ELSEVIER Agricultural and Forest Meteorology 80 (I 996) 67-85

AGRICULTURAL AND

FOREST METEOROLOGY

Methodological issues in assessing potential impacts of climate change on agriculture

John M. Antle Depurtment of Agriculturul Economics, Montunu State Unioersity, Bo~emun, MT597/7-0292, USA

Received 26 December 1994; accepted 21 September I995

Abstract

The purpose of this paper is to discuss how recent developments in the agricultural economics literature could be utilized to advance our understanding of climate change impact and of the potential for adaptation to climate change. The paper begins with a discussion of the economic meaning of impact and adaptation. Noting that analyses of impacts have focused on economic variables such as farm income or value of farm assets, we describe a modeling approach that allows environmental indicators, such as the productivity or value of the ecosystem and its components, to be included in impact assessments. The approach is based on a model of farm-level decisionmaking that represents land-use and crop-specific management decisions, as a function of the spatial heterogeneity of the physical environment, technology, prices of outputs and inputs, and policy variables. Using this model, it is then possible to discuss a number of key issues that arise in modeling impacts of and adaptation to climate change. These issues include the effect of choosing a modeling scale or level of data aggregation; technological innovation and adoption; and changes in economic or environmental policies.

1. Introduction

If indeed human activity induces significant climate change during the next century, humanity will have to adapt to it, and this adaptation will be most critical where biological processes are involved, as in agricultural production. As the comprehensive review of the literature by Easterling (1996) (in this issue) shows, a variety of models and methods have been employed in attempts to assess the impacts of climate change on agriculture. Significant progress has been made in conceptualizing the problem, and preliminary regional and global estimates of impact have been made. Yet as the Easterling review makes clear, and as the work by Mendelsohn et al. (1996) (in this issue) also emphasizes, the studies conducted thus far have not been able to fully account for the potential for adaptation to climate change.

0 16% 1923/96/$ IS.00 0 1996 Elsevier Science B.V. All rights reserved SSDI 0168.1923(95)02317-S

68 J.M. Antle/A~riculturd cd Fore.\t Meteorology 80 (1996) 67-85

The purpose of this paper is to discuss how recent developments in the agricultural production economics literature could be utilized to advance our understanding of climate change impact and of the potential for adaptation to climate change. The paper begins with a discussion of the economic meaning of impact and adaptation. Noting that analyses of impacts have focused on economic variables such as farm income or value of farm assets, we describe a modeling approach that allows environmental indicators, such as the productivity or value of the ecosystem and its components, to be included in impact assessments. The approach is based on a model of farm-level decisionmaking that represents land-use and crop-specific management decisions, as a function of the spatial heterogeneity of the physical environment, technology, prices of outputs and inputs, and policy variables. Using this model, it is then possible to discuss a number of key issues that arise in modeling impacts of and adaptation to climate change. These issues include the effect of choosing a modeling scale or level of data aggregation; technological innovation and adoption; and changes in economic or environmental policies.

2. The economic and environmental meaning of impact and adaptation

Before embarking on a discussion of modeling impact and adaptation, it is important to define what these terms mean. In the literature surveyed by Easterling ( 1996), and in the work by Mendelsohn et al. (1994), it is clear that the impacts of climate change are defined as changes in the quantity or net value of production or as changes in an asset value such as farmland. Thus, impacts are narrowly defined as changes in the value of marketed products produced by agriculture, or by changes in the market value of farm assets.

More generally, of course, we know that environmental change will cause changes in a broader array of natural assets that have value in the production of market goods and in the production of nonmarket goods. Examples of nonmarket goods are the value of natural assets such as clean air and water in sustaining life; the future, but as yet unrealized, market and human health value of certain species and of biodiversity; and the value people attach to environmental amenities.

For sake of argument, we can describe climate and other environmental changes as having economic, environmental and human health impacts within a human population and a geographical region. According to conventional ex ante impact assessment methods used by economists, we can assess the impact of climate change as follows: First, we estimate the present and future values associated economic, environmental. and health indicators under the present climate, and construct a suitable summary statistic of these values, say W( eo), where eO represents the parameters that define the current climate conditions. The function W(e) typically is the present discounted value of present and future changes in economic, environmental, and health values associated with climate change. Second, we estimate a comparable measure of value under a changed climate, say W(e,). The impact of climate change can then be measured as AW = W( e,) - W( e,). There are several aspects of this impact assessment methodology

J.M. Antle/Agriculturul und Forest Meteorology 80 (1996) 67-85 69

that need to be mentioned with regard to the assessment of climate change impacts. (For an overview of impact assessment methods, see Davis et al., 1987; Lee et al., 1992).

If the impact is positive, people do not have an incentive to attempt to offset or mitigate the effects of climate change. But when the impact is negative, there is an incentive to respond to changing climatic conditions. Therefore, we cannot assess impacts holding constant the factors that respond to climate change. Specifically, there may be adaptation by non-human species to climate change, either evolutionary or nonevolutionary, depending on organisms and time scales involved. And there may be adaptation by humans, both in terms of technologies employed in production, in location of production and other activities, and in institutional arrangements and policies that set the rules of the game for human behavior. Thus, let the scalar function (Y(e) represent such factors, so that human welfare is a function W(e, a(e)). The total impact of climate change is then AW = (aW/ih) + (aW/&x)(da/de)Ae. This equation has a straightforward interpretation: the first term represents the impacts of climate change, holding constant the underlying structure of the systems involved (human and nonhu- man); the second term represents the impacts of climate change associated with adaptation induced by climate change.

Another important factor in impact assessment is the choice of a unit of analysis. In biological terms, climate change may have impacts at a very small spatial scale. We know, for example, that agricultural production is highly location-specific and sensitive to microclimatic variation, and this is generally true for most if not all species. Defining climate e; in relation to a spatially referenced physical unit i = 1,. . . ,n, we can then define impacts AW, accordingly. Because each microclimate may have a unique response to global change, it follows that some location-specific impacts may be positive and others may be negative. Furthermore, the algebraic sign of the regional impact, AW = E,AW,, can be determined only by knowing all of the AWi whenever all individual impacts are not of the same algebraic sign. In economic language, the aggregate impacts are generally different than the disaggregate impacts. In biological terms, the distribution of impacts within an ecosystem may be important for assessment of the impact of climate change on characteristics such as biodiversity. The distribution of impacts within human populations play an important role in human welfare as well as in public policy formation.

3. Modeling agriculture-environment interactions

The preceding discussion leads to several implications for measuring climate change impact. First, we need to be concerned, in principle, with not only economic impacts that are realized in markets but more generally with the nonmarket impacts associated with environmental change, and therefore modeling work needs to be able to account for the environmental impacts of human activity. Second, in assessing impact, we must account for changes in the underlying structure of biological and economic systems, that is, we must account for adaptation. Third, we must recognize that because of spatial and temporal variability, disaggregate impacts are generally different than aggregate impacts. Modeling work needs to account for the effects that such spatial and temporal variability may have on the measurement of impacts.

70 J.M. Antle/Agriculturul and Forest Meteorology 80 (1996) 67-85

This section describes recent research on modeling agricultural production decision- making on a location-specific basis (e.g. Just and Antle, 1990; Opaluch and Segerson, 1991; Antle and Just, 1992; Antle et al., 1994; Antle et al., 1996). The motivation for the development of this approach was the recognition that it was not possible to conduct environmental impact analysis with the regional or national units of analysis typically used by economists. Whereas economists use aggregate constructs such as market supply and demand, analogous constructs are not used in the physical and biological sciences. For example, economists typically use equations representing the regional or national demand for pesticides to estimate how pesticide use would change in response to, say, a price change. But from the soil science perspective, it would not make sense to use an average soil to predict leaching of a pesticide into ground water at a regional or national scale. Rather, soil scientists would disaggregate the study area into units of analysis with recognized soil types and other geophysical characteristics, and estimate leaching for each of these units. The approach described here would be to disaggregate the economic analysis in a manner compatible with the soil science analysis, estimate economic and environmental impacts at that disaggregate scale of analysis, and then aggregate impacts to the regional or national level needed for policy analysis.

In the analysis of agriculture-environment interactions, climate determines the spatial and temporal distributions of temperature, precipitation and related phenomena that affect both crop production and the physical processes that determine agricultures environmental impact. When climate is stable, the historical records of temperature and precipitation can be interpreted as realizations of stationary stochastic processes whose parameters can be estimated with historical data. But when climate is changing these distributions become nonstationary, e.g. as in the case where the mean annual tempera- ture is rising and mean precipitation is declining. Such climate changes caused by accumulation of greenhouse gases are believed to be at such a slow pace that farmers would have difficulty perceiving them-indeed, these small year-to-year changes would be of little or no consequence relative to the normal variation in temperature and precipitation. Nevertheless, over a long period of time-30, 50 or 100 years-these changes could be substantial enough to alter crop productivity and the spatial location of agriculture in ways that are significant at the regional or national scale.

3.1. A static spatial model of land-use and crop choice

Thus, we begin with a description of an approach to analysis of production manage- ment on a location-specific basis. using a unit of measurement that is relevant to the location-specific decision making of a farmer and also suitable for physical and biological science research. A simplified, static version of this approach is presented in Fig. 1. At the top of the figure, three groups of parameters are defined: physical/bio- logical (soil type, climate, pest populations), economic (output and input prices, and economic policies), and technological (production technology and capital stock utilized in production). Given these parameters, farmers make land use and crop choice decisions on each unit of land under their management according to a criterion such as expected profitability. Then, conditional on the land use and crop choice decision, the farmer makes other management decisions (seeding rates, fertilizer use, pesticide use,

J.M. Antle /Agricultural and Forest Meteorology 80 (1996) 67-85 71

cultivation practices). These decisions result in economic outcomes (a crop output and a realized profit) and environmental outcomes (soil and water quality on the farm, surface and ground water quality off the farm, species on and off the farm).

To illustrate the analysis of land use decisionmaking, consider a situation where a single crop is produced on a unit of land with the production function F(vi, zi, e,>, where vi is a vector of variable inputs (fertilizers, pesticides), zi is a vector of fixed inputs (machinery), ei is a vector representing the physical environment at location i (soil type, climate). If this production process is not used, the unit of land is put into a conserving use which returns a value ci to the farmer (e.g. the land is returned to natural vegetative cover, and ci could correspond to a government payment for land conserva- tion, such as a Conservation Reserve Program payment; or it could be the value of grazing or recreational use). When production takes place, the maximum expected profit obtainable with crop price p, and variable input price vector w is given by the profit function 7re(p, w, zi, e,> (for mathematical definition of the profit function, see Silberberg, 1990). Define ai = 1 if a farmer produces on acre i with technique j in year t, and 6, = 0 otherwise. Farmers allocate the A acres of arable land in the region according to its highest valued use, hence, crop production occurs on each land unit where 7~~ > ci, otherwise the land is put into the conserving use. Thus, farmers make land-use decisions to solve:

mfx{S,7r(p, w,zi,ei) +(l -&)ci}

For simplicity, we assume the choice of conserving use can be made each growing season. In cases where the conserving use is a long-term decision (e.g. tree planting), the decision problem involves comparing the present discounted value of profits over the planning horizon to the value of the conserving use. The land-use decision is represented by a step function of the form Si( p, w, zi, ei, ci). The acreage allocation to crop production in the region is C,S,( p, w, zi, ei, c,>, and to conserving uses is A - CiGi(p, W, Zi, ei, ci>.

When production takes place, profit-maximizing variable input decisions are obtained by deriving input demand functions. According to the result known as Hotellings lema, the profit-maximizing input use is given by

ui* = -&r( p, w, zi, e,)/aw

These input decisions and the other management activities of the production process lead to location-specific economic outcomes (a realized output and profit), and environ- mental outcomes (e.g. soil erosion, chemical leaching, changes in soil organic matter).

If the unit of land is put into the conserving use, there are corresponding environmen- tal outcomes, but the crop production process does not generate economic outcomes. As the dashed lines in Fig. 1 indicate, there may be feedbacks in both the economic and environmental dimensions into the next periods decisions and outcomes. Economic outcomes may affect the farmers investment in technology and capital; environmental outcomes may affect the biological and physical parameters on the unit of land, and may also result in biological and physical changes in the ecosystem through processes such as soil erosion, chemical runoff, and leaching. A dynamic model is needed to appropri- ately account for these processes.

72 J.M. Antlr /Agricultural und Forest Meteorology 80 (1996) 67-85

3.2. Dynamics of managed ecosystems

The preceding discussion of technology choice and productivity used a static representation in which both physical capital and environmental factors are taken as given. But in most farming systems, and more generally in managed ecosystems, there are important feedback mechanisms from economic activities to the environment. While a static representation may be useful for some purposes, it is clearly not appropriate for obtaining an understanding of long-term sustainability and the effects of climate change. These interactions are particularly important in situations in which production systems and ecosystems are being stressed, due either to the use of unsustainable production systems or to climate change. And as noted earlier, we can construe climate change as causing distributions of weather events to be nonstationary stochastic processes, but with the changes in these distributions occurring slowly over long periods of time. Thus we

Fig. 1. A static spatial model of land use and crop management decisionmaking.

J.M. Antle/Agriculturul and Forest Meteorology 80 (1996) 67-85 73

must necessarily be concerned with behavior over long periods of time when feedback mechanisms are likely to play an important role in the behavior of the system.

A key aspect of the long-term impacts of agricultural activity on the environment is the spatial and temporal pattern of land use. Moreover, as Mendelsohn et al. (1994) emphasize, changes in land use are likely to play an important role in determining the economic impacts of climate change. The preceding discussion showed how land-use decisions play a central role in the analysis of interactions between production agricul- ture and the environment.

To represent the evolution of the production system over time, we can index variables using time subscripts; the choice of time step will generally depend upon the context of the analysis (e.g. 1 h or day for some physical processes, 1 year or more for some economic processes). The physical capital stock changes over time according to the equation of motion zit+, = g(zi,, nit>, where ni, is investment in period r. The ecosystem evolves over time according to ei, + , = hi,(eit, vijr, zij,>, where the time subscript on the function denotes the dependence of climate at each location on exogenous factors such as radiative forcing from greenhouse gas accumulation. This latter function can be interpreted as representing an ecosystem model in stylized form, such as the Century model used to simulate soil organic matter content (Parton et al., 1987).

Using these equations of motion as constraints, farmers behavior can be modeled in a variety of ways. If farmers are economically rational but do not have incentives to account for the impacts of their behavior on the ecosystem, then profit or utility maximization may be the appropriate model, with environmental variables viewed by farmers as constraints. But if farmers recognize the impacts of their management decisions on the environment, and if they recognize that environmental changes may have an impact on their productivity in the long run, their behavior may be represented as the solution to a maximization problem that takes account of the dynamics of the ecosystem. This type of dynamic model can also be used to solve for socially optimal policies, by incorporating into the objective function the value of the ecosystem variables along with the farmers profit.

3.3. Impact analysis

This model of land-use and crop production could be used to conduct a location- specific analysis of the impacts of climate change that would include both economic and environmental effects of climate change, taking as given the production technology of the farmer, the farm capital stock, and prices of inputs and output. This assessment is conducted by imposing a change on the system by varying the elements of the vector ei and inferring the changes in land use, production management decisions. These changes in land-use and management decisions would in turn generate changes in both environ- mental and economic outcomes. The impact assessment would be completed by valuing these changes in terms of a common unit of measurement (typically, in monetary terms), and constructing a location-specific measure of impact AWi(p, w, ci, ey, e,f, zi) = AWiC p, W, ci, ef, Zi) - AW;(p, W, ci, e?, Zi).

74 J.M. Antlr/Agricultural Ural Forest Meteorology 80 (1996) 67-85

Several features of this modeling approach distinguish it from those in the literature discussed by Easterling (1996). First, because the decision model explicitly allows for land-use decisions, it begins to incorporate possible economic adaptation to climate change through changes in land use. That is, if climate change altered crop productivity, there could be a change in production patterns, with some land going out of production and other land coming into production. Second, because the approach allows location- specific land use and production management decisions, it is possible to link the economic models to physical process models and biological models for integrated impact assessments.

A third feature of this approach is that it shows explicitly that the impact of climate change is a ,function of the prevailing prices, policy parameters, capital stock, and technology. But these variables themselves will surely change over the long time periods involved with climate change, and may themselves be functions of climate change. It follows from the discussion of the preceding section, therefore, that such economic or technological adaptations must also be accounted for. The following section focuses on the crucial issue of technological adaptation.

4. Modeling long-term trends in technology and productivity

The analysis of the impacts of global climate change on agriculture can be decom- posed into two parts. First is the assessment of the impacts of climate change on agricultural resource use and production, for given technologies and institutions. This type of assessment requires substantial research to generate needed data, but the methods required to answer them are well developed and the subject of continuing research such as that described by Easterling (1996).

A more challenging task is to predict how agricultural technologies and institutions may evolve over the next 30, 60, or 100 years. Existing productivity research, for example, has focused primarily on explaining historical data, and so provides little guidance on how to analyze and predict future productivity (for a review of these methods, see Capalbo and Antle, 1988). Consequently, studies of climate change impacts have relied on expert opinion or extrapolation of historical trends. The Rosen- zweig and Parry (1994) study reviewed by Easterling (1996) was based on the assumption that world cereal yields would grow on an annual trend until the year 2060 at 0.9% in developing countries and 0.6% in the developed countries. Combined with their assumptions of population growth and aggregate income growth, this technology assumption explains their base scenario result that without climate change real cereal prices would increase by more than 120% to 2060. This prediction contrasts with the downward trend in real cereal prices seen for the past half-century, and also differs from other long-term price forecasts made by USDA (1994) and IFPRI (Agcaoili and Rosegrant, 1994) based on extrapolation of historical productivity growth into the future.

As Ruttan (1991) noted, the existing studies of climate change impacts fail to make use of what we know about the determinants of agricultural research investment, technology adoption, and induced innovation. Another criticism of the literature is that the existing studies, based on a production-function approach, underestimate technologi-

J.M. Antle/Agricultural cmd Forest Meteorology 80 (1996) 67-85 7.5

cal and economic adaptation and thus overestimate climate change impacts. Mendelsohn et al. (1994) propose a Ricardian approach based on estimation of a reduced-form relationship between asset values and environmental characteristics. As we shall discuss in greater detail below, the disadvantage of this approach is that it provides information on land values but does not provide information on agricultural production. Moreover, being based on a reduced form estimated with historical data, it cannot be used to analyze how structural changes, such as the adaptive potential of new types of agricultural innovations or policy changes, would alter climate change impacts.

In this section, I review some the literature on agricultural innovation and discuss how the insights of that literature could be used to construct a model of endogenous technology and endogenous land use and crop choice that could better represent agricultural innovation and adaptation. This model could be estimated with historical data, and then coupled with regional simulation models to generate predictions of agricultural impacts that are consistent with what we know about the environmental and economic factors influencing agricultural innovation, land use, and crop choices.

4.1. The supply of and demand for innovations

There are extensive literatures on various aspects of agricultural research and development (see, e.g. Huffman and Evenson, 1993). It is useful to think of the agricultural innovation process as a market, wherein farmers are the demanders in this market, and both private and public organizations are the suppliers. This market consists of the derived demand for innovations that reflects farmers objectives and the publics demand for food and other agricultural products, subject to the various constraints placed on the process by factors such as physical location, climate, and government policies. The supply side of the market for innovations represents the public and private institutions that participate in the development and dissemination of agricultural technol-

ogy. The market for innovations shows how technological aspects of adaptation are

integrated with economic aspects. The innovation process is interpreted as a sequence of market equilibria. The relative price of an innovation is seen as changing in response to a wide variety of factors that impact the agents who participate in the market for innovations. The induced innovation theory (see Hayami and Ruttan, 1985), in which innovations are hypothesized to be induced by resource scarcity, is compatible with this approach, as it is premised on the assumption that both public and private research organizations perceive and respond to resource scarcity in making decisions about what technologies to develop.

There are three sets of issues raised by climate change that arise in the analysis of the supply of innovations: uncertainty about regional changes; the characteristics of technol- ogy that become more valuable with climate change; and the rate of change. These three issues are closely linked in the analysis of adaptation to climate change. Using the market for innovations, we can organize the factors that may thus affect technological adaptation.

The uncertainty issue arises because climate change alters the basic constraints of the innovation problem. In the conventional innovation problem, resource and climate are

76 J.M. Antle /Agriculturul crnd Forest Meteorology 80 (19961 67-85

taken as a given for a region, and the research task is to develop technology suitable to the resource scarcities created by the regions endowment. In this setting, weather is unpredictable, but climate can be viewed as a stationary stochastic process. Thus, the research managers can utilize historical data to assess the climatic component of the regions resource endowment with a high degree of reliability.

With global climate change, a critical component of the endowment can no longer be taken as a given. Moreover, climate can no longer be described as a stationary stochastic process. This creates a serious new problem for researchers. What kinds of research should be undertaken-what plant or animal characteristics are desirable-given some degree of uncertainty about the future climatic endowment of a region? For example, will average warming or greater variability in temperature occur in a region? Will precipitation increase or decrease? Clearly, a critical issue is how research organizations will interpret climate predictions and integrate them into their attempts to match the supply of technology with the likely future demands by farmers who are responding to evolving climatic conditions.

Much has been learned about how institutions manage the innovation process that is relevant to adaptation. Binswanger (19781, for example, models the decisions of research administrators much like the investment decisions of a cost-minimizing firm. Thus, perceptions of resource scarcity and relative prices enter the research and development process, both through the administrative decisions in public sector research and within the private sector. The response of the supply side to either anticipated or real changes in climate will depend on the institutional arrangements and on the organizations involved in the creation of science and technology.

As participants in the market for innovations, research organizations must form expectations for the future. According to the induced innovation hypothesis, research organizations respond to perceptions of resource scarcity. A key question in forming expectations is the length of the planning horizon and the amount of time required to develop a new innovation in response to a perceived change in resource scarcity. We know that new innovations generally take IO-15 years to develop. Will perceptible changes in regional climates occur over shorter or longer periods of time? If climate change evolves slower than the usual innovation cycle, and if the changes are not extreme, then it is conceivable that the changes may not be any different than what would normally occur in response to changes in technology, population, and policy settings. Indeed, it is quite possible that the effects of gradual climate change would be swamped by other factors.

On the demand side, the key actor is the farm firm who is the demander and user of technology. The ability and willingness to adopt technology will depend on its potential profitability or other desirable attributes, which in turn depend on the farmers ability to use the technology and the incentives to use it created by the economic and policy environment in which the farmer operates. All of these factors will play a role in adaptation, as they will influence the adoption of technologies that become available.

A key question for farmers, and for their behavior, is how climate changes will impact their economic well being. This will affect their willingness and ability to invest in technology, and it will affect their demands for policies to protect their economic interests. Without specifics on the nature of climate change and how it may impact

J.M. Antle/A~riculrural und Foresr Meteorology 80 (1996) 67-85 77

biological processes in particular locations, it is difficult to predict how farmers may respond. If there were an increase in weather variability, we could predict that they would attach a higher premium on technologies, management strategies, and policies that reduce the effects of climate risk. This could involve adaptation of plants and animals to the climate; it could involve a portfolio diversification strategy on the part of farm managers; and it could lead farmers to act in the political arena to lobby for crop insurance or other policies that would compensate them for increased uncertainty.

Farmers demands for innovations are derived from the market demand for their products. This is the linkage from the farm-level demand for innovations to the local, domestic, and international agricultural markets. Population growth and growth in per capita income will play a key role. Location-specific demands for innovations will be driven by the operation of these markets. Thus, it will be essential to understand the behavior of aggregate demand for food and other agricultural products.

4.2. Modeling technology choice at the farm level

Following Antle (1995), a modified version of the model of Mundlak (1988) of a firms choice of technique provides a characterization of the firms demand for technology. Let the existing state of technology at time t be defined as the collection of all possible techniques T, = {F,,( vjr, zjl, ei,)lTK,}, where Fj,(vjl, zjr, e,,) is the production function associated with the jth technique, vjl is a vector of variable inputs used with the jth technique, zjt is a vector of fixed inputs subject to the constraint Cjzjl = z,, and ei, is a vector representing the physical environment at location i in which production takes place at time t.

This representation augments Mundlaks model in two ways. First, the technology set T, is a function of the stock of technological knowledge. Second, the environmental variable ei, is added to the production function to represent the location-specific genotype-environment interaction typical of agricultural production processes. Note that ei, could represent any location-specific factor affecting productivity, such as access to transportation infrastructure.

Mundlak shows that, in a simple static profit maximization problem with factor prices w, and output prices pt, the solution takes the form vj,tpp,, w,, ei,, z,, T,) 2 0 and zj$pr, wI, ei,, z,, 7,) 2 0 where the inequality holds for the most profitable technology. It follows that the implemented technology can be defined as ZT(p,, w,, e,,, z,, T,> = (Fj,(vj,? Zjt? ei,)lFj,(vj; 9 Zi;, if e ) f 0, Fj, E T,}. Thus, the implemented technology is a function of product and factor prices, the local physical environment, the physical capital stock, and the available technologies.

4.3. Modeling innovation

The supply of agricultural innovations has been the subject of extensive research. The stylized model of Antle (1988) of the innovation process illustrates how the supply of innovations could be modeled. Following the characterization by Evenson (1988) of the stages of the technology development process, the stock of basic scientific knowledge, K,, evolves according to the equation K,, , = 6, K, + k, + K,, where 6, is a depreciation rate reflecting knowledge obsolescence, k, is systematic investment in basic research,

78 J.M. Antle/Agricultural md Forest Meteorology 80 (1996) 67-85

and K, is a random term representing scientific advance that is not the result of purposeful investment.

Evenson (1988) describes several steps that are typically involved in the transforma- tion of basic knowledge into implementable technologies. Let the result of those steps be described as the stock of technological knowledge TK,. The equation of motion for the stock of technological knowledge is TK,, , = p,TK, + IK,(R,, K,, pt. wt> + T,, where p, is a depreciation rate representing the obsolescence of technical knowledge, ZK, is gross investment in new technical knowledge, and T, is a random term. ZK, is a function of spending on applied research R,, the stock of basic knowledge K,, and prices pt and w,. Technological knowledge is thus a function of the current and past sequences of research investment, stocks of basic knowledge, and prices.

Induced innovation enters the model through the effects that prices have on the type of technical knowledge that is developed. We know that research administrators and researchers make conscious decisions to orient efforts towards certain areas of science and certain technologies. The induced innovation theory argues that research is generally oriented towards products that are expected to have higher output prices, and towards reducing the use of relatively more expensive inputs. To incorporate this consideration into the model, the stock of technical knowledge, TK,, can be interpreted as a vector of knowledge stocks that are specific to the techniques contained in the technology set q.

Combining together the representation of the implemented technology with the model of investment in technological knowledge, the implemented technology is a function IT., = IT(p, w, R, K, z,, e;,), where the superscript denotes a vector of current and past variables, e.g. p = (p,, p, _ , , . . . 1. The implemented technology is a result of present and past prices, investments in applied research, stocks of basic knowledge, the physical capital stock, and the environmental characteristics of the location.

Using these constructs, it is possible to use existing data to model the dynamic properties of the innovation process. Huffman and Evenson (1993) review the literature on studies that estimate the lag relationship between research investment and agricultural productivity; Antle (1988) provides an analysis that accounts for dynamics created by the induced innovation process; Chavas and Cox (1992) provide an analysis using nonparametric statistical methods. These studies provide a rich literature upon which models could be built to characterize the agricultural innovation process.

These models could then be coupled with aggregate economic simulation models under climate change scenarios to generate predictions of the variables driving the innovation process-namely prices and expenditures on research and development. Changes in agricultural innovation would in turn feedback into the production process, modifying patterns of land use and production, and in turn changing future market equilibrium prices and production. Presumably, long-term predictions of future produc- tion and productivity growth would be more credible than simple linear extrapolations of past trends or other ad hoc assumptions about productivity growth.

5. Implications for modeling impacts of climate change

Combining the elements discussed in the preceding sections, it is possible to formulate a comprehensive model and to consider its implications for modeling impacts

J.M. Anrle/Agriculturul and Forest Meteorology 80 (1996) 67-85 79

of and adaptation to climate change. Following the example described above, we assume the farmer chooses to produce a crop on a unit of land or place the land in a conserving use. In this more general model, the farmer managing i = 1,. . . ,f fields makes capital investment decisions and location-specific land-use and management decisions to maxi- mize economic returns, subject to prices, government policies, and constraints imposed by available technology, the available capital stock, and the environment. Letting p, be a discount factor that puts future monetary values in present terms, the maximization problem is:

max tPt('irme( P s,,. *t,=o

,,~~,z~,e~~,T,)+(l-~~,)c~,}, i=l,...,f

subject to:

Vi), = are( Pr 7 WI 7 Z, 3 ei,, r,)/aw,

Z;jt = Zjr( P, 9 w, > Z, 9 ei, 7 rf)

Z,= CjCiZ;jl

Z t+1 =g(z,, 4)

eit + 1 = hit( e;,, jt 9 Zjt)

In addition, the production technology T, evolves according to the system of equations

T Ii I = T( TK,)

TK,, I =p,TK,+IK,(R,,K,,p,,w,)+7,

K I+ I = 6, K, + k, + K,

Following previous notation, p, and w, are output and input prices; ci, is the value of the land in a conserving use, and may be set by government policy; z, is the farms capital stock; zTjt is the allocation of capital to the ith land unit for production with the jth technique; ui>, is the vector of variable inputs allocated to the ith land unit and jth technique; ei, is the vector of environmental attributes of the ith land unit; T, is the set of available production techniques at time t; TK, is technical knowledge, IK, is investment in technical knowledge, R, is spending on applied research, and K, is the stock of basic knowledge.

Generally, the solution to this type of dynamic optimization problem is difficult to obtain in closed form, and depends on the functional forms specified for the various relationships. The solution is known to be a function of the parameters of the problem: the prices of outputs and inputs (and more generally, price expectations, as the investment problem involves making decisions to maximize present and future expected profits); policy parameters (such as ci,); the parameters of the ecosystem embedded in the function hi,; and the parameters defining production technology and governing technological innovation, such as research spending R, and basic knowledge K,.

80 J.M. Antle/Ap-icultural uncl Forest Mrteorology 80 (1996) 67-85

5.1. Aggregation and modeling scale

The above model characterizes economic and environmental outcomes at the scale of the individual land unit, typically a farmers field. Generally, however, information on climate change impacts are needed at a larger unit of analysis, such as a geographic region or political unit such as a state or nation. In economics, the problem of adding up smaller units into larger ones and then analyzing the properties of the larger units is known as the aggregation problem. In the physical and biological sciences, this is often referred to as the problem of modeling scale.

We know that at the individual field level we can accurately characterize the farmers management decisions as a function of physical, economic, and technological variables, and we can model the environmental impacts of these management decisions. We can, thus, accurately assess the impacts of climate change at that level. As we discussed earlier, the location-specific impacts can be represented as a function of the form AW,,(p,, w,. cilr ei:, ei:, z;,). The aggregate impact for the region composed of i= I,... ,N land units, at time t, would be CiAWj,(p,, w,, c;,, ez, et, z;,). Alterna- tively, production and environmental data could be aggregated to the regional level, and an impact analysis could be conducted with the aggregate data. The result would be a measured impact of the form AlV(p,, w,, C,, E,!, E:, Z,>, where C,, Ef, Ef, and 2, are the aggregated data for the region (note that prices are not aggregated, the same prices are assumed to be faced by all farmers in the region). This latter aggregate impact measure is the type that all of the studies reviewed by Easterling (1996) have used. What differences are there between location-specific impact measures aggregated to the regional level, and impact measures derived from aggregate data? And which type should be used to assess climate change impacts?

A first observation concerns the form of the relationships. It should be obvious that, unless the relationships were linear, it would not be possible for the function c,AkV,,( p,,

Wf, C,,, ei:, e:,, z;,) to be equal to the function AW(p,, w,, C,, Ef, E,!, Z,), a result established long ago in the economics literature on aggregation. A deeper question, however, is whether it is possible to measure aggregate impacts (e.g. the total change in agricultural output for the region, or the total damages caused by soil erosion) and to express this total quantity as a function of the aggregate variables (such as total quantities of inputs used in agricultural production in the region, or average values of physical variables such as soil depth and precipitation). It can be demonstrated that such aggregate relationships can be constructed (Antle, 1988, provides the result for an aggregate production model). However, the aggregate relationships are defined for a given spatial distribution of the underlying location-specific factors that define the individual land units in the region, such as environmental characteristics or technological characteristics of the farm. Therefore, if these spatial distributions change over time, the aggregate relationships also change.

To illustrate the difficulties that arise in aggregation of agricultural-environmental impact analysis, consider what would happen if agricultural policy were liberalized and the existing system of production subsidies and production controls (e.g. the acreage reduction program and the conservation reserve program) were eliminated. These programs clearly have served to significantly reduce the amount of land in agricultural

J.M. Antlr/ Apkdtural und Forest Mrtrorolo~y 80 (19961 67-85 81

production in the United States, and the value of the program benefits have been capitalized into land values. Elimination of the programs would clearly alter the size and type of farms in agriculture, and the types of crops they produced and where they are produced. Generally, larger, more capital intensive farms would be observed under policy liberalization, and production in marginal areas (e.g. low-productivity dryland grain production areas in the Great Plains) would be reduced if not eliminated. In other words, the underlying distribution of farm characteristics and technologies would be changed. Consequently, the impacts that climate change would have on land use, crop production, the economic well-being of farmers, and the environment, would also be different under policy liberalization.

Under these circumstances, aggregate relationships estimated before policy liberaliza- tion took place would not provide accurate predictions of production activities that would take place after liberalization, and by the same logic, these aggregate relation- ships would not provide accurate estimates of climate change impact. However, observe that the accuracy of location-specific estimates of production functions and environmen- tal processes are independent of policy, and could be used to estimate climate change impacts under either policy scenario.

5.1.1. An empirical example of the effects of aggregation in analysis of agriculture-en- vironment interactions

To further illustrate the effects of aggregate, we consider a recent study of a crop production system in the Ecuadorian Andes (Antle et al., 1996). While this study was not designed to addresses the effects of climate change, it was designed to address the effects of spatial heterogeneity on the measurement of the environmental impacts of agriculture. For this purpose, detailed field-level data and biophysical data were col- lected for a group of 40 farms distributed in several watersheds ranging from about 2800 to about 3300 m elevation. A detailed economic simulation model was built to represent the response of farmers to changes in prices and related policy factors, and this simulation model was integrated with a physical process model that estimates the leaching of agricultural pesticides below the crop root zone.

Fig. 2 illustrates the simulated effects on the leaching of fungicides used in potato production, for two different agro-climatic zones and for the aggregate of the entire study area. These outcomes are the result of simulating the land-use and pesticide-use decisions of potato producers under a wide range of possible price policies-policies that would either tax pesticides and thus limit production and chemical use, or policies that would subsidize production and thus increase chemical use. The points closest to the origin in the figure represent the lowest level of production and pesticide use, whereas points farther from the origin represent higher levels of production and pesticide use. In the environmentally vulnerable zone 4 fungicides generally leach more, and changes in production and pesticide use result in relatively large changes in the distribution of leaching events-both the mean and the variance of fungicide mass leached increase as production increases. In contrast, in zone 2 leaching is relatively low and there is little change in response to production changes because the soil and climate conditions there are not conducive to leaching. Consequently, the aggregate changes for the entire

82 J.M. Antle /Agricultural und Forest Meteorology 80 (1996) 67-85

2

1.75

1.5

P E

p 4 1.25

OI s

p 1

I= B 8 0.75 c .I

0.5

0.25

0 I

II

- Aggregate -A-- Zone 2 - zone4

0 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 0 Mean Fungicide Leaching (kg)

Source: Crissman, Antle and Capalbo (1995).

Fig. 2. Aggregation of environmental impacts in an Andean case study. Source: Crissman et al. (1995).

watershed-measured as an average over all the agroclimatic zones-show higher levels of leaching than zone 2 but much lower than zone 4. Moreover, the aggregate shows some variation in response to the price policy changes, but the aggregate clearly fails to reflect the low degree of environmental vulnerability in zone 2 and the high degree of vulnerability in zone 4.

This example provides several important lessons for agricultural-environmental impact analysis, including attempts to estimate the impacts of climate change. First, any estimate of impacts based on a representative farm could substantially over- or under-estimate impacts. In the example presented here, researchers seeking a representa- tive farm probably would have used data from zone 2, and thus would have underesti- mated the potential for fungicide leaching that existed in zone 4. Second, the example shows that the aggregate data are likely to understate the variability of impacts that exist in the population. This problem is particularly important because the social costs of environmental impacts are typically associated with the impacts on the most vulnerable members of the population. In the context of climate change and agriculture, it is generally believed that the greatest adverse impacts of climate change will occur in regions where production is vulnerable to increases in temperature or decreases in precipitation, and in regions where adaptation is most limited. It is unlikely that aggregate analyses of the type that have been conducted thus far (see the review by Easterling, 1996) are capable of adequately representing spatial differences in agricul- tures vulnerability to environmental change.

J.M. Antle/Agricultural ad Forest Meteorology 80 (1996) 67-85 83

5.2. The Ricardian approach

Mendelsohn et al. (1994) propose the Ricardian approach to assess climate change impacts. Essentially, they observe that land values generally embody the market value of the lands environmental attributes. Therefore, by measuring the relationship between land values and environmental characteristics, such as temperature and precipitation, it is possible to predict what the economic effects of climate change might be. The advantage to this approach, they argue, is that the observed relationship between asset values and environmental characteristics subsumes all of the adaptations to climate that people make. In contrast, the production function approach requires that scientists estimate and model adaptation, something they can only do to a limited degree. Moreover, the studies of climate change impacts do not allow for land use to be adapted to climate change, and thus are likely to overstate the adverse economic impacts of climate change.

Following the preceding discussions of impact assessment, the Ricardian approach can be summarized by saying that, holding prices fixed, the value of farm land should be a function of environmental characteristics. If we ignore nonmarket effects of climate change, so that we can interpret the total impact as the market impact, then the Ricardian approach is to statistically estimate the relationship W$e,,> using historical data, where W, is measured as the market value of land, and then use this relationship to estimate the effects AWi of changing e, in a manner predicted by climate models.

While the Ricardian approach would embody adaptations that some previous studies have ignored, such as changes in land use, it has limitations of its own. As we noted above in the discussion of the static spatial model, measuring impact in this way would be valid only if there were no changes in technology, policy, or any other temporally varying factors that would affect the land-use and production management decisions of farmers, or the value of alternative uses of the land. Thus, as we noted in the preceding discussion of aggregation, if agricultural policy liberalization occurred, we would expect there to be a major change in land values in the United States. If one estimated the relationship Wi(ei,) in year t,, and then policy changed in year I,, this relationship would not provide accurate estimates of the impacts of climate change that occurred in year t,. The same argument would hold for technological innovation. Changes in technology would alter the relationship between environmental characteristics and land values, so it would not be appropriate to use the relationship Wi(ei,) estimated with historical data to estimate the effects of climate change on land values.

5.3. Policy change and climate change

Two final points are worth noting about policy change and the assessment of impacts of climate change. First, because climate changes will take place far into the future, there can be little doubt that there will be significant changes in economic and environmental policies. The long-term impacts of these changes can easily be as significant as the long-term changes in technology and productivity. Observe, for example, the political changes in the former Soviet states, or the recently passed international trade agreements to liberalize international trade over the course of the next lo-15 years.

84 J.M. Antlr/A~riculturul cmd Forest Mrtrorolo~y 80 (1996) 67-85

Second, if there is significant global climate change, there can be little doubt that policy will respond to it in various ways that will impact adaptation. In the context of the above discussion of innovation, for example, it is very likely that a perceived threat to world food supplies would be met with a substantial increase in the public funding of agricultural research. Other policies, such as those that remove large areas of land from production in the United States, would also be likely to be changed, and so forth. While our ability to predict what kinds of changes might occur is quite limited, the fact that policy is likely to change significantly in the long run serves to reinforce the concerns about the accuracy of impact assessments that do not account for the effects of possible policy changes.

6. Conclusions

This analysis characterizes agricultural production as a process that varies spatially and temporally. Modeling efforts that disregard either the spatial or temporal heterogene- ity of agriculture will be inaccurate to some degree. Of course, all applied research must make simplifying assumptions, so we are left with the need for research to consider the degree to which the simplifying assumptions of economic impact studies may introduce systematic biases in estimates of the impacts of climate change. The example presented from a recent study of the environmental impacts of agriculture does suggest that aggregate data may substantially understate the mean level as well as the variability in impacts measured at a smaller scale, and this result should be cause for concern especially for studies of impacts on those agro-ecosystems that are most vulnerable to the potential effects of climate change.

We do not possess the data needed to model biological, economic, or physical processes on a location-specific basis for large areas of the Unites States or other parts of the world. Our analysis suggests that it would be useful, therefore, to conduct regional studies that are able to assess impacts on a location-specific basis and compare the results to aggregate studies that do not rely on location-specific data. These comparative studies should provide the basis to determine what modeling scale is needed to provide a sufficient degree of accuracy for impact assessment. These studies would also provide climate modelers with information about the degree of resolution that will be needed to conduct useful impact assessments.

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