year is only
statistically significant in July for soybeans.
The majority of the coefficients on squared
precipitation are negative and significant for corn and soybeans which implies that too much
precipitation in these months will decrease yields. Segerson and Dixon found similar results. As
with temperature, increases in the variance of precipitation were found to decrease average yields of
corn and soybeans. The coefficient of variation in rainfall had no effect on winter wheat yield. The
interaction variable between average temperature and precipitation of growing season had no
significant effect on mean yield of corn and soybeans but was found to positively affect winter
wheat yield.
The monthly weather variables models present problems of multicollinearity as measured by
VIF test.
VIF calculates the variance inflation factors (VIFs) for the independent variables
specified in the fitted model. The highest levels of collinearity arise from the weather variables.
The implications of collinearity are that the estimated coefficients should be interpreted carefully.
For example, some results of insignificant coefficients should be not evidence of an irrelevant
variable. Considering that these models present good overall fit, they can be used to forecast the
impact of climate change where a similar proportion changes the temperature variables or the
precipitation variables.
4.2.
Variance of Yield
The resultant estimated impacts of weather variables on variance of yield models determined
with a Just and Pope-production function approach are displayed in Table 5 for corn, Table 6 for
soybean and Table 7 for wheat. Since the Breusch-Pagan and Breusch-Pagan/Cook-Weisberg tests
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rejected the hypothesis of homoskedastic errors for corn and winter wheat but failed to do so for
soybeans.
The variance models have low values for the adjusted-R2 with only a few of the explanatory
variables statistically significant. An increase in the seasonal variability of precipitation
significantly increases the variability of winter wheat yield.
More variability in seasonal
temperature will decrease the variability of corn yield. Length of growing season has a positive and
significant effect on the variance of corn yield but the opposite for winter wheat. An increase on
mean temperature significantly increases the variance of corn yield and decrease the variance of
winter wheat. The interaction variable increases the variance of winter wheat yield.
5. Summary
This study examined the effects of climatic and non-climatic factors on the mean and variance
of corn, soybean and winter wheat yield. The models were estimated with a panel data of 8
counties in southwestern Ontario over a period of 40 years. Average crop yields were determined
largely by input use, soil quality and technological advances. Weather variables do enhance the
explanatory power of the regression models of mean crop yield but productivity enhancements over
time appear to offset annual fluctuations in weather. The major weather variables influencing
average crop yield is length of the growing season with monthly temperature particularly important
early in the growing season across all three crops. Total precipitation over the growing season is
especially important for wheat but precipitation in certain periods, such as during pollination for
corn, does have an impact on individual crop yield. Increases in the coefficient of variation in
seasonal temperature and precipitation do decrease yield.
The estimated results suggest climate change may have an ambiguous effect on average crop
yield. The predicted increase in temperature would act to enhance yield while the projected
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increases in the variability of temperature and rainfall would offset the increase to some extent. The
projections would also depend on future technological developments, which have generated
significant increases in yield over time despite changing annual weather conditions.
While improving the tolerance and yield capability of crops through genetics and other
technologies may be a public adaptation response to climate change, individual producers can also
respond by re-allocating cropping area or by insuring their crops against yield loss.
Table 1: Mean, standard deviation and coefficient of variation of dependent and explanatory
variables
Variable
Crop Yield (bu/acre)
Corn
Soybeans
Winter Wheat
Explanatory Variables
Input change
Corn
Soybean
Winter wheat
Crop Area
Corn
Soybeans
Winter Wheat
Temperature seasonality (CV)
Precipitation Seasonality (CV)
Total precipitation growing season (mm)
Growing Degree Days
Mean temperature growing season (Co)
Mean Monthly Minimum Temp (Co)
April
June
August
Mean Monthly Precipitation (mm)
April
June
August
Mean
Standard
Deviation
Coefficient of
Variation (CV)
97.90
32.20
52.60
20.90
6.90
13.01
0.21
0.22
0.25
3.606
8.389
4.859
1.067
2.087
1.765
106,714
93,067
40,702
3.538
41.831
193.40
327.80
12.70
53,224
80,781
20,920
0.224
8.799
48.60
9.60
1.13
0.49
0.86
0.51
1.73
12.82
14.61
1.57
1.70
1.63
0.90
0.13
0.11
79.61
83.62
85.20
25.99
32.79
39.31
0.32
0.39
0.46
0.25
0.03
0.09
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Table 2: Mean corn yield models
Explanatory
Variable
Intercept
No WEATHER
Variable Model
Coefficient
34.78 (5.27)***
Input use change
0.15 (13.59)***
0.01
Soil quality
0.33 (4.30)***
0.28
Crop area
-3.78 (0.28)
-.004
Time trend
1.47
(27.59)***
0.33
County Dummies
Perth
Elast
Seasonal
WEATHER Model
Coefficient Elast.
-37.01
(-1.93)*
0.14
0.01
(13.86)***
0.50 (5.70) 0.43
-4.29 (0.32)
1.33
(23.35)***
-0.004
0.29
Monthly
WEATHER Model
Coefficient Elast.
48.66
(0.96)
0.10
0.007
(12.76)***
0.48
0.41
(4.60)***
-7.24 (-0.008
0.40)
1.52
0.34
(24.69)***
0.94 (0.37)
1.03 (0.38)
0.19
(2.54)**
Haldimand
Middlesex
4.13 (1.98)
Lambton
0.88 (0.41)
Elgin
3.63 (2.09)**
Kent
11.35 (4.13)***
0.85
(0.40)
-3.78 (1.60)
-0.76 (0.40)
2.98 (0.92)
Essex
1.19 (0.46)
0.82
(0.36)
-4.16 (1.57)
-0.52 (0.22)
3.04
(0.89)
-7.67
(-2.09)**
Growing season
Mean
temperature
Total
precipitation
Temperature CV
0.81
-5.69
(-2.84)***
-0.24
(-5.99)***
0.0008
(0.92)
0.82
1.83
1.87
Precipitation CV(
Temp*Precipitati
on
Adjusted Rsquared
Durbin Watson
-6.95 (2.38)
0.19
(5.63)***
3.13
(4.00)***
0.00 (1.08)
0.44
0.46
0.02
-0.20
-0.11
0.02
0.85
1.50
t- statistics in parenthesis; Elast.= elasticity
***indicates coefficient significant at the 1% significant level
** indicates coefficient significant at the 5% significant level
* indicates coefficient significant at the 10% significant level
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Table 3: Mean soybean yield models
Explanatory Variable
Intercept
Input use change
Soil quality
Crop area
Time trend
County Dummies
Perth
Haldimand
Middlesex
Lambton
Elgin
Kent
Essex
Growing season
(days)v
Mean temperature
Total precipitation
Temperature CV
No Climate Variable
Model
Coefficient Elast.
15.29
(4.21)***
0.05(25.09) 0.005
**
0.072(1.61) 0.19
*
0.00 (1.48)
0.04
Seasonal Climatic
Model
Coefficient Elast.
-24.05
(3.37)***
0.05
0.005
(25.06)***
0.15(3.20)* 0.40
*
0.00
0.07
(2.77)**
0.27
0.19
(5.76)* **
Monthly Climatic
Model
Coefficient Elast.
-29.9(1.83)*
0.04
0.004
(16.73)** *
0.15
0.40
(3.31)**
0.00 (2.59)* 0.06
0.10(0.09)
0.42 (0.32)
0.30 (0.25)
1.25(1.19)
0.92(0.65)
1.55(1.50)
-0.52(-0.49)
-2.71(-1.76)
-0.65 (0.58)
-1.43(-0.78)
-3.89 (-2.10
0.69 (5.91)
-0.44 (-0.37)
-2.83 (-1.76)
-0.43 (-0.37)
0.38
(7.84)***
0.25
4.01(2.45)*
1.50(0.93)
1.98 (7.60)
0.00 (2.00)
-1.88 (2.98)
-0.08 (6.10)
-0.00 (0.61)
Precipitation CV
Temp*Precipitation
Adjusted R-squared
Durbin Watson
0.77
1.76
0.31
(6.59)***
0.21
-1.37 (-0.71)
-3.73 (-2.15)
0.48
0.89
0.05
-0.20
-0.10
-0.01
0.82
1.71
0.84
1.72
t- statistics in parenthesis; Elast.=elasticity
***indicates coefficient significant at the 1% significant level
* *indicates coefficient significant at the 5% significant level
* indicates coefficient significant at the 10% significant level
Table 4: Mean wheat yield models
Explanatory
Variable
No Climate Variable
Model
Coefficients Elast.
Seasonal Climatic
Model
Coefficients Elast.
Monthly Climatic
Model
Coefficients Elast.
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Intercept
Input use change
Soil quality
Crop area
Time trend
County Dummies
Perth
Halidmand
Middlesex
0.11(15.92)
0.54 (8.84)
0.00 (6.36)
0.75(19.37)
0.01
0.86
0.09
0.31
0.11(15.66)
0.60 (9.43)
0.00 (5.25)
0.70(17.18)
0.01
0.95
0.07
0.29
.09 (13.69)
.43 (5.78)
.00 (6.15)
.81 (16.20)
0.75 (0.42)
0.47 (0.28)
0.73 (0.38)
-4.51 (-2.81)
-5.24 (3.32)
-5.49 (3.16)
-4.85 (3.30)
-5.45 (2.52)
-6.09 (3.11)
0.00 (0.37)
-2.80 (-1.64)
Lambton
-5.15 (-3.13)
Elgin
-3.32 (-2.20)
Kent
-3.77 (-1.86)
Essex
-4.00 (-2.24)
Growing season
(days)
Mean temperature
Total precipitation
Temperature CV
Precipitation CV
Temp*Precipitation
Adjusted R-squared 0.80
Durbin Watson
1.70
1.50 (3.28)
0.01 (3.74)
0.16 (0.14)
-0.00 (0.26)
.00 (1.65)
0.81
1.75
0.009
0.68
0.09
0.33
-2.36 (-1.19)
-1.37 (-0.78)
0.27 (0.11)
-0.17 (1.59)
0.04
0.41
0.13
0.01
-0.006
0.05
0.86
1.73
t- statistics in parenthesis; Elast.=elasticity
***indicates coefficient significant at the 1% significant level
** indicates coefficient significant at the 5% significant level
* indicates coefficient significant at the 10% significant level
Table 5: Variance of corn yield with Just and Pope production model
Explanatory
Variable
Intercept
Input use change
Soil quality
Crop area
Time trend
County Dummies
Perth
Halidmand
Middlesex
Lambton
No Climate Variable
Model
4.51 (2.93)**
0.005 (2.37)*
-0.04 (-1.88)*
7.7e-06 (1.84)*
0.02 (1.54)
Seasonal Climatic
Model
-4.89 (-0.87)
-0.00007 (-0.03)
0.005 (0.24)
6.84e-06 (1.70)*
-0.0002 (-0.01)
Monthly Climatic
Model
12.389 (0.65)
3.32e-06 (0.00)
-0.021 (-0.78)
6.74e-06 (1.20)
-0.0039 (-0.19)
0.68 (1.13)
0.25 (0.46)
-0.04 (-0.08)
-0.20 (-0.38)
0.62 (1.15)
-1.68 (-3.26)***
-0.38 (-0.68)
-1.09 (-2.03)*
-0.02 (-0.03)
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Elgin
Kent
Essex
Growing season
(days)
Mean temperature
Total precipitation
Temperature CV
Precipitation CV
Temp*Precipitation
-0.25 (-0.50)
0.52 (0.82)
1.31 (2.17)**
Adjusted R-squared
Durbin Watson
0.04
1.93
-1.00 (-1.95)**
-0.84 (-1.14)
-0.85 (-1.16)
0.01 (1.51)
-1.36 (-1.81)*
-0.77 (-0.80)
-1.003 (-0.84)
0.44 (2.01)*
0.0009 (0.76)
-1.06 (-1.69)*
0.01 (1.01)
-0.0002 (-1.14)
0.05
1.96
0.16
1.91
t- statistics in parenthesis
***indicates coefficient significant at the 1% significant level
** indicates coefficient significant at the 5% significant level
* indicates coefficient significant at the 10% significant level
Table 6: Variance of soybean yield with Just and Pope production model
Explanatory
Variable
Intercept
Input use change
Soil quality
Crop area
Time trend
County Dummies
Perth
Halidmand
Middlesex
Lambton
Elgin
Kent
Essex
Growing season
(days)
Mean temperature
Total precipitation
Temperature CV
Precipitation CV
Temp*Precipitation
Adjusted R-squared
Durbin Watson
No Climate Variable
Model
1.16 (0.83)
0.001 (0.81)
0.002 (0.13)
7.8e-07 (0.15)
0.0006 (0.03)
Seasonal Climatic
Model
1.53 (0.27)
0.001 (0.78)
-0.03 (-1.23)
2.1e-06 (0.38)
-0.01 (-0.45)
Monthly Climatic
Model
14.37 (0.87)
0.0008 (0.29)
0.005 (0.21)
1.58e-07 (0.03)
-0.02 (-0.66)
-0.01 (-0.03)
0.59 (0.88)
-0.30 (-0.51)
-0.62 (-1.29)
-1.08 (-1.31)
-1.42 (-2.74)***
-0.44 (-0.51)
0.31 (0.45)
-0.27 (-0.44)
-0.95 (-0.95)
-0.98 (-1.43)
-0.29 (-0.25)
0.08 (0.08)
-1.38
-0.91
-1.51
-0.64
-1.04
0.06
1.72
0.44 (2.02)**
0.002 (1.48)
-0.09 (-0.15)
-0.02 (-1.73)*
-0.0004 (-1.58)
0.09
1.94
0.16
1.80
(-2.28)**
(-0.97)
(-2.32)**
(-0.50)
(-0.81)
t- statistics in parenthesis
***indicates coefficient significant at the 1% significant level
** indicates coefficient significant at the 5% significant level
* indicates coefficient significant at the 10% significant level
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Table 7: Variance of wheat yield with Just and Pope production model
Explanatory
Variable
Intercept
Input use change
Soil quality
Crop area
Time trend
County Dummies
Perth
Haldimand
Middlesex
Lambton
Elgin
Kent
Essex
Growing season
(days)
Mean temperature
Total precipitation
Temperature CV
Precipitation CV
Temp*Precipitation
Adjusted R-squared
Durbin Watson
No Climate Variable
Model
2.66 (1.64)*
0.003 (1.15)
-0.033 (-1.54)
4.2e-06(0.46)
0.06 (4.07)*
Seasonal Climatic
Model
14.11 (1.96)
0.002 (0.61)
-0.06 (-2.53)*
-8.22e-06 (-0.76)
0.06 (3.16)*
Monthly Climatic
Model
0.00004 (0.01)
-0.04 (-1.57)*
1.07e-06 (0.14)
0.03 (2.00)*
-0.04 (-2.66)*
0.05
1.96
-0.55 (-1.94)*
0.0006 (0.40)
1.23 (1.53)
0.03 (1.96)*
0.0005 (1.81)*
0.03
1.97
0.07
1.97
t- statistics in parenthesis
***indicates coefficient significant at the 1% significant level
** indicates coefficient significant at the 5% significant level
* indicates coefficient significant at the 10% significant level
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