266 J.R. Anderson Agriculture, Ecosystems and Environment 82 2000 261–271
state of the art has advanced to the point where any sort of standard can be imposed is moot, although
the Schulze 2000 exposition may lead to a more common language.
While the progress that has been made is certainly something to be excited about, this observer remains
pessimistic about the robustness of some of the interim findings, and the operative call does indeed seem to be
one for further self-critical research. Some of the rese- arch needed concerns best use of the new tools them-
selves, especially the information-intensive GIS meth- ods e.g., Wood et al., 1999. For others the needed
research is at the biophysical process level itself, as indicated by the Schlesinger 2000 discussion of car-
bon sequestration and, for a rather different example, by the pesticide resistance dynamics relationships in
different forms of IPM e.g., Archibald, 1988; Schill- horn van Veen et al., 1997. Lest it seem that there
is some prejudice here against the natural sciences, it should be noted that there are ample controversies to
be resolved among the social sciences. One bridging issue relates to the aggregation concept of “gross natu-
ral product”, especially as a relevant indicator when it comes to environmental policy e.g., de Groot, 1992,
p. 254. To take another rather different case relevant to a discussion of agricultural aggregation, consider
Cochrane’s Treadmill Hypothesis. Cochrane 1958 viewed farmers as the victims of technological change,
because only early adopters of new and more produc- tive innovations would benefit and then only briefly,
as the increased output induced by the improved productivity depressed prices assuming inelastic
aggregate demand, and while consumers benefited from lowered commodity prices, farmers had to keep
running the treadmill to try to survive. Fortunately, the grain of truth in this hypothesis does not apply in
many if not most instances, as persuasively argued by Alston and Pardey 1996, p. 180. But it is instructive
to remind evaluators of applied agricultural research, as they seek to aggregate up from perhaps plot-level
estimates of improved agricultural productivity occa- sioned by some research activity to estimates of the
returns to research investment, that empirical issues of market structure are key to determining the nature
and distribution of the benefits of research — a topic dealt with in instructive detail by Alston et al. 1995.
It would be inappropriate to conclude this section on other than a positive note, however. The encour-
aging thing for the evolution of better policy analy- sis concerning world agriculture, such as alluded to
by Alexandratos 1995 and Anderson 1995, is that there is now real dialogue among policy makers work-
ing at the regional and global levels, and the existence of cogent scaled-up models, notwithstanding the vary-
ing degrees of refinement, has surely informed and facilitated such dialogue. But there is room for im-
provement in practice.
4. Risk and aggregation
4.1. Conceptual A world devoid of risk would be one in which global
analysis and pontification was relatively easy but it would probably for most be really boring. Fortunately,
this problem of boredom seldom exists, as risk is alive, if not well, in models of global or other large aggre-
gate dimension. In this section, attention is refocused on the disturbance terms u and U in Eqs. 1 and 2,
and any other sources of uncertainty such as unpre- dictable climatic variables, which may be elements of
z and Z that may enter into the probability distribu- tions of the performance measures y and Y. The trans-
formation from the level of u to the defined universe level of U is seldom straightforward except in trivial
cases of linear aggregation. The encouraging news of the contemporary Computer Era is the readiness with
which stochastic processes can be modeled and thus in-principle combined in explicit aggregations.
Anderson 1976 considered several phenomena through the lens of the Uncertainty Principle of Mod-
eling, concluding unsurprisingly that it was a highly applicable principle. For instance, in a general review
of weather-driven crop-growth models that in sum are representative of models described by Eq. 1,
he distinguished some 15 components that would be highly likely to warrant explicit inclusion of uncer-
tainty as part of a refined representation, and naturally the combined model of these components could thus
only properly be stochastic, an opinion reinforced by the contributions in Muchow and Bellamy 1991,
particularly Williams et al. 1991, and more recently by the survey of Oriade and Dillon 1997. Analogous
but different considerations led Austin and Arnold 1989, for instance, to comment on the inherent
J.R. Anderson Agriculture, Ecosystems and Environment 82 2000 261–271 267
variability and the modest contribution to it by plant breeders of British cereal yields. Crop growth mod-
els, even at the plotmodel level, clearly already in- volve some aggregation of component responses and
risks. The question to be addressed here is how these model-level risks aggregate to risks at the level of
some defined universe, which may be a field, a farm, a district, a region or beyond. Although he went on
to examine models of economies and of the world, Anderson regrettably did not explicitly deal with the
question of aggregating from one level to another.
At one level, such aggregation is conceptually simi- lar to the aggregation of response without explicit
risk consideration, being analytically difficult but amenable to block-busting simulation procedures. But
since in this case: a it is sets of likely multivari- ate distributions describing the uncertain behavior of
micro-systems such as Eq. 1 and b the aggrega- tion of these to those distributions describing Eq. 2
must also deal with the complexities and stochas- tic dependencies involved in the transformation, it
seems appropriate to characterize this new aggrega- tion problem as being of an order of magnitude more
demanding of information, technology, and analytical skill. Add on the further challenge of embodying the
adaptive risk-management behavior of farmers con- fronted with such uncertainties as climate change, and
it is readily apparent why analysts such as Southworth et al. 2000 deserve our admiration. Clearly, the task
of attempting to validate such data-intensive exer- cises, let alone present findings in a comprehensible
form, is a potentially daunting one.
This is not the place to become distracted with the technicalities of measuring risk. Procedures for elici-
ting and processing distributions that in many cases are necessarily subjective are detailed in many sources
e.g., Hardaker et al., 1997. Many devices can be used to describe risk, most generally by reference to
complete distribution functions. For simplicity here, use is made of a convenient simple and therefore
demonstrably imperfect measure, the coefficient of variation CV or C[.], namely the ratio of a standard
deviation to its corresponding expected value. The convenience stems from the fact that this is a dimen-
sionless measure but is one with some intuitive appeal that can be compared across very different variables.
To take some concrete examples of values of CVs at different levels, consider some of the data reported
by Anderson 1979 for the Australian rural sector. Net farm incomes of wool-growing farms had CVs
of about 0.8 and farm wheat yields had CVs of about 0.4, so farm experience at this level is quite risky see
also Anderson et al., 1989. At the aggregate level, however, things are much less variable, although still
the source of considerable risk at the regional level and a still significant contributor to macro-economic
instability. At that time, Australian net farm income had a CV of about 0.09, and the gross value of ru-
ral production about 0.29. Anderson was at the time trying to assess what proportion of such aggregate
variability was attributable to climatic variation per se, and concluded that about 40 of the CVs was the
result of climate. He has not had the opportunity to reassess the situation, but would hazard a guess that
with the most recent decade of experience, climate has become an even greater source of risk to the
rural sector Anderson, 1991, while agriculture has continued to decline as a share of the total economy.
For those of global-modeling bent, it is perhaps more interesting to ask questions about the extent to
which technology and climate change have contributed to changing risk experience in the diverse niches of
world agriculture Anderson and Scandizzo, 1984. Soon such modelers will also wish to ask in addition
how globalization and new trade agreements have al- tered the risk environment. All such good questions
are likely to involve taking some stance on how risk is aggregated in the models assembled for analysis.
4.2. Practical Hitherto here, the importance of grappling with risk
has been portrayed as only being to ensure reliable estimation of the all-important means of uncertain
quantities. It is especially the case that special steps need to be taken in models, where component uncer-
tain quantities are asymmetrically distributed andor correlated, and when they are combined in non-linear
mathematical operations Anderson and Doran, 1978. These special steps are readily enough handled in
modern spreadsheet-based programs such as Risk and CrystalBall, with the proviso that the applicable
multivariate distributions can be adequately elicited and specified.
Among the practical applications of aggregate risk assessment vis-à-vis that at the level of individual
268 J.R. Anderson Agriculture, Ecosystems and Environment 82 2000 261–271
farms is design of crop insurance schemes. Among many aspects to be considered is the nature of the
distribution of yields of insured crops. Under the sampling independence assumptions of the Central
Limit Theorem, it would be anticipated that yields that are averages would tend towards being normally
distributed. Indeed, Just and Weninger 1999 found the normality of yield to be almost impossible to
reject in a diversity of US crop yields measured at various levels of aggregation. To the extent that yields
are approximately normalGaussian, probability spec- ification and risky choice are greatly simplified, as is
any aggregation of probability distributions.
An increasing amount of analytical work in the agricultural sector is being done at a multi-market
level, recognizing that a focus at the farm level tells a diminishing part of the sectoral story. Techniques for
analyzing flows of agricultural product through the complete marketing chain to the ultimate consumers
are becoming more readily available, and are even now to hand for the rather specific issue of evaluation
of the effects of changes brought about through re- search and development activities at the various levels
e.g., Alston et al., 1995, p. 71. Dealing adequately with risk in such multi-market settings is, however,
still a rather untilled field, involving as it does usually challenging aggregation problems.
For reasons of potential balance in these disciplinary judgments, let this partially informed observer make a
tentative best-practice award nomination. It has long been a strong impression that, when it comes to the
technology of modeling, scaling, validating and inter- preting for managerial purpose, the hydrologists are
doing best. Perhaps this enthusiasm has to be qualified somewhat by noting that they usually work on more
bounded systems, where verification possibilities are relatively available, and the level of aggregation is in
most cases not beyond a river basin, but there is clearly considerable challenge in modeling both the response
and stochastic relationships, which are usually handled impressively e.g., as illustrated by the contributions
in Sposito, 1998, and in this Theme by Schulze, 2000.
In the world of crop modeling it seems that there has developed some concern for a reverse aspect of those
discussed above, namely procedures usually based on empirical regressions for “downscaling” model re-
sults analogous to the Davidson case of small real plot results discussed earlier so that predicted mean
yields match those observed at farm level more closely e.g., Lansigan et al., 1997. In terms of the topic of
this section, the surprising thing is that these authors did not express the same concern for reconciling pre-
dictions of the riskiness of yields. Perhaps this issue often may be deserving of closer attention?
For the themes of the GCTE Conference, the han- dling of risk at the aggregate level seems still some-
what undeveloped, perhaps reflecting some of the modeling challenges mentioned, perhaps for a lack
of appreciation of the possible roles of risk and risk aversion in decision making at this level Anderson
and Dillon, 1988, perhaps because of a perception that risk is a second-order consideration in the grand
scheme of things Anderson et al., 1987, perhaps because of ignorance, or even prejudice.
4.3. Policy Just how important formal accounting for risk might
be is a good question. For conventional investments there can be a rough and ready test of whether risk
per se is worth being troubled by at all. For instance, Hardaker et al. 1997 offer a general approximation
procedure based on CVs of what is being considered C[x], of what it is being added to C[y], the correlation
between x and y g, the size of the mean of x relative to that of y B, and a measure of relative risk aver-
sion R a number between, say, 1 and 2, viz. D = RC[x]{0.5C[x]B + gC[y]}, and then risk can be dis-
regarded if the deduction D is “small”, say 0.02.
Problems at the global level do not fit well into this crude guideline, since the quantities at stake may
be very large, and even though society as a whole may be close to risk-neutral in large public decisions,
the future of the planet and humanity is a significant issue, and on a scale worthy of attention and potential
invocation of the Precautionary Principle. But what is inescapable is that, to the extent that risk-averse peo-
ple play active parts in the processes whose effects are being aggregated in global perspectives, risk is
inherent to the reality being modeled, and can be ig- nored only if there is no real concern for relevance of
findings.
One field of global concern that is littered with un- certainty is environmental policy related to the land
and water resources underpinning agriculture. Even in an aspect as prosaic as soil conservation, there is
J.R. Anderson Agriculture, Ecosystems and Environment 82 2000 261–271 269
profound uncertainty about effects, benefits and even costs Anderson and Thampapillai, 1990; Stocking,
1996; Shaxson et al., 1997. Much progress has been made in this field e.g., El-Swaify, 1999 but, espe-
cially in the developing world, the significance of soil erosion and land degradation more generally is
still too poorly understood which is to say, poorly measured and modeled, especially at other than rather
local levels of aggregation Biot et al., 1995.
It is well and good to speak of solving problems of scaling up to answer questions of global change, but
how the global estimates are to be variously validated and evaluated is a key question of method and poli-
cy. In spite of increasing efforts and commitment to such work, the adequacy of these seems both uncer-
tain and unlikely e.g., Rawlins, 1994; World Bank, 1997b. Surely, progress will involve refinements of
GIS, as well as national and international efforts to as- semble conformable and cogent data on indicators of
status and change. Only through such more effective monitoring will it be possible to assess the adequacy
of the scaling methods that will increasingly come to be relied upon. The cross-checking through use of a
multiplicity of sources, such as is used by USDA FAS for crop assessment, seems an appropriately cautious
approach.
5. Conclusion
