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Climate Change Impacts on the Intensive and Extensive Margins
of US Agricultural Land
Jonathan R. McFadden
PhD Candidate
Department of Economics
Iowa State University
Ames, IA 50011
[email protected]
John A. Miranowski
Professor
Department of Economics
Iowa State University
Ames, IA 50011
[email protected]
Selected Paper prepared for presentation at the Agricultural & Applied Economics
Association’s 2014 AAEA Annual Meeting, Minneapolis, MN, July 27-29, 2014.
Copyright 2014 by Jonathan McFadden and John Miranowski. All rights reserved. Preliminary:
please do not quote or cite without permission from the authors.
Climate Change Impacts on the Intensive
and Extensive Margins of US Agricultural
Land∗
Jonathan McFadden and John Miranowski†
May 28, 2014
Abstract
How does current weather and climate change impact cropland use and allocation? Using
2010 ARMS data on several thousand central US farms, we estimate a two-step model
that controls for expected relative prices, local soil characteristics, and self-selection into
primary crop. We find that: (i). early-season and late-season temperatures and rainfall
are most significant for selection into corn, while mid-season weather impacts soybean
selection; (ii). sensitivity to nonlinear weather effects varies substantially within season
and across crops; (iii). soil characteristics are important and should be accounted for in
climate studies; and (iv). crop switching may occur under mild climate change.
Keywords: Cropland use, climate change, selection, ARMS.
JEL Codes: Q54, Q15, Q12.
∗
We thank Jae-hoon Sung and Brian Gelder for valuable assistance. All remaining
errors are ours.
†
Department of Economics, Iowa State University, Ames, IA 50011. Individual addresses: McFadden: 468A Heady Hall, [email protected]. Miranowski: 382B Heady
Hall, [email protected].
1 Introduction
In the United States, the share of land among cropland, pasture and rangeland, and
forests has changed little over the past fifty years. In 2007, cropland use was 408 million
acres, grassland pasture and range was 614 million acres, and forests accounted for 671
million acres. The Natural Resources Inventory (NRI) shows that 96-99 percent of private
cropland, pasture and rangeland, and forests remained in the same use during 20022007 (Nickerson, 2012). However, these aggregate data veil interesting and economicallymotivated transitions among and between uses. During 1997-2007, five million acres of
pasture, six million acres of Conservation Reserve Program (CRP) land, and 11 million
acres of hay became cropland, while 11 million, 12 million, and 16 million acres converted
from cropland to pasture, CRP land, and hay, respectively (Claasen et al., 2011). In
well-functioning land markets, these transitions reflect an array of local economic factors,
including changes in production environments and climatic conditions.
Minor changes in production environments, such as crucial resource endowments, improvements in bio- and information technologies, and capital equipment, can substantially
alter firms’ productivity and profitability. As a key factor of production for modern agricultural and resource-based firms, weather is a classic example of a (stochastic) input with
interactive and nonlinear impacts on production. In an era of suboptimal climate mitigation, evolving weather patterns will impinge on many aspects of producers’ economic
behavior (and conversely, given the feedbacks between localized climate and production).
As Earth heads toward temperature increases of 1.5 ◦ C by 2100 (relative to 1850-1900),
climate models predict warmer and more frequent “hot” days, warmer and fewer “cold”
days, expanses in areas prone to drought, and increases in heavy precipitation (IPCC,
2013; Jarvis et al., 2010; Groisman et al., 2012). It is poorly understood how US farms
and other agricultural firms will mitigate or adapt to climate change by 2100, as perhaps important future policies and technologies have not yet been engineered. However,
near-term impacts can be more reliably forecasted based on currently observed behavior.
Many climate adaptation strategies exist for US farms (McFadden and Miranowski,
2013; Ortiz-Bobea and Just, 2013). In the short run, firms can adjust quantities and
1
timing of irrigation water, fertilizer, and pesticides, plant earlier in the season or adjust acreage allocations, and adopt drought-tolerant seeds or no-till production practices.
In the long run, land can be substituted towards less water-intensive crops or biofuels
feedstocks, retired from production, or relocated to less impacted regions. Very recent
adaptation options include “prescription agriculture” (seeds designed to meet individual
operations’ requirements) and non-traditional, “early-warning” weather insurance products. Conditional on severity of climate change, farmers are likely to adjust cropland
allocations or crop choice, especially in regions where other adaptation strategies are
unavailable or too costly. For example, in response to reduced access to irrigation water, farmers engaged in irrigated agriculture may need to alter planted acreage, whereas
others may switch crops (Hornbeck and Keskin, 2014; Hendricks and Peterson, 2012).
The question that our research seeks to answer is three-fold: (i). How does weather
impact selection of major crops in the central US? (ii). Conditional on crop choice, what
are the weather effects on harvested acreage? (iii). How might climate change influence
cropland use and cropland allocation in this region? To address these questions, we implement well-known two-step estimation routines on cross-sectional farm data in 17 states.
The estimation accounts for selection into three crops: (i). corn, (ii). soybeans, and (iii).
all other crops, while controlling for county-level differences in soil characteristics that
may contribute to inherent productivity. The balance of the paper is arranged as follows.
The next section briefly surveys recent studies on cropland use and climate, with an emphasis on selection models using farm-level data. Section 3 describes the basic empirical
model, and Section 4 explains data sources and construction of variables. The subsequent
section lays out the empirical results and provides implications about near-term climate
change. The final section concludes, and the appendix contains econometric results.
2 Related Research
In more recent years, the chief economic sources of land-use change in developed countries
are government policies, technical change, energy feedstock demands, increasing export
2
demands, and climate change. To evaluate the impacts of each of these factors on land
use change and conversion requires careful econometric work. For example, Mendelsohn
and Dinar (2009) reviews the following well-known feedback loop: land use ultimately
influences climate change through greenhouse gas (GHG) emissions, while climate change
and frequency of extreme climate events can alter land use. In the first part of the
feedback loop, cropland use emits carbon and nitrogen dioxide, harvesting mature timber
and forest conversion to agriculture emits carbon, and livestock emit methane. These
emissions contribute to adverse climate change and have welfare effects, sometimes with
negative or positive implications for localized agriculture. For example, recent climate
research suggests changes in cropping patterns in the central US influence the water cycle,
with forecasted increases in intense precipitation (Groisman et al., 2012). The second
part of the climate-land use feedback loop draws on econometric analyses of yields or
land values, crop simulation or farm simulation models, and general equilibrium models.
The results vary widely, but they all underscore the continued importance of an evolving
climate for agriculture (Mendelsohn and Dinar, 2009).
A related study by Massetti et al. (2013) uses a panel of 2,406 US counties at five-year
Agricultural Census intervals during 1982-2007 to examine the effects of various degree
day and temperature variables in Ricardian models of farmland values and net revenues.
The researchers test the significance of: using degree days rather than daily temperature, using truncated rather than untruncated degree days, cold degree days, existence
of a 34 ◦ C threshold, and differences in degree day and daily temperature impacts across
the growing season. Controls include gridded weather data from the National Climatic
Data Center’s (NCDC) North American Regional Reanalysis (NARR), socioeconomic
variables, and soils variables (innate characteristics and index numbers) from the US
Geological Survey (USGS). They find no practical difference between regression coefficients of daily temperatures, degree days, and truncated degree days, no evidence of a 34
◦
C threshold, and significant differences across seasons in precipitation and temperature
variables. Results are robust to: using degree hours, omitting the last two years, applying
cross-sectional rather than panel methods, and using various soils data.
3
Similar to the above study and our current research, the Anderson et al. (2012) working paper uses an underlying multinomial logit model to motivate loglinear regressions of
crop shares on interactions of county soil and climate characteristics. The authors consider interactions between degree days, minimum temperatures, precipitation, sunshine,
various soil variables, and plant characteristics. Tentative findings point out significant
effects of these interactions on crop shares.
An additional strand of the applied agricultural economics research places more emphasis on structural econometric techniques. Fezzi and Bateman (2011), Lacroix and
Thomas (2011), and Kaminski et al. (2013) is a group of closely-linked studies starting from underlying models of farmers’ profit maximization to examine the relationships
between climate and land use in England, France, and Israel, respectively. The first
paper implements quasi-maximum likelihood for two systems of Tobit equations characterizing livestock supplies and land use shares, incorporating various environmental and
climatic data. Among their findings is that shares of cereals land, root crops, and permanent grasslands are highly nonlinear in soil suitability indices. Lacroix and Thomas
(2011) estimates elasticities of output, land, and fertilizer using a model that accounts
for multivariate selection, i.e., weather shocks influence a certain crop’s yields while also
affecting probability of planting various crops. The last paper in this group starts from
an expected-profit maximizing farmer with a (Pope and Just, 2003) yield function to
ultimately derive climate’s impact on technology, which impacts land allocations. They
consider four technological attributes (yield potential, input requirements, yield tolerance
to suboptimal input use, and managerial costs) and conclude that climate adaptation research should mainly target input requirements’ sensitivity to precipitation.
Another complementary set of empirical studies estimates relationships among major
crop yields and weather variables, with forecasts based on differing climate scenarios. McFadden and Miranowski (2013) use Bayesian dynamic linear regression and dynamic beta
models on a sample of 11 US states to estimate time-varying coefficients (productivities)
of weather variables and nitrogen-weather interactions in explaining state-average corn
yields. They find that Corn Belt yields will increase by 28-33% and Great Lakes states
4
yields will increase by 37% during 2011-2031. Further, there is evidence that late-season
temperatures and precipitation have more substantial impacts in later years of the 19602011 sample. This research builds on Miranowski et al. (2011), who fit autoregressive
(AR) and linear trend models to annual corn yields for a similar time period and sample
of states. Break testing procedures point out that some states have multiple breaks,
and the sample is accordingly partitioned to develop short run and long run forecasts
to year 2030. Long run forecasts from linear trends indicate growth of 1-2 bu/ac per
year, and short run models project 3-4 bu/ac growth in recent years, though weather
effects are not included. Schlenker and Roberts (2009) fit eighth-order polynomials to
county-level yield data on corn, soybeans, and cotton for 1950-2005 while controlling for
several weather effects. Their main result is that increasing temperatures are beneficial
up to a certain point and then detrimental to yields. Additional studies are Ortiz-Bobea
(2013b), Ortiz-Bobea and Just (2013), and Ortiz-Bobea (2013a), which further stress the
importance of nonlinearities, growth-stage (seasonally disaggregate) variables, and soil
moisture impacts on corn yields.
Regarding methodology, a body of work in empirical energy economics uses selection
models, usually two-step methods, to analyze fuel switching (electricity, natural gas, fuel
oil, and so on) and subsequent energy demand (Mansur et al., 2008; Newell and Pizer,
2008; Hanemann et al., 2013). This line of research adapts earlier work on selection
and models that relate first-stage choices with second-stage choices via correlations in
disturbances (Heckman, 1979; Lee, 1983; Dubin and McFadden, 1984). Across studies,
there is much variability regarding the key drivers of first-stage decisions, though most
are firmly grounded in economic theory. For example, Mansur et al. (2008) uses climate,
firm-specific information, building characteristics, and demographic data to explain fuel
choice for residential and commercial buildings, finding that climate change will likely
boost electricity use for cooling and reduce other fuels for heating. In a similar study,
Seo and Mendelsohn (2008) use data on 949 farmers in South America (Brazil, Chile,
Uruguay, Argentina, Ecuador, Venezuela, and Columbia) to estimate a multinomial logit
model of crop choice. Although the intensive margin (land allocation) is not estimated,
5
they find that farmers will switch from wheat, potatoes, and corn to squash, vegetables,
and fruit through year 2100.
Finally, the research seeks to learn from previous studies incorporating the ARMS data,
a complex stratified dataset that has been underemployed in environmental economics.
The ARMS data have been used for many empirical objectives, but all can provide
insight into methodologies, variables selection, and data differences over the cross sections
(Goodwin and Mishra, 2005; Kirwan, 2009; Mayen et al., 2010; Gillespie et al., 2010).
There are known limitations with the dataset, most notably that it does not contain
panel data on farms (though some operations may be sampled in multiple years), and
the current analysis must be careful to take these limitations into consideration (National
Research Council, 2008).
3 Empirical Model
The two-step estimation procedure used to correct for selection in the acreage equation
is the discrete-continuous framework of Dubin and McFadden (1984). This is a wellknown selection correction technique and is more robust and general than the Lee (1983)
approach. Despite potential problems arising from multicollinearity between regressors
and selection terms, the Dubin and McFadden (1984) method requires fewer assumptions
and can provide adequate correction when the Independence of Irrelevant Alternatives
(IIA) assumption does not hold (Bourguignon et al., 2007; Schmertmann, 1994).
Following the notation of Bourguignon et al. (2007), assume that agricultural producers
maximize utility by choosing a primary crop, c, and then planted acreage, Ac .1 For a
choice c ∈ C set of crops, the producer receives latent indirect utility:
Vc∗ = zc γc + ηc .
(1)
In the above equation, zc is a vector of observable variables, ηc is an unobserved distur1
Although US farmers make seasonal choices related to crop rotations, the data requirements for
discrete choices over crop rotations are too stringent. Moreover, the goal of the research is not to
examine climate impacts on optimal cycles (rotations); rather, we are more interested in the longer term
effects of climate on predominant crops.
6
bance, and the analyst observes Vc = 1 if c is chosen (and zero otherwise). After selecting
crop c, the firm’s cropland allocation decision (conditional input demand) is:
Ac = xc βc + uc ,
(2)
where xc is a vector of exogenous factors that influence allocations, and uc is a random
error. Note that E(uc |x, z) = 0 and V ar(uc |x, z) = σc2 . Selection occurs as a result
of Corr(u, η) 6= 0, which renders ordinary least squares (OLS) estimates of βc in (2)
inconsistent.
A producer chooses crop c if it yields highest indirect utility:
Vc∗ > max Vj∗ .
(3)
j6=c
Assuming that ηc is distributed type I extreme value, then the multinomial logit model
ensues, and as shown by McFadden (1973), the probability of (3) is:
exp(zc γc )
∗
.
Pc ≡ P rob zc γc > max(Vj − ηc ) = PC
j6=c
j=1 exp(zj γj )
(4)
Beyond this, Dubin and McFadden (1984) impose a restrictive assumption that the
conditional expectation E(uc |ηc , . . . , ηC ) is linear in (ηj − E(ηj )), which further restricts
distributional forms for uc since ηj is given a type 1 extreme value distribution. Bourguignon et al. (2007) relaxes this assumption and permits normality of ηj by computing
ηj∗ = Φ−1 (G(ηj )), where Φ−1 (·) is the standard normal inverse cumulative distribution
function (CDF). Correcting for selection, (2) becomes:
Pj
Ac = xc βc + σ rc∗ m(Pc ) +
rj∗ m(Pj )
Pj − 1
j6=c
X
!
+ wc ,
(5)
where rc∗ = corr(uc , ηj∗ ), m(Pc ) involves integrating over values of Φ−1 (·) centered at
log Pj , and wc is an independent error. See Bourguignon et al. (2007) for more details.
As pointed out by Mansur et al. (2008), the correction terms in the above equation
provide some economic insight. Particularly, the correction term for crop j in equation
7
c measures the impact on acreage of crop c for those farmers predicted to have selected
crop j. For example, if there is a statistically significant and positive correction term for
soybeans in the OLS regression of corn acreage, then soybean farmers are predicted to
boost corn acreage. Importantly, these selection terms partially absorb the impacts of
crop rotations, thus helping to alleviate omitted variables bias in the acreage equations.
In the following econometric analysis, equations (1) and (5) are of primary interest. A
Maximimum likelihood routine is used to estimate the multinomial logit model in (1) for
c ∈ {Corn, Soybeans, Other}, with standard errors for fitted choice probabilities given
by the delta method. Having corrected for selection, OLS is applied to (5) for the three
separate crops. As is common with multi-stage estimation, the bootstrap is used for
computing standard errors.2
4 Data
The Agricultural Resource Management Survey (ARMS) is a key source of information
about agricultural production, management practices, financial conditions, and household attributes of US farms. In its current format since 1996, it dates back to earlier
surveys starting in 1975 regarding farm costs and returns, chemical use, and cropping
practices. The survey occurs over three phases in a year (June through April) with stratified sampling over two mutually exclusive frames: a list frame of farms with certain
production aspects and an area frame that randomly samples land segments. Over the
sample period, the number of surveyed farms in phase III fluctuates from 9,573 in 1996
to 20,406 in 2011, though sample sizes are roughly 20,000 starting in 2003. Among the
phase II data are observations on field-level production practices, e.g., choices of capital,
applied fertilizer, pesticides, and irrigation, and tillage, though only one field is randomly
sampled for each surveyed farm. The phase III data contain observations on farm-level
practices, business and household finances, technology adoption, and labor allocation
(on-farm and off-farm) (ERS, 2013).
2
The number of bootstrap replicates is set equal to the sample size for each of the second-step
regressions, except for the “Other” crop, which we assign 1000 bootstrap replicates. All estimation is
done in Stata 13 with the selmlog command (Bourguignon et al., 2007)
8
Farm-level data for a 17-state area are taken from the 2010 ARMS Phase III Cost and
Returns Report (CRR) questionnaire.3 We consider cross-sectional data in 2010 for the
following reasons: (i). 2010 is a year in which corn farms are extensively surveyed in
phase II of ARMS, (ii). in-sample variation among oilseeds and grain farmers is large,
in part because of interesting weather patterns (e.g., local flooding in the Midwest) and
increased biofuels production, and (iii). it is one of the more recent years for which data
are available.
There is rich variability across an array of production and management variables in
the survey data. However, our approach is a straightforward and transparent application
of well-known discrete-continuous methods, so the resulting data requirements are less
stringent. Farms are classified as primarily corn, soybeans, or other crops farms based
on which crop’s value of production accounts for 50% or more of the farm’s total 2010
production value. This is a common farm classification approach and is consistent with
categories used in the US Census of Agriculture. Adopting this criterion, our sample
consists of 2,119 corn farms, 975 wheat farms, and 9,401 other farms. Owing to relatively
small sample sizes, we are not able to reliably estimate the second-step regressions in
(5) using reported planted acreage. Harvested acres are instead used as the dependent
variables in the least squares regressions. In recent years, harvested acreage has been
consistently and stably proportional to planted acreage, which renders it a suitable proxy.4
Data on harvested acres are reported in section B of the 2010 CRR questionnaire.5 Table
1 in the Appendix contains descriptive statistics for the ARMS variables.
3
States included in the sample are Colorado, Iowa, Illinois, Indiana, Kansas, Kentucky, Michigan,
Minnesota, Missouri, North Dakota, Nebraska, Ohio, Oklahoma, Pennsylvania, South Dakota, Texas,
and Wisconsin. These states are generally the most productive regions in the US for corn, soybean, and
wheat and are similar to samples in related research (USDA-NASS, 2013; McFadden and Miranowski,
2013; Miranowski et al., 2011).
4
At a national level, price variables are endogenous to harvested acres, but individual farms are
price-takers. Moreover, rather than realized prices, our empirical specification includes expected prices,
which are determined prior to harvest.
5
Other harvested acreage is the sum of: corn for silage and greenchop, cotton, peanuts, potatoes,
rice, sorghum for grain and silage, tobacco, barley, oats, hay, canola, other oilseeds, sugarcane and
sugarbeets, dry edible peas/beans/lentils, vegetables for processing, all other vegetables and melons,
fruits, nuts, and berries, nursery and greenhouse crops, and all other crops. This extensive summation
masks important crop-specific variability and adds complexity to regression interpretations. Yet, this
meets the assumption for discrete choice models that alternatives are collectively exhaustive. A failure
to satisfy this assumption precludes estimation.
9
Following much of the land-use change literature, we control for time-invariant geologic and hydrologic factors in soils that contribute to soil productivity. Generally, soil
structure and land characteristics have much bearing on land use and allocations, and
the significance of these factors for farms’ decision making may increase with an evolving
climate. However, the full economic implications of soil quality and soil productivity are
difficult to assess and require a fuller understanding of soil sciences. The data are from
the most recent version of the Soil Survey Geographic database (SSURGO), a bank of
data collected by the National Cooperative Soil Survey over the century (USDA-NRCS,
2013). Spatial areas of analysis are in units of “map unit polygons,” with states being
comprised of hundreds of thousands or millions of soil polygons. To get county-level
measures of soil attributes, we include all polygons within a county and weight according
to each polygon’s area. For certain soil features, data are reported at multiple soil layers
(depths) within a polygon, and we compute a simple average over these layers.6
Soil variables and their summary statistics are reported in Table 1 of the Appendix.
Slope (representative across polygons) measures the relative difference in elevation. The
“Depth to Water Table All Year” variable reports the distance between the soil surface
and the nearest wet soil layer (water table), which is expected to have important impacts
in irrigated farming. Similarly, “Top Depth” is the distance from surface to a soil restrictive layer, a proxy for topsoil thickness. Regarding soil texture, the percentage of silt
and clay are included to capture substantial qualitative aspects of soils.7 Closely related
to these innate soil characteristics are saturated hydraulic conductivity (Ksat), available
water capacity (AWC), and the K factor. The first variable relates to permeability and
measures the soil’s ability to transfer water, whereas AWC is the amount of water that
a soil can store for plant use. The K factor indicates vulnerability of soils to common
types of water erosion.8 Lastly, we include electrical conductivity (EC) and soil organic
6
By averaging across soil horizons, the data reflect agronomic considerations at two critical areas:
surface effects near the uppermost layers of topsoil and root zone effects in lower layers.
7
For production of corn and soybeans, loam soils are ideal because of their capacity to retain nutrients
and water while permitting drainage of excess water. In general, soils that have an equitable composition
of sand, silt, and clay are more productive than soils dominated by any single component.
8
The K factor is calculated as one of several factors in the (Revised) Universal Soil Loss Equation
(RUSLE). As such, it is not an innate characteristic of the soil. As a robustness check for erosion, we
used a variable that indicates whether or not the soil (averaged at the county level) has been visually
10
matter (OM). Conductivity is affiliated with salinity, and plants with high concentrations
of salts do not absorb water as efficiently. Organic matter is residue from decomposed
plants and animals and is a source of nitrogen and other nutrients (USDA-NRCS, 2013).
Weather data are from the Parameter-elevation Regressions on Independent Slopes
Model (PRISM). These involve simple regressions of climate variables (e.g., temperature,
precipitation, dewpoint) on elevation using nearby, weighted station data for various
“topographic facets” (slopes). The PRISM model outputs interpolated weather data
for grids of size 800m x 800m (roughly), which can be used to construct county-level
measures (Daly et al., 2008). For the months of May, June, July, and August 2010,
we average daily PRISM data for the corresponding months and then add the relevant
grids for each county. Although recent research identifies more complex weather controls,
for transparency, we include basic measures of temperature and precipitation and their
squares. Table 1 in the Appendix lists summary statistics.
Lastly, we construct state-level expected prices for corn, soybeans, and wheat according
to the methods of (Barr et al., 2011).9 For corn and soybeans, we first average the daily
February 2010 close prices of the December 2010 corn futures contract and November 2010
soybean futures contract traded on the Chicago Board of Trade (CBOT). Next, basis (the
difference between the cash and futures price) is subtracted from these February averages.
To calculate basis, we first average the daily November and December 2010 close prices for
the soybean and corn contracts ending in these same months (the futures prices). From
these figures, we subtract state-level corn and soybean prices received by farmers in the
2010 marketing year (the cash prices), which are published by the National Agricultural
Statistics Service (NASS). By accounting for basis, we eliminate possible bias that would
arise from systematic differences between spot and futures prices. To derive expected
prices for wheat, we start with the average of February 2010 daily closing prices for the
July 2010 CBOT wheat contract.10 Basis is calculated (and subtracted from the February
identified as eroded. Results are comparable, though this measure is sometimes insignificant.
9
There are several reasons why farms have geographically distinct price expectations. Local ethanol
plants and livestock-feeding operations create relative price differences across markets, in addition to
outside contracting and export opportunities.
10
Since wheat is included in other crops, we hypothesize a link between cropping patterns of other
crops and wheat prices.
11
averages) in a similar way, except the harvest-time contract is July. See Appendix Table
1 for the in-sample summary information.
5 Empirical Results
The multinomial logit results for choice of corn (the extensive margin) are provided in
Table 2. Column one shows results for a general model that includes expected prices for
corn, soybeans, and wheat and focuses on soil textures rather than soil properties (i.e.,
hydraulic conductivity, available water capacity, and K factor).11 Overall, the model uses
5,306 farm observations, and the fit is adequate: the model is jointly significant at the
0.01 level and performs better than an intercept-only model (pseudo R2 ). Note that a
relatively smaller sample size arises because of incomplete soils variables in some counties.
For the first specification (column one), many coefficient estimates have the expected
sign and reasonable magnitudes. Across soil variables, the log odds of growing corn,
relative to the other crops category, is increasing in depth to water table, percentages
of silt and clay, and organic matter, and is decreasing in salinity and slope. For the
Midwest and Northern Plains states, corn is primarily grown on relatively level to gentlyrolling cropland with non-saline soils. Relative to soybeans and other crops, corn requires
significant amounts of nitrogen and other nutrients, so the positive relationship with
organic matter makes intuitive sense. The modest impact of distance to water table
reflects the fact that corn is generally grown in rainfed regions not requiring irrigation.12
For aquifer-irrigated regions in western Texas, Oklahoma, Kansas, and Nebraska, the
distance to wet soils is more important, though these areas grow considerable wheat and
other crops. Lastly, the positive effects of silt and clay (clay restricts drainage) may
illustrate these soils have more suitable drainage, nutrient-binding, and water-retaining
properties than sandy soils.13
11
For space considerations, we do not report coefficients on expected prices. In our preferred model,
the coefficient on the corn/soybeans relative expected price in the corn selection equation is 10.8 and
significant at the 0.01 level.
12
For an individual operation in a single year, it is reasonable to assume that distance to water table
is exogenous.
13
Due to sand’s limited water-holding capacity, irrigation is common on sandy soils, which motivates
the use of soil texture-irrigation variables. Analysis of these interactions and their implications in a
12
Among the weather variables, we find significant concave relationships between choice
of corn and May and August precipitation. This is consistent with agronomic evidence
that early-season water is vital for germination, while late-season rainfall not only assists
plant cooling but grain filling during hotter periods. Temperature variables have similar
timing with rainfall: effects are strongest at the beginning and end of the season. Relative
to the other crops category that includes several cool-season crops (e.g., winter wheat,
potatoes, sugar beets), corn is chosen in locations with relatively warm springs and
warmer summers. Under scenarios of mild climate change, choice of corn as a primary
crop in these regions will not drastically change, other things equal.
Columns two, three, and four of Table 2 present robustness checks for included regressors. The model in column two uses hydraulic conductivity, available water capacity, and
the K factor in place of silt and clay content. The third column has the same specification
as the second column, except corn and soybean price ratios (relative to wheat price) are
used. The last column is a nested version of the third model that includes only lateseason temperature and precipitation variables. All specifications are jointly significant
and have comparable “explanatory power” in terms of pseudo R2 .
Across specifications, steeper slopes and greater erosion potential (K factor) reduce the
log odds of choosing corn, while permeability (hydraulic conductivity), available water
capacity, and distance to wet soils increase the log odds of corn. These estimated relationships are intuitive: corn should be grown in non-eroded soils with good water transfer
and retention properties. In comparison to other commodities, corn is a “thirsty” crop
that requires large quantities of water for high yields but also sufficient drainage. The
coefficient of organic matter switches sign, likely because of collinearity with the K factor.
The K factor (erodibility) depends on soil textures and organic matter. Weather effects
are also similar among models. Choice of corn tends to be concave in response to May
and June precipitation and June and August temperatures, while convex to May temperatures.14 In the last specification, all soil variables have significant impacts on corn
changing climatic environment are left to future research.
14
A well-known feature of any weather data is sizeable correlations over nearby months. For example, the simple correlation between July and August temperatures is 0.97. Multicollinearity remains a
challenge in most studies examining linkages between climate and agriculture.
13
choice, but among weather variables, only August temperatures matter. This is comparable to other studies showing that temperatures (and their extremes) matter more
than average precipitation, but not necessarily intense precipitation (McFadden and Miranowski, 2013). The fourth specification is preferred because of parsimony and use of
relative expected prices, which are more economically meaningful than expected prices
in level terms.
Table 3 gives estimated impacts of weather and soil characteristics on the soybeans
extensive margin. Coefficients among models are comparable and relate intuitively to
the first-step regressions for corn. More steeply-sloped land surfaces with greater erosion
susceptibility and permeability (Ksat) reduce the log odds of choosing soybeans. Relative
to corn and most other crops, soybeans root more deeply and can permeate denser and
less porous layers (suggesting a less important role of lower-layer permeability). As with
corn, the minimum distance to a restrictive soil layer (e.g., bedrock) is largely insignificant, though slightly positive in the fourth model. Regarding weather, June and July
rainfall have positive and negative effects (respectively) in the majority of specifications,
and August temperature has a positive impact. In the fourth specification, the linear
and quadratic impacts of August temperature on soybeans choice are roughly half those
for corn choice. As such, choice of soybeans relative to the other crop category is less
sensitive to late-season temperatures, implying that soybean choice is likely to be resilient
to modest temperature increases under mild climate change.15 This reduced (choice) sensitivity to late-season temperatures is also consistent with soybeans large presence in the
southern US, where average July and August temperatures exceed those in the Midwest.
The second-step regression results, including estimated selection terms and disturbance
correlations, are used to explain intensive margin (or harvested acreage) adjustment and
are shown in Table 4. Signs on regressors are similar to those in Tables 2 and 3, but
the magnitudes are generally significantly larger because we use harvested acreage as
the dependent variable. Many explanatory variables have limited impact on corn and
15
Reported multinomial logit coefficients may be influenced by the choice of crop in the previous
season, i.e., rotation effects. In the absence of good instruments, these variables are excluded from the
model.
14
soybeans acreage once these crops are selected but are significant in predicting other crop
acreage. This may be because lower sample sizes are used in the second-step corn and
soybeans equations.16 Intuitively, decreases in soil slope and increases in water capacity
and top layer depth are associated with an expanding acreage of other crops besides corn
and soybeans. Higher July temperatures and increased July rainfall decrease other crop
acreage but August temperatures have a positive effect. Given the composite nature
of other crops, many interpretations of the weather-acreage relationships are possible.
With respect to near-term climate change, consider the following scenario. At the sample
mean, a 1 ◦ C increase in July and August temperatures impact harvests by 114.6 and
-91.6 acres, respectively. This is roughly half of the 230 mean harvested acres for the
other crops category in 2010. If we have July and August mean temperatures of 26 ◦ C
(mild climate change), a marginal increase in July and August temperatures would change
other crops acreage by 326 and -388, respectively. These acreage impacts exceed average
harvested acres in recent years and suggest possibly crop switching or reduced plantings,
depending on how climate change alters the distribution of late-season temperatures.
While the selection terms (S1 , S2 , S3 ) in the corn and soybeans equations are not
significant, the correction terms for corn and soybeans in the other acreage equations are
positive. This has the following intuition. The subset of farms predicted by the discrete
choice model to be other crop farms would be likely to increase corn and soybeans acreage
had they not been other crop farms. Similarly, each of the acreage equations has at
least one significant association between disturbances in the first-step and second-step
regressions. For instance, corn acreage is negatively associated with selection into other
crops (-1.06), while soybeans acreage is negatively associated with selection into corn
(-1.84). This is important for two reasons. Firstly, it lends support to the selection
framework and suggests that applied cropland use studies that do not account for selfselection have potentially biased results. Secondly, it suggests that selection terms in the
regression equations are a possible option for controlling rotation effects (assuming that
predicted crop choice is roughly equal to actual crop choice).
16
A potential solution would be to pool the cross sections across multiple years and include time fixed
effects, which we leave for upcoming work.
15
Apart from climate change influences on harvested acreage (discussed above), we are
interested in climate change outcomes on crop selection. Figure 1 examines fitted choice
probabilities of corn, soybeans, and the other crops as functions of July weather, evaluated
at the sample means of all other regressors.17 In particular, the horizontal axis considers
combinations of July temperature and rainfall at the 10th -90th percentiles of the sample
distribution. For corn, we find a relatively smooth pattern: at low July temperatures and
rainfall, choice of corn is very high, but at relatively high July temperatures and rainfall,
the selection probability decreases. As in other agriculture-climate studies, this suggests
that the limiting factor in corn production is largely temperature. Choice probabilities
for soybeans are flat, while other crops exhibit the mirror image of corn. Although there
are potentially offsetting effects of more July rainfall, as average July temperature rises,
adoption of other crops increases. Taken together, the results give partial-equilibrium
predictions about near-term climate impacts, e.g., mild switching from relatively “thirsty”
crops to less moisture-sensitive crops in vulnerable areas.
6 Conclusion
A growing body of empirical work in agricultural and environmental economics indicates that changes in short-run weather and long-term climate patterns will impact crop
production, contingent on farmers’ mitigation or adaptation behavior. We add to this
literature by posing the following questions: (i). How does weather impact the choice
of growing corn, soybeans, and other crops in the central US? (ii). Conditional on crop
choice, how does weather impact harvested acreage? (iii). What are the climate change
effects on cropland use and cropland allocation? Using cross-sectional data on several
thousand Midwest and Northern and Southern Plains farms, we estimate a two-step selection model that controls for local soil characteristics and productivity, expected relative
prices, and self-selection into a primary crop. Our main findings are: (i). early-season and
late-season temperatures and rainfall are most significant for selection into corn, while
17
Future analysis should also account for changes in relative prices: given high relative prices of corn,
choice of corn could be sustained under moderate climate change.
16
mid-season weather impacts soybean selection; (ii). sensitivity to nonlinear weather effects varies substantially within season and across crops; (iii). soil characteristics and
productivity play an important role and should be accounted for in agriculture-climate
studies; and (iv). crop switching may occur under mild climate change, given recent
relative prices and technology options.
Although the results are provisional, there are important economic and policy implications. Firstly, estimated concave relationships between crop selection and late-season temperatures suggest “diminishing” impacts on crop choice, at least for in-sample weather.
Nearly all climate models predict that adverse outcomes, e.g., more extreme temperatures, reduced average rainfalls, and more frequent heat waves, will intensify in one to
one-and-a-half decades. Therefore, the geographic distribution and allocation of major
crops in the central US is not likely to dramatically change in the near term. A second
and related point is that adoption of modern technologies, such as drought-tolerant seeds,
advanced information technologies, and high-efficiency irrigation systems in some areas,
may markedly limit the downside impacts of climate change. The role of technological innovation is sometimes omitted in climate studies, partly because innovations are difficult
or impossible to forecast. To the extent that oligopolistic biotechnology firms persist in
innovation and farmers continue to adopt new technologies, estimated long-term impacts
of climate studies could be overstated. Thirdly, our econometric results highlight the continued importance of soil productivity. One intermediate-run climate adaptation strategy
is improvement in soil organic matter. Adoption of no-till or reduced tillage practices
boosts fields’ organic matter, providing more nutrients to plants, better drainage, and
reduced erosion. If intra-seasonal rainfall becomes more concentrated in shorter, more
intense events (rather than more evenly spread across the season), then there may be
larger adaptation gains by curtailing nutrient leaching, runoff, and soil erosion.
The estimation results are preliminary, and there are several avenues for future work.
The current analysis uses cross-sectional variation for a single year. Straightforward robustness checks should be implemented to examine the impacts at differing survey years.
Similarly, sample data can be pooled across two or more years to improve degrees of free-
17
dom and determine if specific year results involve significant changes in fitted coefficients.
Regarding specification, we can also test the significance of various weather interactions,
soil-weather interactions, other weather variables (e.g., dew points and evapotranspiration), and other nonlinear transformations. The literature is divided concerning a “best”
specification, and the useful nature of our farm-level cropping and county-level weather
and soils data may shed new light on this issue. Lastly, a system of input demands can
be estimated in the second-step regressions. In addition to acreage, the system could
include irrigation and tillage practices, nutrient and chemical use, and would provide a
more comprehensive, farm-level framework for assessing weather impacts.
18
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23
Appendix
Table 1: Acreage, Soils, Weather, and Prices
Variable
Acreage
Corn (ac)
Soybeans (ac)
Other (ac)
Soils
Slope (%)
Depth to water table all year (cm)
Top Depth (cm)
Silt (%)
Clay (%)
Hydraulic conductivity (µm/s)
Available water capacity (in./in.)
K Factor
Electrical conductivity (mf/cm)
Organic matter (%)
Weather
May Temperature (◦ C)
June Temperature (◦ C)
July Temperature (◦ C)
August Temperature (◦ C)
May Precipitation (cm)
June Precipitation (cm)
July Precipitation (cm)
August Precipitation (cm)
Expected Prices
Corn ($/bu)
Soybeans ($/bu)
Wheat ($/bu)
Obs.
Mean
Std. Dev.
Min.
Max.
2119
975
9241
600
411
230
818
646
634
122 (1st Quartile) 800 (3rd Quartile)
77 (1st Quartile) 471 (3rd Quartile)
2 (1st Quartile)
185 (3rd Quartile)
6414
6414
5821
5302
5302
5302
5302
5302
5302
5302
4.6
26.2
72.5
45.3
25.2
13.8
0.16
0.35
0.11
1.75
16.9
16.9
32.9
12.7
6.4
14.8
0.026
0.07
0.17
1.41
0.16
0
0
3.3
3.7
1.7
0.075
0.05
0
0.53
29.98
89.1
161.6
70.2
46.9
91.7
0.208
0.50
1.1
16.6
12495
12495
12495
12495
12495
12495
12495
12495
16.9
22.8
24.6
24.7
0.35
0.53
0.45
0.25
3.5
3.3
2.2
2.8
0.16
0.23
0.19
0.15
2.18
9.6
11.8
10.3
0.001
0.005
0.04
0.007
27.7
30.5
29.4
31.5
1.08
1.22
1.2
1.03
12495 3.57
12495 7.71
12495 5.39
0.30
0.46
0.38
3.07
6.93
4.94
4.53
8.63
6.61
Table reports descriptive statistics for harvested acreage, soils, weather, and expected
prices data. See text of Section 4 for details.
24
Table 2: Multinomial Logit Results, Corn
(1)
Textures
Slope
Depth to water table
Silt
Clay
Ksat
−0.145***
(0.014 )
0.005*
(0.003 )
0.032***
(0.005 )
0.060***
(0.009 )
-
May Temp2
June Temp
June Temp2
July Temp
July Temp2
August Temp
August Temp2
May Rain
May Rain2
June Rain
June Rain2
July Rain
July Rain2
August Rain
August Rain2
Prices
Full Climate Controls
Observations
Likelihood Ratio Statistic
Pseudo R2
0.017***
(0.005 )
38.24***
(3.62)
−6.78***
(1.57)
−0.320
(0.311 )
−0.125***
(0.043 )
0.002
(0.002 )
−5.62***
(0.781 )
0.186***
(0.025 )
9.34***
(2.84)
−0.208***
(0.064 )
−3.58
(5.82)
0.054
(0.119 )
7.15**
(3.36)
−0.131*
(0.069 )
6.99***
(1.93)
−7.89 × 106 ***
(2.27 × 106 )
2.53**
(1.27)
−0.013
(0.008 )
0.010
(1.02)
−0.002
(0.009 )
0.251
(0.961 )
−0.020*
(0.011 )
-
Levels
Yes
Relative
Yes
Relative
Reduced
5306
927.9***
0.103
5306
979.2***
0.108
5306
978.0***
0.108
5306
814.5***
0.09
-
May Temp
-
−0.096***
(0.013 )
0.013***
(0.002 )
-
Levels
Yes
K Factor
Top Depth
-
−0.108***
(0.014 )
0.007***
(0.003 )
-
(4)
Rel. Prices - Reduced
−0.991***
(0.314 )
0.117***
(0.034 )
0.0003
(0.002 )
−3.47***
(0.761 )
0.108***
(0.025 )
3.94
(2.67)
−0.081
(0.061 )
−0.897
(5.77)
−0.003
(0.119 )
12.76***
(3.56)
−0.248***
(0.074 )
6.81***
(1.90)
−7.41 × 106 ***
(2.22 × 106 )
1.38
(1.26)
−0.004
(0.008 )
0.834
(1.01)
−0.006
(0.009 )
1.66*
(0.937 )
−0.026**
(0.010 )
-
OM
−0.109***
(0.014 )
0.006*
(0.003 )
-
(3)
Rel. Prices
0.017***
(0.005 )
37.49***
(3.69)
−6.81***
(1.56)
−0.249
(0.319 )
−0.124***
(0.043 )
0.002
(0.002 )
−5.52***
(0.786 )
0.181***
(0.026 )
9.05***
(2.85)
−0.201***
(0.064 )
−2.10
(6.01)
0.022
(0.123 )
5.85*
(3.61)
−0.102
(0.075 )
7.01***
(1.93)
−7.93 × 106 ***
(2.27 × 106 )
2.50**
(1.28)
−0.012
(0.008 )
0.089
(1.02)
−0.003
(0.009 )
0.221
(0.961 )
−0.019*
(0.010 )
AWC
EC
(2)
Properties
0.026***
(0.005 )
34.65***
(3.46)
−3.96***
(1.46)
−0.811***
(0.286 )
−0.145***
(0.041 )
0.005***
(0.002 )
-
−4.57
(3.03)
0.092
(0.062 )
16.27***
(3.03)
−0.329***
(0.062 )
−0.940
(0.953 )
0.004
(0.009 )
−1.13
(0.883 )
−0.010
(0.010 )
Table presents fitted coefficients of the multinomial logit model for selecting corn. The dependent variable is categorical, indicating whether the operation is primarily a corn, soybeans, or
“other” farm. For space considerations, the value of the optimized log likelihood is omitted,
but convergence is quick. See text of Section 5 for details.
25
Table 3: Multinomial Logit Results, Soybeans
(1)
Textures
Slope
Depth to water table
Silt
Clay
Ksat
−0.115***
(0.020 )
0.006
(0.004 )
0.003
(0.008 )
0.047***
(0.011 )
-
May Temp2
June Temp
June Temp2
July Temp
July Temp2
August Temp
August Temp2
May Rain
May Rain2
June Rain
June Rain2
July Rain
July Rain2
August Rain
August Rain2
Prices
Full Climate Controls
Observations
Likelihood Ratio Statistic
Pseudo R2
−0.032***
(0.008 )
10.86**
(4.53)
−7.33***
(2.12)
0.212
(0.423 )
−0.086
(0.065 )
0.0009
(0.003 )
−0.097
(1.21)
0.012
(0.037 )
−3.58
(3.81)
0.081
(0.084 )
12.12
(8.09)
−0.245
(0.164 )
2.64
(4.39)
−0.053
(0.089 )
0.304
(2.77)
−2.06 × 105
(3.02 × 106 )
5.46***
(1.85)
−0.031**
(0.013 )
−4.30***
(1.34)
0.035***
(0.013 )
−0.803
(1.21)
0.003
(0.013 )
-
Levels
Yes
Relative
Yes
Relative
Reduced
5306
927.9***
0.103
5306
979.2***
0.108
5306
978.0***
0.108
5306
814.5***
0.09
-
May Temp
-
−0.098***
(0.019 )
0.015***
(0.003 )
-
Levels
Yes
K Factor
Top Depth
-
−0.104***
(0.02)
0.006
(0.004 )
-
(4)
Rel. Prices - Reduced
−0.152
(0.417 )
0.071
(0.052 )
−0.0002
(0.003 )
0.274
(1.24)
−0.003
(0.038 )
−5.26
(3.69)
0.122
(0.082 )
10.66
(8.09)
−0.221
(0.165 )
5.99
(4.58)
−0.119
(0.094 )
1.35
(2.80)
−1.41 × 106
(3.05 × 106 )
5.13***
(1.87)
−0.027**
(0.013 )
−4.00***
(1.35)
0.033***
(0.013 )
−0.511
(1.20)
0.003
(0.013 )
-
OM
−0.105***
(0.020 )
0.006
(0.004 )
-
(3)
Rel. Prices
−0.033***
(0.008 )
10.47***
(4.69)
−7.37***
(2.56)
0.253
(0.431 )
−0.084
(0.066 )
0.0007
(0.003 )
−0.085
(1.21)
0.011
(0.037 )
−3.62
(3.81)
0.082
(0.085 )
12.69
(8.32)
−0.258
(0.168 )
2.11
(4.63)
−0.041
(0.095 )
0.317
(2.77)
−2.14 × 105
(3.02 × 106 )
5.46***
(1.85)
−0.031**
(0.013 )
−4.24***
(1.35)
0.034***
(0.013 )
−0.827
(1.21)
0.003
(0.013 )
AWC
EC
(2)
Properties
−0.029***
(0.008 )
11.43***
(4.35)
−6.80***
(1.94)
−0.300
(0.385 )
−0.098
(0.061 )
0.004**
(0.002 )
0.785
(4.42)
−0.003
(0.089 )
8.58**
(3.84)
−0.177**
(0.078 )
−3.09**
(1.24)
0.028**
(0.012 )
−1.38
(1.13)
0.004
(0.012 )
Table presents fitted coefficients of the multinomial logit model for selecting soybeans. The
dependent variable is categorical, indicating whether the operation is primarily a corn, soybeans,
or “other” farm. For space considerations, the value of the optimized log likelihood is omitted,
but convergence is quick. See text of Section 5 for details.
26
Table 4: OLS with Selection, Benchmark Model
(1)
Corn
(2)
Soybeans
(3)
Other
-8.94
(39.0)
Depth to water table
-2.90
(4.34)
Ksat
6.14
(16.4)
AWC
2.76 × 103
(1.34 × 104 )
K Factor
-242
(1.24 × 103 )
EC
91.4
(470)
OM
-35.7
(48.8)
Top Depth
1.89
(2.68)
July Temp
4.80 × 103 *
(2.67 × 103 )
2
July Temp
-93.5
(54.0)
August Temp
−4.41 × 103
(6.35 × 103 )
2
August Temp
88.0
(128)
July Rain
980
(849)
July Rain2
-10.2
(7.98)
August Rain
-417
(890)
August Rain2
4.06
(9.09)
Intercept
−6.45 × 103
(6.18 × 104 )
29.1
(36.1)
-5.15
(3.77)
-20.4
(16.8)
−1.22 × 104
(1.28 × 104 )
-540
(1.38 × 103 )
377
(456)
11.4
(52.9)
-2.04
(2.68)
589
(2.97 × 103 )
-7.75
(59.5)
−4.52 × 103
(5.78 × 103 )
89.8
(116)
−1.63 × 103
(1.14 × 103 )
15.0
(10.58)
-366
(926)
11.5
(10.2)
4.84 × 104
(5.69 × 104 )
-44.2***
(8.48)
-0.89
(1.15)
6.71
(4.28)
9.54 × 103 **
(2.50 × 103 )
−1.62 × 103
(652)
-130
(144)
-82.8***
(17.6)
2.19***
(0.778)
−3.60 × 103 ***
(1.21 × 103 )***
75.5***
(25.5)
5.54 × 103 ***
(1.46 × 103 )
-114***
(30)
-729*
(415)
4.17
(3.96)
-301
(354)
-1.56
(4.04)
−2.37 × 104 **
(1.12 × 104
S1
-428
(883)
325
(1.14 × 103 )
−1.10 × 103
(845)
1.06 × 106
(1.04 × 106 )
-0.415
(0.570)
0.314
(0.806)
-1.06*
(0.575)
−2.95 × 103
(2.73 × 103 )
164
(377)
-582
(1.35 × 103 )
2.58 × 106
(5.26 × 106 )
-1.84*
(1.11)
0.102
(0.260)
-0.362
(0.841)
2.26 × 103 ***
(804)
1.17 × 103 ***
(455)
180
(333)
1.82 × 106 *
(9.67 × 105 )
1.67***
(0.330)
0.868***
(0.337)
0.133
(0.249)
1353
573
3093
Slope
S2
S3
σ̂c2
ρ̂1
ρ̂2
ρ̂3
Observations
Table reports fitted coefficients for second-step OLS regressions. Note that S1 , S2 , and S3 are
Bourguignon et al. (2007)’s refinement of the Dubin and McFadden (1984) selection terms. The
ρ̂ terms indicate correlations between disturbances in the indirect utility and acreage equations.
Standard errors are bootstrapped, with 1353, 573, and 1000 replicates for the three equations,
respectively. See text of Section 5 for details.
27
Figure 1: Fitted Choice Probabilities and July Weather, Benchmark Model
(a) Corn Probabilities
(b) Wheat Probabilities
(c) Other Crop Probabilities
28