YIELD RESPONSE AND BIOFUELS: ISSUES AND EVIDENCE ON THE EXTENSIVE MARGIN
Roman Keeney
Department of Agricultural Economics—Purdue University
Paper presented at the World Congress of Environmental and Resource Economists
ABSTRACT
Recent demand growth for biofuel feedstock has generated interest in model based estimates of the
land use impacts of increased production. This increased production arises from the extensive
margin (area expansion) and intensive margin (yield enhancement). An interesting element that is
often omitted in economic models that account for each of these is the potential for expansion onto
land of lesser production quality to contribute to declining average yields. This represents an
important piece of empirical information underlying model assessments of land use change
requirements for biofuel demand shocks. This paper contributes to the biofuel and land use change
literature by surveying empirical estimates of the ratio of marginal to average yields, examining
available data on trends in area expansion and yield growth for crops, and organizing this
information to assess the sensitivity of model findings on land use change to this factor.
YIELD RESPONSE AND BIOFUELS: ISSUES AND EVIDENCE ON THE EXTENSIVE MARGIN
Roman Keeney
The pursuit of alternative energy sources in the United States (US) and other developed
regions has generated a mixed set of results. The sharp upturn in mid-decade fossil fuel prices and
use of biofuels as gasoline additives seemed to forecast a future stream of benefits capable of paying
off years of public investment in the nascent alternative energy industry. Crude oil prices reached
levels that made corn ethanol processing economically competitive on an energy equivalency basis
and standard measures of life-cycle carbon accounting consistently identified corn ethanol
replacement of fossil fuels as a source of GHG reduction. Amidst the sharp expansion in domestic
US and EU biofuel industries, economists and natural scientists began taking a closer look at where
a surging global biofuel market would find arable land on which to grow biofuel feedstock and how
this might alter the GHG life-cycle accounting.
A much publicized study by Searchinger et al. (2008) brought the debate over land use
change impacts on GHG emissions into clearer focus. These authors used a global agricultural
model to show that rapid expansion of corn ethanol production would not generate twenty percent
reductions in emissions but would in fact double the emissions occurring over the next thirty years
due to land cover change and subsequent release of carbon currently sequestered in forest and
grassland plant material. Of particular interest for the present paper is the treatment of land
productivity in Searchinger et al. (2008). When prices for crops increase (e.g. due to a biofuel demand
shock) farmers are expected to use yield increasing inputs more intensively on currently planted
lands, thus the expectation is that average yield (productivity) increases in the biofuel crop . These
same price increases will also produce a reallocation of land between uses as well as increasing the
probability of converting land not currently managed for agricultural use into production. This
expansion at the extensive margin should have average yield depressing effects since the land is
expected to be of lower productivity.
Searchinger et al. (2008) make use of the counteracting effects on average yields to assume
that the net impact on average yields (apart from trend growth due to technical change) is zero
following economy-wide adjustment to the increase in biofuel demands. Several studies generated
both from advocacy and academic institutions have taken issue with this simplistic treatment of
yields. Notably, Keeney and Hertel (2009) identify the response of yields to prices (in addition to
other global modeling parameters) as a key source of uncertainty in determining global land use
change. Hertel et al. (2010) extend Searchinger et al.’s (2008) study finding that emissions increase
from indirect land use change (ILUC) is only some twenty-five percent (800 v. 3000 gCO2/MJ) of
the earlier estimate using their global computable general equilibrium (CGE) framework and
reasonable yield response assumptions. As they detail their ILUC derived GHG estimate, Hertel et
al. (2010) point explicitly to the knowledge gap in yield response and subsequent uncertainty it
contributes to the ILUC debate.
The purpose of this paper is to identify what is known about expected equilibrium yield
adjustment, particularly that at the extensive margin. Agricultural productivity is one of the more
well-studied and published topics in the literature, but offers surprisingly little to draw directly from
in terms of adopting the needed parameters for a global model of agricultural supply and demand
(with land markets). With this type of model representing the state of the art (and tool of choice) for
understanding ILUC, we review past analytical and empirical approaches that are most consistent in
producing partial elasticities consistent with this framework. From there, we conduct sensitivity
[1]
experiments with a global computable general equilibrium model (CGE) to improve understanding
of how parametric uncertainty translates into uncertainty about simulated ILUC estimates.
In the next section, we offer a simple discussion of the economic modeling of yield
adjustment recognizing the role of prices, area, and technological advance. Following that, we
consider the literature examining changes in yields as the planted area base is adjusted. The third
section takes a look at available data on trend in yields and area planted to provide some insight
toward the possible extensive margin yield deficits that might guide systematic empirical
investigation into appropriate model parameters. From there, we report results from a series of
sensitivity simulations using the same modeling framework as in Hertel et al. (2010), closing with
conclusions and recommendations.
Yield Response Components
Summary yield response in policy models is the outcome of a number of parameters
interacting through a set of equilibrium conditions to determine response (see e.g. Keeney and
Hertel, 2008 for the constant elasticity of substitution approach). In empirical work, yield
adjustments are most frequently modeled as a function of time, explicitly assuming that all changes
in yield are due to disembodied (i.e. non-responsive to the crop’s market) technological advance.
Fewer studies have examined the role expected prices play in causing farmers to adjust expected
yields (reviewed in Keeney and Hertel, 2009). Another subset of empirical yield studies has
considered the role of land heterogeneity in yield changes most of which focus on production
slippage which accompanies land set-aside programs. Those studies represent the bulk of the work
we review in the next section.
To set the stage for review and analysis of that empirical work, we first formulate a simple
model of yield response. Equation [1] below represents a levels yield growth equation between two
time periods where Yt i is the level of yield realized on land of type i in time period t. The
components of growth may be land type specific and are denoted by  the rate of disembodied
technical change and   p̂ the rate of change due to price response (with  being a yield elasticity
with respect to the output’s relative price and p̂ representing a proportionate change in that relative
price).

Yt i1  Yt i 1   i   i

[1]
For simplicity, assume there are only two land types i  h, l(high and low quality), then we
can write an expression for the average yield in time period t+1 as the share weighted average of
yield on high and low quality land. Let  i be the share of planted area for a crop for quality i land,
and we have the expression given as [2] below for the current period’s average yield, Yt 1 .
Yt 1 

ih ,l

Y 1  i  i
i
i
t 1 t

[2]
In figure 1 below, we demonstrate the influences on observed yield changes laid out in [2].
On the left hand axis, we plot three sets of yield values against time. The top most line (YLD_AH)
represents land that is in production in period 1 and which remains in production through period
10. Yields on this land start at an index value of 100 and through the process of technical change
(yield growth assumed at two percent per year) and increasing prices increase by some forty-three
percent over the ten year horizon. The line directly below this (YLD_AVG), shows that due to
expansion onto less productive land, average yields observed grew slightly less than forty percent
[2]
over the time period (YLD_AL, third line from the top). The assumptions on price changes and area
expansion that lead to deviations from trend yield growth are given by the bottom two lines (p,
Sh_L) measured on the right hand axis of Figure 1.
150
1.00
0.80
Yield Index
130
0.70
0.60
120
0.50
110
0.40
0.30
100
0.20
90
Proportion
(Low quality land or price increase)
0.90
140
0.10
80
0.00
1
2
3
4
5
6
7
8
9
10
Year
YLD_AL
YLD_AH
YLD_AVG
p
Sh_L
Figure 1. Yield adjustment over time.
We can decompose the example yield changes given in figure 1, as shown in figure 2.
Beginning with the observed change in expected relative price from period 2 through period six, we
see that doubling prices over five years is the dominant effect while the price change is occurring,
and assuming the new higher price level is sustained represents a shift to new average input use and
thereby yield. Ignoring the interaction in yield change components, we see that the ten year twopercent annual growth in yields produces a nearly equivalent yield impact to that of the doubling of
the equilibrium relative price of the output. Finally, we see that expanding acreage has a yield drag
effect in this example assuming two types of land where low quality land is ninety percent as
productive as high quality (see figure 1).
From the example, and the underlying equation [2], we can envision performing a similar
decomposition of yield data over time. Aside from controlling for weather effects which has proven
complicated, it is evident from [2] that parametric identification is a problem. The growth rate in
yield from period t to period t+1 encompasses both a price response factor and a technology factor.
Houck and Gallagher (1976) admonish the profession’s study of yield and supply response for
ignoring the contribution of price to yield, but the variability in their set of published estimates
elucidate the difficulty of measuring this effect. An entire literature of the economics profession has
arisen over the past sixty years without settlement to the debate on the appropriate way to model
[3]
farmer price expectations. Add to this the complexity of identifying land type specific response rates
for prices and technical change, as well as the fact that land quality is appropriately measured on a
continuum of productivities rather than a dichotomous typing and the challenge of knowing how to
treat yield adjustment in policy models is formidable.
40.00
35.00
Yield
(Level Change in Index Value)
30.00
25.00
20.00
15.00
10.00
5.00
0.00
1
2
3
4
5
-5.00
6
7
8
9
10
Time
Trend
Price
Area
Total
Figure 2. Decomposition of Yield Changes over Time
With a particular interest in the area expansion component of yield response in this paper,
we are fortunate to have some guidance from past studies of land set aside schemes. While this
policy regime falls short of the type of natural experiment we would hope to use to characterize land
heterogeneity’s impact on yields, it does offer some insight that allows us to move forward into an
examination of the data. Assuming that technology and price’s impact on yields is constant across
land types, note that we can rewrite equation [2] as below, the weighted average of the current
period’s observed yields on two land types. Rearranging [3] as in [4], we have an expression for the
yield on low quality land.
Yt   thYt h   tlYt l
  Y  
Yt l   tl
1
[3]
h h
t t
Y

[4]
If we assume that changes in planted area for a crop from year to year reflect the response of
producers moving their most productive land into and out of a crop, then [4] would have an
[4]
empirical analogue from which we could derive an estimate of productivity at the extensive margin
(i.e. the marginal yield). In this case, we would just designate high quality land as the previous year’s
planted area with its associated yield. The change in planted area for the current year relative to the
total would then provide the appropriate shares which along with the current year’s average yield
allows for a calculation of the unknown productivity of marginal lands. A form of [4] (dividing all
terms by the average yield as shown in [5]), is similar to the slippage calculation offered by Hoag,
Babcock, and Foster (1993) which relates marginal yields to the average yield.
 
Yt l
  tl
Y
1
h

h Yt 
1




t
Y 

[5]
Hoag, Babcock, and Foster’s (1993), concern was estimating the slippage in output reduction
associated with land set-aside due to farmers optimally choosing to first idle least productive
cropland. From this perspective, we consider a retraction in total land planting with the share of
idled land representing a government mandated reduction in planted acreage to control supply and
support prices received by farmers. We next turn to the literature critiquing the efficacy of set-aside
policy as a supply control mechanism to summarize empirical evidence (albeit in inverse form)
related to the yield drag effect demonstrated in figure 2.
Review of Literature
Hoag, Babcock, and Foster (1993) use field level data to measure land quality slippage (yield
gains from idling least productive land) in six North Carolina counties. The theoretical prediction
that farmer’s will optimally plant areas in order of declining productivity is called into question by
these authors due to several mitigating factors in the farm-level decision framework in which the
farmer operates. Prominent among these limitations on unit-by-unit decision making for farmers are
the rotational considerations of land allocation in multi-crop systems as well as the lack of contiguity
of most productive lands which increases the cost of selective set-aside. Hoag, Babcock, and
Foster’s (1993) distribution of estimates are presented in figure 3 below, showing that the majority
of estimates at the field level are less than three percent (average yield gain from idling land). The
authors use these findings to conclude that land quality slippage at the farm-level cannot be a
significant contribution to the larger aggregate estimates of the era (ranging from 25 to 58 percent).
With only a minor contribution to large yield gains arising from set-aside at the farm level,
Hoag, Babcock, and Foster (1993) turn to aggregate compositional effects as a means of explaining
observed slippage. Thus, at the national level we can surmise that productive farm operators with
high yielding land will abstain from the commodity program requiring set-aside with participation
higher as we move further from these conditions. This type of aggregate observation arising through
heterogeneity in producer response and land is quite similar to the argument Hertel, Stiegert, and
Vroomen (1996) make in explaining nitrogen substitution for land at the aggregate level in the face
of evidence that individual farm operators make only minor adjustments in response to relative
prices of fertilizer. Babcock, Foster, and Hoag (1993) are able to confirm their prior conclusion
about participation and slippage occurring via the composition of participants by estimating a choice
model of acreage diversion. They show that farmer’s with lower mean quality land and higher
variability in the quality of land had a higher propensity to participate in a land set-aside program.
Studies of European set-aside policy have similarly confirmed the importance of compositional
effects in the movement of average yields (and thus national output), with rotational considerations
often dominating the quality driven land set-aside choice at the field unit level (Rygenstad and
Fraser, 1996; Fraser, 2001).
[5]
12
10
Observations
8
6
4
2
0
<= 0
0 to 3
3 to 6
6 to 9
>= 9
Percent Yield Gain when Marginal Land Diverted
Figure 3. Distribution of Slippage Coefficients for North Carolina Counties in Hoag,
Babcock, and Foster (1993)
Together these studies suggest that understanding how land use change affects average
observed yields is an aggregate phenomenon which may be hard to observe at the micro level. This
is convenient since the policy models used in analysis of biofuel induced land use change embody
decision making by representative agents at regionally aggregated levels, and estimates of the
tendency of yields to move inversely with growth in area planted can be exploited. Table 1 presents
estimates from five national level studies of yield for different U.S. crops.
In table 1, we see that the estimates of the ratio of marginal to average yields (M/A) vary
widely. Love and Foster (1990) estimate a range for corn from 0.43 to 0.53, indicating that for the
period of their estimation land was being set aside that was poorly suited for the crop. Aside from
this outlying low estimate, the range of M/A in table 1 range from marginal land that is about twothirds as productive as average land to land that contains about ninety percent of the productivity.
The range from 0.66 to 0.90 is consistent with Ogg, Webb, and Huang’s (1984) estimate that idled
land were during the 1978 land retirement program was predominantly from soil groups that were
sixty-five and ninety-five percent as productive as the national average.
[6]
Table 1. Literature Estimates of the Ratio of Marginal to Average Yield (M/A)
Crop
Weisgerber
Ericksen and
Collins
Love and
Foster
Norton
Ash and Lin
Wheat
0.90
0.80
0.67
0.66
0.75
Corn
0.82
0.70
0.47
0.69
0.72
Sorghum
0.85
0.90
--
--
0.88
Cotton
0.80
0.65
--
--
0.73
Soybean
--
--
0.66
--
--
Notes: Love and Foster estimates are midpoint of given ranges, Ash and Lin are unweighted averages over regional yield estimates.
Observing past estimates from the set-aside era in the U.S. provides some confidence that 1)
there will be a measurable difference in yields on land converted to biofuel production and 2) that
we would expect marginal land to a crop to be no more than ninety percent as productive as that
previously planted, and may produce as little as two-thirds of the average yield. The example in
figure 1, used a 0.90 value for M/A. With marginal land contributing 25% of the year 10 planted
area, this amounts to a 2.5% reduction in expected yield relative to the case where marginal and
average yields are equal. If that yield gap were to fall from 10% (=100%*(1-0.9)) to a value of 35%
(=100%*(1-0.65)) then the reduction in expected yield is nearly nine percent. Thus, the uncertainty
about M/A evident in table 1 constitutes a severe limit on our ability to predict the required land use
change necessary to meet a crop demand target for an expanding biofuel sector.
Following the slippage/land set-aside era in the literature, the interplay between yields and
area has received only limited attention. Recent work by Lywood, Pinkney, and Cockeril (2009)
would seem to indicate a renewed empirical interest in measurement of economic yield response.
These authors consider a host of single region and crop time series estimates in an effort to
summarize weather independent yield changes over time as they respond to changes in prices and
technology. These authors find that there are significant price responses to yields in the European
Union and the United States but detect not evidence of lagging yields on newly planted acreage.
Importantly, these authors are able to identify significant heterogeneity across countries showing
that growth in total output in the U.S. and EU are primarily due to yield growth whereas in most
other countries’ crops sixty-plus percent of growth in output is due to area expansion. We next turn
to this very issue as we briefly examine yield and area time series data from selected countries.
Data on Yields and Area
While most of the empirical literature has focused on U.S. and EU policies and how yields
and output react to these, it is clear from studies such as Searchinger et al. (2008) and Hertel et al.
(2010) that we need to have a better understanding of global agricultural production to remove
uncertainty about land use and GHG issues. For example, even if the U.S. biofuel mandate is met
with domestic production, it is likely that some export destination is displaced in the disposal of U.S.
output meaning that some competing exporter will need to fill the gap. Thus, a complete accounting
of land use change is going to require an increased knowledge base. We examine six pairs of time
series (yields and area) to offer insight into how we might begin to summarize differential response
of yields in a multi-region context.
[7]
Figure 4. Maize Area and Yield in Egypt, 1995-2008 (five year moving Olympic averages)
Figure 5. Maize Area and Yield in Canada, 1995-2008 (five year moving Olympic averages)
In figures 4 and 5 we plot the area and yield for the national maize crops of Egypt and
Canada. These time series are detrended in a fashion similar to that taken by Lywood, Pinkney, and
Cockeril (2009), as we plot for each time period the five year Olympic moving average of yield and
area. We plot the five year Olympic moving average as a shortcut method for smoothing the data to
free it of the influence of dramatic weather factors that can occur in an individual year. By the same
token, this five year smoothed trend should remove some of the effects of prices since the data
could be interpreted as a medium run equilibrium yield and area observations. The area versus yield
in each of these countries for maize evidences a striking inverse relationship. In particular, the data
for Canada post 1998 (when the data will reflect NAFTA implementation) show distinctive declines
in average yields corresponding to increased maize area. The same general relationship can be seen
in Egypt in figure 4. These countries are distinguished for having some of the highest corn yields
among nations, both having an average 2008 maize yield near that of the United States.
[8]
Contrasting figures 4 and 5 with the plots in figures 6 and 7, we get an idea of how the story
changes when considering maize yields in countries which would not be considered global yield
leaders in the crop. From the right hand side axes in figures 6 and 7, we see that yields in China are
roughly half those in Canada and Egypt while yields in Brazil are currently one-third that level. This
difference in the current yield level relative to global leaders helps explain the contrast in the
relationship between yield and area in these two countries relative to Canada and Egypt. Crosscountry yield gaps and convergence in agricultural productivity under open markets are well-known
phenomena so that we might reasonable assume that the lack of an inverse relationship in figures 6
and 7 is the product of rapid technology induced yield growth. This interpretation is of course
facilitated by the post 2000 growth in both yields and area marking a five year average that fully
includes post Uruguay Round reform that opened agricultural markets by limiting tariffs and quotas
as well as developed country domestic subsidies.
Figure 6. Maize Area and Yield in China, 1995-2008 (five year Olympic moving average)
Figure 7. Maize Area and Yield in Brazil, 1995-2008 (five year Olympic moving average)
[9]
Figure 8. Soybean Area and Yield in China, 1995-2008 (five year Olympic moving average)
Figure 9. Soybean Area and Yield in Brazil, 1995-2008 (five year Olympic moving average)
Figures 8 and 9, again show data for China and Brazil but in this case for soybeans, a crop in
which these two countries are much nearer the technical yield potential. The graphs show much
more of an inverse relationship for this crop where yield gaps (relative to global leaders) are
diminished. The limited evidence does seem to indicate that land heterogeneity impacts realized
yield through the differential between marginal to average yields. In both developed and developing
countries where yields can be judged to have minimal gaps relative to the most productive countries
for a given crop an inverse relationship is evidenced in our smoothed yield series. Thus, we can
conclude that an accurate accounting of yield response in a policy model is going to require a fair
amount of regional and crop specificity. From figures 4-9, it seems clear that modeling the inverse
relationship is less a matter of the agricultural or economic development of the country but more a
matter of how near the technical yield ceiling for a particular crop that country may be. An inverse
relationship may well exist for crop country pairs well below yield ceilings but the same price signals
[10]
that are driving area expansion are likely inducing technical adoption at a rapid rate overwhelming
any identifiable drag on yield growth that might occur through lowering land quality.
Experimental Results from a Global Model
Having reviewed a stylized yield growth model, literature on the extensive margin, and time
series data on planting and yields, we now turn to a global modeling framework to assess the
implications for global land use predictions from varying assumptions on yield drag at the extensive
margin. Figure 10 offers some results on land use change that occur in Brazil following a U.S.
biofuel demand shock equivalent to 15 billion gallons. We use the same modeling framework of
Hertel et al. (2009) and vary both the elasticity of yields to price (horizontal axis) and the ratio of
marginal to average yields (vertical axis) for regions in the developed world (referenced in the figure
as South).
Figure 10. Sensitivity of Brazilian Land Conversion to Yield Parameters
In the figure, the individual cells (bubbles) represent millions of hectares converted to
cropland when the U.S. institutes a 15 billion gallon increase in corn ethanol demand. Moving
northwest in the graph we see that increasing yield response to prices lowers the pressure on land
conversion as well as does increasing the ratio of marginal to average yields. The value in the top
right of the graph indicates that only 190,000 additional Brazilian cropland hectares are needed in
equilibrium as opposed to the lower left corner where limited yield response to prices and severe
drop off in yield potential in Brazil would require more than twice as much land conversion. The
center of the graph represents a somewhat midpoint assumption for southern regions as 0.25
represents the yield elasticity adopted by Keeney and Hertel (2009), and 0.75 is near the average of
reported ratios of marginal to average yields reported here. Finally, we note the diagonal line
traversing the graph which represents something of an iso-land conversion line, connecting yield
elasticity and M/A values that produce the same land use change. Thus, error in one of these
estimates can be linearly offset by an opposing error for the other parameter if for instance
identification of the two parameters separately were an issue. However, compounding these errors
(e.g. maintaining a yield response assumption) with an errant M/A value will move the estimate of
[11]
land use change to a new area of the graph and compound the parametric error. The relationship
provide strong impetus for attempts to try and jointly identify price and area influences on yields to
minimize the likelihood of misplacing the set of parameters on the wrong iso-land change level
curve.
Final Thoughts
The present paper has reviewed issues and evidence on the extensive margin of agricultural
production, with an eye towards strategies for parameterizing a global commodity and factor
markets model suitable for prediction of land use change. Three points emerge consistently through
this survey. First, as with many economic phenomena identification of yield determinants presents a
daunting challenge, but one that is prerequisite to informed policy on GHG emissions from land use
change following expansion of alternative energy sources. Second, just as regional specificity is
critical for models in terms of economic accounts data so too will be the judged assumptions on
economic response applied to these countries. Time series data show very different patterns of joint
land use change and yield growth which must be reconciled and represented to ensure the pattern of
land use change as predicted is consistent with available evidence. Finally, econometric identification
of parameters determining yields in model construction need to be jointly determined from the data
to limit compounding of errors by assumption and in that same light the framework for econometric
estimation should match that of the model structure (or a reduced form of that structure) as closely
as possible.
[12]
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