11 A Model of Endogenous Technological Change through Uncertain Returns on Innovation – Technological Change and the Environment

Chapter 11

A Model of Endogenous
Technological Change through
Uncertain Returns on Innovation

Arnulf Grübler and Andrii Gritsevskyi

11.1   Introduction

Changes in products, devices, processes, and practices—that is, changes in technology—largely determine the development and consequences of industrial society. Historical evidence (e.g., Freeman 1989; Mokyr 1990; Maddison 1991; Grübler 1998) and economic theory (Tinbergen 1942; Solow 1957; Denison 1962, 1985; Griliches 1996) confirm that advances in technological knowledge are the single most important contributing factor to long-term productivity and economic growth. Technology is also central to the long-term evolution of the environment and to development problems now on policy agendas worldwide under the general rubric, “global change.” Although technology is central, technological change is typically the least satisfactory aspect of global change modeling. Each of the factors that determine the wide range of projected emissions of, say, carbon dioxide (CO2)—such as the future level of economic activity (largely driven by advances in productivity), the energy required for each unit of economic output, and the carbon emitted for each unit of energy consumed—is a function of technology. This also applies to the technological linkages in any kind of macro or sectoral production function (Abramovitz 1993). Consequently, technology largely accounts for the wide range seen in published long-term carbon emission estimates. A recent review of the literature (Nakicenovic et al. 1998b) indicates an emissions range spanning from 2 GtC (gigatons, 1015 grams, of elemental carbon) to well above 40 GtC by 2100. This wide span is largely explained by differences in technology-related assumptions such as macroeconomic productivity growth, energy intensities, and availability and costs of low- and zero-carbon technological alternatives.

In this chapter we outline a model of endogenous technological change that is applied to the energy sector and the CO2 emissions problem. Like any model, it is an abstraction of our understanding of how “the system works.” Therefore, we begin by outlining a number of stylized abstractions from our review of the theoretical and empirical literature (Section 11.2). We emphasize in particular that, like all knowledge, improved technological knowledge can exhibit increasing returns. These are, however, highly uncertain, resulting in diverse innovation strategies reflecting different technological “expectations” (Rosenberg 1996) by a multitude of actors. Adopting the term “innovation” in the Schumpeterian sense means that all innovative activity is essentially economic, that is, technology arises from “within” (Schumpeter 1934) the economy and society at large. Innovation is costly, requiring up-front expenditures in improving technological knowledge in its disembodied form [typically research and development (R&D)] and in its embodied form (plants and equipment). This leads to the formulation of a multi-actor, multiregion model of uncertain increasing returns to technological innovation. In this model, innovation costs include both R&D and expenditures on physical plants and equipment that lead to improvements via learning by doing and learning by using. The basic elements of the model and its most salient parameterizations and input assumptions are outlined in Section 11.3 in a nonmathematical way. Section 11.4 presents some illustrative quantitative model results, exploring in particular changes in patterns of technology diffusion and carbon emissions under alternative assumptions concerning uncertainty about resource availability and costs, energy demand, technology characteristics, and the existence of uncertain environmental limits that are examined in both the absence and the presence of uncertain increasing returns phenomena. Conclusions are presented in Section 11.5, highlighting in particular the implications for analytical “next steps” toward the challenge of a deeper theoretical and empirical understanding of the mechanisms and incentives driving technological change.

11.2   Main Features of Technological Change

11.2.1   Introduction

A review of the literature and of empirical case studies (e.g., Freeman 1994; Grübler 1998) suggests that technological change can be summarized as being dynamic, cumulative, systemic, and uncertain in nature. Technological change is by definition dynamic, as it is characterized by the continuous introduction of new varieties (“species”) and continuous improvements and modifications of existing ones. These new and improved technologies essentially represent new forms of technological knowledge that cannot be created ex nihilo (i.e., without prior knowledge), hence technological change is inherently cumulative. Change is also systemic: because of technological interdependencies and infrastructure needs, any change in a component of a larger technological system requires corresponding changes in other up- or downstream components of that system. Finally, technological change is inherently uncertain. The outcomes of the innovation process (the form and applicability of new technological knowledge) as well as of technology diffusion (market potentials, economics, etc.) cannot be known beforehand.

How should the above features be factored into a model of technological change? Basically, we argue that traditional representations of technological change need to be extended—first, by considering the types and characteristics of technological knowledge as well as who creates and uses it, and, second, by explicitly considering uncertainty and the systemic aspects of technological change.

11.2.2   Forms of technological knowledge

The dynamic nature of technological change poses an epistemological problem. The nature of the object under investigation, “technology,” is very different at its conception, at its introduction into the market, and at the point when it is widely applied. Ayres (1987) reviews various conceptualizations and formulations of technology life-cycle models. Although Ayres is skeptical of the integrative capability of the model as a theory “of everything” in technological change, his review demonstrates the powers of the technology life-cycle model as a conceptual classification tool for understanding the different stages of technological change and the very different mechanisms at work transforming the technology itself as well as the market (and ultimately even the social) environment in which it is embedded.

Different technology life-cycle stages can be distinguished using a variety of criteria pertaining to characteristics such as technology performance, market volume and structure, etc. While of interest, they do not address the issue of sources and mechanisms of technological change proper. Distinctions based on the relative contributions of different forms of knowledge generation (Cowan and Foray 1995) or of disembodied versus embodied technological change (Grübler 1998) are more relevant for the discussion here.

A simple four-stage taxonomy of a technology's life cycle drawing on the work of Schumpeter (1911, 1934) distinguishes four stages in a technology's evolution: invention, innovation, niche markets, and diffusion. Whereas the invention stage (the first demonstration of the feasibility of a new solution) and the innovation stage (the first regular production of a new technology) are discrete time events, the niche market and (large-scale) diffusion stages overlap. The distinction between invention and diffusion in terms of mechanisms of technological change is straightforward. At the invention stage, change is by definition disembodied and new technological knowledge is generated exclusively via directed research activity (e.g., basic R&D). By contrast, during the diffusion phase, technological change is largely embodied (in the form of new plants, equipment, and products) and improved knowledge is generated primarily via learning by doing and learning by using—that is, in direct connection with embodied technological change (change in capital stock via investments). Knowledgewise, there is also an important contribution from applied R&D (involved, e.g., in process modifications or in scaling up the unit size of technological installations). The innovation and niche market phases combine both embodied and disembodied technological change— knowledge generation via R&D as well as actual “hands-on” experience.

It is important to emphasize that the technology life-cycle model is used here as a conceptual and terminological framework. It does not imply a linear causality chain or a strict temporal sequence, as the literature is unanimous in rejecting such models of technological change because of the multitude of interlinkages and feedbacks at work [for a review of the literature, see Freeman (1994)].

In a conceptual simplification, in the subsequent discussion we merge the above two dichotomies. Disembodied technological change takes the form of “blueprints” (e.g., a patent application) resulting from directed research activity (e.g., basic R&D, with an emphasis on research). Embodied technological change represents changes in hardware; technological knowledge improves primarily via hands-on experience in market applications, with a costwise relatively small but knowledgewise important contribution from directed research activities (applied R&D, with an emphasis on development work).1 We recognize that no embodied technological change can proceed without disembodied change; in other words, investments in new plants and equipment usually also require changes in production organization, management, marketing strategies, etc. There are also important feedback mechanisms at work between embodied technological change and disembodied (technological and other) knowledge generation, for example, in the form of new instrumentation and measurement technologies that improve scientific analysis and understanding (Foray and Grübler 1996). For the analysis of technological change, however, the above distinctions, even if oversimplified, appear to be more useful than the traditional dichotomy between science and technology [conceptualized as applied science; see Toynbee (1962)]. This is because many of the improvements in technological knowledge have less to do with advances in science than with gaining hands-on experience, improving management, etc.—factors generally subsumed under the heading, “learning by doing.”

An important, if evident, observation is that, in addition to the different forms of technological knowledge generation, there is also a large variety of actors that develop that knowledge. Heterogeneity of agents is therefore an important aspect emphasized throughout the economics and sociological literature dealing with the creation and diffusion of technological knowledge (or, in our terminology, the development and application of disembodied and embodied technological knowledge). Heterogeneity is a central theme, for instance, when discussing the influence of industry structure on invention and innovation (e.g., Scherer 1980); when explaining differences in the adoption rates of industrial process innovations among different firms (e.g,. Mansfield 1968, 1977); or for understanding differences in adoption rates and levels of consumer products (Rogers 1983; Mahajan et al. 1991).

While different technologies or technology life-cycle phases are characterized by different relative contributions of tangible and intangible elements of technological change, it is worthwhile to recall two main conclusions from the literature. First, different forms of knowledge generation (basic applied R&D, learning by doing, and learning by using) are more complementary than substitutable (Rosenberg 1990; Pavitt 1993). Second, knowledge is acquired from both internal and external sources. The relative proportions vary widely across industries and technologies, and with firm characteristics [see the review by Freeman (1994) and the model of Silverberg (1991)], yet complementarity prevails over substitutability. New technological knowledge cannot be assimilated exclusively from external sources without corresponding internal knowledge. As Freeman (1994) notes, “all firms make use of external sources [of learning].” In other words, technological knowledge cannot be increased exclusively by internal efforts. Cohen and Levinthal (1989) have shown empirically the positive relation between the generation of internal technological knowledge (measured by R&D efforts) and the ability to assimilate external technological knowledge. Recognizing the importance of external knowledge sources for technological innovation and change raises an important externality problem: new knowledge is expensive to generate, but comparatively inexpensive to assimilate. “Leaky” (Mansfield 1985) technological knowledge implies that benefits do not necessarily accrue to those generating new knowledge, but rather to those who can most effectively apply new knowledge. This externality accrues first at the level of individual technology actors rather than at higher levels of aggregation (economic sectors, national economies, society at large).

Thus, at the highest level of abstraction, the following features of technology dynamics appear to be relevant for trying to model technological change as an endogenous process. First, the simple technology life-cycle model allows a separation of two distinct phases of technology genesis. At its earliest phase (invention), technological change is by definition “disembodied” (i.e., does not give rise to investments in new plants, equipment, and products), and knowledge generation relies exclusively on dedicated activity (typically R&D). Apart from the fact that such activities require resources and provide the essential basis for potential subsequent innovation, the act of invention is basically an act of human creativity that cannot be modeled. The second phase is characterized by complementary relationships between disembodied and embodied technological change as sources of improved knowledge. The relative proportions of different forms of knowledge generation (e.g., R&D, versus learning by doing) are highly variable over a technology's life cycle and across different technologies. As a generalization, we might conclude that the further a technology progresses in its technology life cycle, the more “embodied” technological change becomes. However, strict and neat separations in terms of cause-and-effect relationships and temporal sequences are not possible. Thus, second, both disembodied and embodied technological change, as well as different forms of knowledge generation, must be treated as interrelated and interdependent. Third, there is no social planner devising new technologies and improving existing ones. The existence of a multitude of different actors, as well as the fact that knowledge “leaks” and spillovers are central to technological evolution, gives rise to an important knowledge externality and results in different attitudes and behaviors of technology actors.

11.2.3   Characteristics of technological knowledge

New scientific and technological knowledge builds on previous knowledge and experience (de Solla Price 1965). Like all forms of knowledge, it is nonrival, complementary, and cumulative. A new technological artifact, like a new biological species, is seldom designed from scratch. Evolving designs (e.g., for successive generations of aircraft models or semiconductors) are perfect examples of evolutionary strategies of technological change. Moreover, they illustrate that the improvements in design, performance, economics, etc., that a new technology represents are deeply rooted in the experience and knowledge gained by designing (and using) its predecessors. From that perspective, most technological innovation is Usherian (incremental) rather than Schumpeterian (revolutionary), to paraphrase Ruttan's distinction (1959). Knowledge as applied in production also exhibits cumulativeness: initial defects are eliminated progressively as production volumes grow, production processes are scaled up, costs fall, model varieties and regional product differentiations are introduced, etc. Knowledge concerning the use of technologies (like knowing how to drive a car) is also cumulative. The need for extensive consumer learning in order to use novel artifacts has well-demonstrated effects of slowing down diffusion (see Rogers and Shoemaker 1971).

If technological knowledge is cumulative, then the development of a new design, the organization of a new production run, the use of an improved consumer product, etc., all benefit from the entirety of previous experiences and knowledge generated (subject to knowledge depreciation, discussed below). This can substantially improve the performance and costs of the latest technology “species” produced and speed its diffusion. In short, cumulativeness of knowledge implies the possibility of increasing returns. The most popular example of this in the technological literature is manufacturing “learning” or “experience” curves (Wright 1936; Arrow 1962; Alchian 1963; Argote and Epple 1990). Even comparatively “simple” technological learning processes, such as reductions in labor requirements in the mass production of a standardized technological artifact, build on whole series of earlier prototypes. In other words, a design and engineering competence needs to be accumulated before any large-scale industrial production can take place. A good example is the detailed case study of the B-17 Flying Fortress bomber by Michina (1992, 1999). That case study also demonstrates that learning by doing in manufacturing involves the accumulation of managerial and production organizational knowledge far more complex than simple scale economies or improved performance of repetitive production tasks by individuals and the work-force as a whole. Improved technological knowledge thus draws on a multitude of sources that cannot be reduced to single mechanisms or actors involved (Cantley and Sahal 1980).

Two important caveats are appropriate. First, technological innovation is a high-risk, high-uncertainty business. Few of the proposed solutions ultimately succeed, and anticipated future improvement rates for particular technologies are uncertain at best. While the payoffs from possible increasing returns on technological innovations are indeed enormous, they represent the extreme tails of distribution functions that cover the ultimate fate of all technological innovations, including those that never see widespread diffusion. Second, while technological knowledge is cumulative, it also depreciates if it is not applied (or is applied in a “stop-and-go” fashion). To paraphrase Rosegger (1996), the corollary of learning by doing is “forgetting by not doing.” Numerous examples from the aircraft industry are given in the literature (Epple et al. 1996; Michina 1999). Watanabe (1995, 1999) identified a time lag of about three years in the translation between disembodied and embodied technological change for Japanese photovoltaic (PV) cells, and a depreciation of the technology-specific knowledge stock (measured by cumulative R&D expenditures) of about 20 percent per year (owing to the relatively short lifetime of about five years for a given PV technology, a result of rapid technological progress).

Again abstracting from our review of the literature, we arrive at the following generalizations. Technological improvements result from the accumulation of different sources of knowledge. The cumulative nature of technological knowledge can result in increasing returns. In other words, the more a technology is researched, experimented with, and tried out (including market applications), the better its performance, the lower its costs, etc. Sources of improved technological knowledge include both changes in design and experience gained in the production and utilization of new artifacts, and it is impossible to draw neat distinctions between the two without reverting to the now widely dismissed linear model of innovation. Yet, accumulation of technological knowledge does not automatically result in improved technology. Uncertainty is inherent: a few “big hits” can lead to significant jumps in productivity and efficiency [i.e., what Nordhaus (1997) considers to lie outside “routine innovations”], and most technological innovations are bound for oblivion, either as straightforward failures or as examples of innovations that never enjoyed widespread market application (i.e., diffusion).

Uncertainty is pervasive and persistent in technological evolution, representing both risks and opportunity for technological innovation. For those emphasizing the risk aspect of uncertainty, technological innovation can be seen as simple contingency planning. For those emphasizing the opportunity aspect of uncertainty, innovation corresponds to Schumpeter's (1934, 1942) conceptualization of the expectations of exceptional rates of profit to be reaped from temporary monopolies after the introduction of successful innovations. Both supply- and demand-side aspects of uncertainty need to be considered. Taking the example of energy technologies, uncertainties in energy demand and resource availability and costs (development of exploration and production technologies) need to be considered, along with uncertainties in future states of energy supply and enduse technologies (e.g., availability and costs) and the expenditures necessary to arrive at that future state—if it can be realized at all. Recognizing the importance of technological expectations points up the significance of heterogeneity of risk/opportunity perceptions among actors, which needs to be reflected in modeling. Technological expectations are also inherently subjective, defying any attempts to capture technological uncertainty under increasing returns with classical probability analysis.

11.2.4   Technology systems

Technological evolution is systemic. It cannot be treated as a discrete, isolated event that concerns only one artifact. A new technology not only needs to be invented and designed, but it needs to be produced as well. This requires a whole host of other technologies. Consequently, Kline (1985) refers to technology as “socio-technical systems of production and use” of artifacts. In most cases, technologies rely on infrastructures. A telephone needs a telephone network. A car needs both a road network and a gasoline distribution system, each of which consists of whole “bundles” of individual technologies. This interdependence of technologies frequently results in “lock-in” phenomena (Arthur 1983, 1989) that cause enormous difficulties in implementing large-scale changes, specifically in dealing with technological obsolescence in the sense of Frankel (1955), or what has more recently been referred to as technological “inertia” (e.g., Ha-Duong et al. 1997). But this interdependence is also what causes technological changes to have such pervasive and extensive impacts once they are implemented. The systemic aspects of technology are well recognized in the economic and technological literature in the form of “forward” and “backward” linkages (see, e.g., Fishlow 1965, von Tunzelmann 1982, and Freeman 1989) and “network externalities” (Katz and Shapiro 1985), as well as in conceptualizations of technological “families,” “trajectories” (Dosi 1982), or “clusters” (Grübler 1998). In the absence of a priori knowledge of all possible systemic linkages between up- and downstream individual technological realizations, and with the daunting empirical problems of taxonomic classification methods such as morphological analysis (Foray and Grübler 1990; Godet 1997), simplified approaches that focus on key relationships (demand and supply of new technologies, their related infrastructures, and “upstream” technologies for the most important factor inputs) may not do justice to the complexity of large technical systems. Nonetheless, they represent an advance over conceptualizations of singular, “island” technologies, as typified by classical concepts advanced in the literature, such as that of “backstop” technologies (Nordhaus 1973).

Thus, as a basic conclusion, we retain the need for a (even if highly simplified) “bottom-up” representation of technological systems that aims at representing the most important technological/infrastructural interdependencies as well as possible synergies and spillovers within various “families” or clusters of technologies.

11.3   A Stylized Model

Below, we present the main features of a stylized model of endogenous technological change. It is a multiregion, multi-actor model of uncertain increasing returns on technological innovation that also considers most of the salient uncertainties in the market environment in which technology choice takes place (e.g., demand, resource availability, environmental limits). A distinguishing feature of the model is that the omniscient social planner is replaced by a set of actors, each of which optimizes its own part of a global system while remaining interdependent via negotiated energy and technology trade flows. In other words, the concept of a global optimum (viz. cost minimum) is replaced by a Pareto-optimal formulation.

“Optimality” in this model is not based on finding a cost-minimum solution (which could be calculated only with perfect foresight) or on simply minimizing an expected value of corresponding energy systems costs (the most common approach using the so-called best guess technique). Instead, an optimal solution represents the best hedging strategy vis-à-vis a large number of persistent uncertainties; that is, uncertainties that are not assumed to be reduced at any arbitrary future date, as is done in classical stochastic optimization models. Some of these uncertainties cannot be estimated using classical statistical approaches because of the lack of reliable data. Others, as in the case of future performance of new technologies, are impossible to quantify because of their strong dependence on intervening policy actions (e.g., R&D expenditures, taxes, and other forms of market interventions). In such cases, subjective estimates based on “expert” judgments and model scenario analyses under a range of assumptions are unavoidable.

The model takes a global long-term perspective representing a stylized energy sector in which technology choice is studied under conditions of uncertainty. Model formulations draw on previous modeling work at the International Institute for Applied Systems Analysis (IIASA) (Golodnikov et al. 1995; Messner et al. 1996; Messner 1997; Grübler and Gritsevskyi 1998; Gritsevskyi and Nakicenovic 2000), with parameterizations largely derived from recent studies of long-term energy perspectives (Nakicenovic et al. 1998a; IPCC 2000) in which inter alia major long-term uncertainties for the energy sector were analyzed based on a scenario approach. The model overview presented here is short and nonmathematical. For a more formal exposition, see Grübler and Gritsevskyi (1998), and Chapter 10 in this volume.

11.3.1   The actors

The model presented here does not assume the existence of a global social planner with perfect foresight. Instead, different actors are distinguished, all of which operate under uncertainty. Figure 11.1 gives a schematic overview of the actors in the model and their main interdependencies. Endogeneously determined flows are denoted by straight lines (e.g., Pareto-optimal trade flows between regions); uncertain model variables, by zigzagged lines. Uncertain model variables are both exogenous (e.g., demand, resource availability, etc.) and endogenous (e.g., future costs as a function of cumulative demand, in the case of uncertain increasing returns).

First, we distinguish between developers/users of energy sector technologies and the energy sector proper; that is, the aggregation of actors that supply the exogenously specified, uncertain energy demand. Energy technology developers/users or agents are differentiated based on differences in their technological competences (knowledge) and other characteristics, most notably financing capability. At one end of the spectrum are truly “global” agents that have vast financing capabilities and that, through their size and financial resources, can diversify their investments across all regions and technology portfolios. Such agents have or can acquire technological competences over the entire technology spectrum. A typical example is a company like Shell, a global player in the oil and gas business that recently has begun diversifying into a wide range of other energy technologies, including biomass plantations, independent power production, fuel cells, manufacturing of PVs, etc. At the other end of the spectrum are small, innovative actors with highly specialized technological knowledge and limited financial resources (e.g., the joint venture between DaimlerChrysler and the fuel cell manufacturer Ballard, or a wind turbine manufacturer cooperating closely with a “green utility” in Denmark). Intermediate actors are agents that essentially operate at a regional scale and at intermediate levels of technology specialization. A typical example is a large national or regional electric utility that builds and operates a diversified electricity generating park (coal, nuclear, hydropower, etc.) as well as transport and distribution infrastructures.

Figure 11.1. Schematic Overview of Actors and Their Main Interdependencies in the Model.

Flows denoted by straight arrows are endogenously determined variables. Zigzagged arrows indicate uncertain variables. Note that for clarity of exposition only two of five regions are illustrated in the figure. The three types of technology actors shown at the bottom are modeled via one representative agent each.

The second group of actors consists of five representative energy-producing/consuming regions. These five regions follow a geographical breakdown that is by now customary in global integrated assessment modeling. Countries are grouped on the basis of similarities of socioeconomic development status, economic and energy systems structure, export/import balances, and resource availability. The model distinguishes two Organisation for Economic Co-operation and Development (OECD) regions (Canada, the United States, Australia, and New Zealand, on the one side; Western Europe and Japan, on the other), the reforming economies of Central and Eastern Europe and the former Soviet Union (EEFSU), and two developing regions (Asia; and Latin America, Africa, and the Middle East).

11.3.2   The objective function and interaction between actors

Components of the Objective Function

Figure 11.2 summarizes the various elements of the objective function. Moving from the top of the figure down, more and more elements of uncertainty are represented in the objective function. In the model runs reported in Section 11.4, we consider step-by-step increases in the levels of uncertainty; thus the overall objective function becomes increasingly comprehensive. These various levels of uncertainty are separated by dashed lines in Figure 11.2. The various model runs (labeled A to F) of Section 11.4 corresponding to these levels are also shown in Figure 11.2. For any level (and model run), the objective function includes all those components of the particular level plus all previous ones, as summarized in Figure 11.2.

At the most fundamental level, three different approaches and levels of comprehensiveness of the objective function can be differentiated. In the simplest case (level A in Figure 11.2), the objective is to minimize total discounted global energy systems costs under perfect foresight, or, more strictly speaking, to minimize the total expected value for these systems costs. This is the approach of traditional optimization models assuming a social planner and is considered here for comparison purposes only. In a second case (level B in Figure 11.2), the global optimum is replaced by a Pareto-optimal formulation, assuming no uncertainties (with “best guess” central values used as expected mean values). Each region acts as a cost-minimizing agent on its own regional energy systems costs; in other words, each has its own objective, all of which are summed into a global Pareto optimum based on regional weights. Finally, in a third category of cases (level C and onward in Figure 11.2), uncertainties are explicitly considered. The regional agents (typified, for instance, by departments of energy or similar national/international planning agencies) are assumed to have foresight, subject to stochastic uncertainties (demand, resource quantity–cost relationships, technology availability, costs, etc.). These uncertainties are quantified costwise in a risk function and are integrated into the objective function.

Representing Uncertainty

Following the approach described in Golodnikov et al. (1995), Messner et al. (1996), and Grübler and Gritsevskyi (1998), uncertainties are represented as follows. Unless otherwise indicated, the uncertainty space around all salient variables is represented by a normal distribution function around a mean expected value. The model solution with all variables set at mean expected values yields the (minimized) expected costs (denoted as E in Figure 11.2; these are exactly the costs considered in traditional optimization models with perfect foresight). To these expected costs we add a risk function (denoted as R in Figure 11.2) to the objective function. (Note that for clarity of exposition we break the expected costs E into various components in Figure 11.2. Deviations around these expected cost items are not listed separately in Figure 11.2; they are all summarized in the regional risk functions denoted as Rr in the figure.)

Figure 11.2. Overview of Representation of Increasing Sources of Uncertainty in the Model and Their Consideration in the Objective Function.

Corresponding model runs (from Section 11.4) are labeled A to F. E = expected costs, R = risk function term, PO = Pareto optimum; index r refers to components of regional objective functions, index a refers to components of the objective function that represent the technology agents.

Simultaneous random draws “poll” the uncertainty space, and a model solution is calculated for each draw. Deviations from the mean expected costs are summed into the risk function that is added to or subtracted from the objective function. Sampling continues until the uncertainty space is statistically sufficiently explored and an overall “robust” cost-minimal solution including the risk function can be calculated. Representative sampling of the uncertainty space around the mean expected value means that the risk term integrated into the objective function is the product of cost differences (compared with the expected costs) and their respective probability of occurrence (as reflected in the uncertainty distribution around the mean expected values). It is important to emphasize that the costs are discounted (at 5 percent in all calculations reported here)2 and refer to the entire simulation horizon. The resulting changing energy systems structure and profiles of technology development over time are frequently referred to as “strategies” to emphasize their dynamic nature and the interdependence between important variables (such as cumulative demand and costs for technologies, in the case of increasing returns).

In other words, our modeling approach assumes that, during the planning process, the regional actors probe all of the most important uncertainties and contingencies of their region's energy development that deviate from their mean expected values to finally arrive at an optimal (cost-minimal) contingency or hedging strategy vis-à-vis multiple uncertainties. We assume that the planning process proceeds conservatively; that is, future realizations that lead to energy systems costs that are higher than mean expected values are considered to be more important for decision making than realizations that lead to lower-than-expected costs. In other words, risk aversion takes precedence over opportunity seeking.3 For computational simplicity, we assume a linear risk function [see Grübler and Gritsevskyi (1998) for alternative, nonlinear formulations], with the risk-aversion gradient being twice as large as the opportunity-seeking one. We assume that a 10 percent cost overrun (costs turn out to be 10 percent higher than mean expected values) is weighted twice as high as a negative deviation of 10 percent (costs turn out to be 10 percent lower than expected). The risk function includes an additional weighting factor, representing different degrees of risk aversion. The risk factor is conceived as being different across regions and actors.

The agents interact through energy trade and technology flows. Regions interact via endogenously determined energy trade (for simplicity, only some energy products are traded in the model—coal, crude oil, natural gas, and methanol/ethanol). Regions “negotiate” an intertemporal energy trade flow pattern in which each region's total energy costs (including the net balance between exports and imports) can no longer be improved without a deterioration of the total energy costs of all regions (i.e., a Pareto optimum). Export prices are assumed to be close to marginal resource extraction costs; resource extraction for domestic use is determined based on average extraction costs. Financial transfers are accounted for: export revenues are added as negative energy systems costs to the producing regions, and import costs are added to the energy systems costs of importing regions.

The technology agents interact with one another and, if regionally based (i.e., all agents except “multinationals”), also with their respective regional agent. Because the technology agents are subject to laws and regulations, they cannot act as regional social planners. However, their relative success (or lack of it) in technology development and diffusion is assumed to be considered at least at the global level. The interaction between the technology agents and the regions proceeds via the interactions between technology demand (by regions) and technology supply (by agents). As the export market for energy technologies is essentially global, different technology demands (resulting from expected technology costs plus all other salient model drivers) across regions are not independent of one another. Realization of potential learning effects (cost reductions) depends on global technology demand rather than on regional demands alone. This again leads to a Pareto-optimal solution of the global demand for energy technologies. In other words, the technology actors and the energy-consuming/producing regions “negotiate” an intertemporal technology demand pattern, whereby each region's costs can no longer be improved without a deterioration of the costs of all regions.

Technology agents then supply that demand at expected cost values to the regions—subject, however, to uncertainty—with different technology agents exhibiting different degrees of risk aversion. Uncertainty is again represented via stochastic sampling, the results of which are incorporated into the overall objective function via a risk term, as explained above. These risk/benefit terms (i.e., technology actors supply technologies to the region at lower- or higher-than-expected costs) are then added to the sum of regional energy systems costs (i.e., at the global level), ensuring that the risks of the technology agents are considered in the Pareto-optimal global solution.

11.3.3   Energy demand

Two distinguishing features characterize the energy demand of our stylized model: first, future demand (growth) is uncertain, and, second, quality matters. The five regional energy economies demand three homogeneous energy goods, characterized by their energy form (and their exergetic form value): solids, liquids, and grids. Within each energy form, different combinations of primary resources and conversion technologies can satisfy the demand. In other words, we assume perfect substitutability within each energy form. For instance, the demand for high-quality energy carriers (“grids”) can be satisfied via electricity generated from coal or from PVs or wind turbines, or alternatively by natural gas. We assume asymmetric (and partial) substitutability between energy forms; that is, substitutability is only possible in the direction from high to low exergetic energy forms. Electricity (“grids”), for instance, can replace coal (“solids”) as a final energy carrier, but the reverse is not true. We consider this model feature to be an important improvement over conventional energy models which have focused only on quantities and prices, largely ignoring energy quality.

Quantitatively, the model is parameterized based on the long-term energy scenario study reported in IPCC (2000). These scenarios span a wide range of future uncertainties in energy demand, with the added benefit of having been carefully peer reviewed. Uncertainty in demand is represented by normal distributions around a mean expected value of energy demand per category, assumed to correspond to the numerical projections of the “middle ground” Scenario B2 in IPCC (2000). It must be emphasized that the demand uncertainty thus represented in our model is significantly smaller than the entire uncertainty range spanned by the full set of IPCC scenarios.

The treatment of demand uncertainty is analogous to the procedure outlined above. Supply expansion reflects successive random draws from the demand uncertainty space around a mean expected value. Lower-than-expected demand translates into excess supply (i.e., lower capacity utilization); higher demand translates into a supply shortfall. For the latter case, the model does not employ “hard” constraints, but instead uses a penalty function approach, analogous to the treatment of uncertainty in our model. The final result is again an optimal supply expansion path vis-à-vis an uncertain future evolution of energy demand.

11.3.4   Technologies

Systems Structure

The technologies represented in the model provide the necessary links (as a rule, conversion processes) between primary resources, on the one hand, and final energy demand, on the other hand (Figure 11.3). Three demand categories (solids, liquids, and grids) and five different primary resource categories (coal, oil, gas, biomass, and other zero-carbon energy sources) are modeled with 56 technologies in between. The reference energy system of our model includes 4 extraction technologies; 3 backstops; 23 transport/distribution, trade, and other energy systems balance technologies; and 26 energy-conversion technologies proper, 12 of which can exhibit increasing returns (indicated in Figure 11.3). The reference energy system of our model represents an intermediate level of complexity compared with the stylized three-technology model presented in Grübler and Gritsevskyi (1998) and the full-scale complexity of the model presented by Gritsevskyi and Nakicenovic (see Chapter 10 in this volume), which requires massive parallel computing.


To reduce model complexity and allow for analytical solutions within reasonable computing times, a number of simplifications were introduced. First, only technologies past their innovation stage are considered. Technologies therefore need to have demonstrated their technical feasibility and established a small commercial niche market, even if that market is infinitesimally small by the standards of the energy sector. Thus, cold or hot fusion is not considered, but wind turbines, fuel cells, etc., are. Second, technologies represented in the model are kept as generic as possible. Hydrogen-powered fuel cells are not distinguished from related technologies using natural gas, but the hydrogen generation and distribution technologies upstream in the energy chain are included in the model. Third, for simplicity the model considers only levelized costs: no distinctions are made between investment and operating costs. Expenditure “bulkiness” is, however, reflected by considering the different unit output sizes of technologies. In other words, a unit of output expansion leading to possible technological learning is more expensive for nuclear reactors than for solar PVs. Finally, a distinction is made between existing, mature technologies and new technologies. “Existing” technologies in the model mainly serve as accounting identities; costs are not treated as uncertain and technologies do not exhibit potential increasing returns. Typical examples are oil pipelines, international coal shipping, and conventional coal-fired power plants. For new technologies, both initial costs and future costs as a function of intervening efforts (investments in R&D and niche market installations) are treated as uncertain. Two generic categories of new technologies are considered: incremental and revolutionary. These two categories differ in terms of their initial costs, the potential for cost reductions with accumulated experience, the associated uncertainties, and the relative importance of disembodied versus embodied technological change (R&D intensity).

Figure 11.3. Reference Energy System of the Model Showing Energy Flows (Arrows and Boxes) and Conversion Technologies (Circles).

For each technology level, the number of technologies represented in the model is indicated at the bottom of the figure. All technology costs outside transport and distribution technologies are treated as uncertain. Technologies that can exhibit uncertain increasing returns are shown in full circles; roman numerals indicate the technology cluster within which spillover effects are assumed to occur. T = long-distance transport; T/D = transport and distribution.

Disembodied versus Embodied Technological Change

The sources of potential increasing returns on new technologies are treated as interdependent and complementary. Thus, disembodied technological change (“learning” via R&D; i.e., new design blueprints) and embodied technological change (learning by doing and learning by using) are considered the necessary two sides of the same coin. Therefore, the model does not formally distinguish between R&D and plant expenditures: the necessary R&D component for new energy technologies is simply added as a fixed percentage to the technology costs. To avoid the criticism of underestimating R&D costs, we make the conservative assumptions of 20 percent for “revolutionary” technologies [based on Watanabe (1995)] and 10 percent for all other new technologies. Initial mean costs of new energy technologies are derived from a statistical analysis of the technology inventory CO2DB available at IIASA (see Strubegger and Reitgruber 1995). Formally, R&D expenditures are represented simply by increasing the intercept of initial technology costs by an R&D component in the functional formulation, where future costs can decline as a result of cumulative output. R&D expenditures are thus considered to be necessary as long as technologies exhibit increasing returns.4

Uncertain Increasing Returns

Learning rates (progress ratios) are treated as uncertain and are varied only parametrically and in an extremely simplified way. We assume mean expected learning rates of 10 percent (for a doubling of cumulative output) for all technologies that are classified as incremental innovations (e.g., a biomass-fired gas combined-cycle turbine compared with natural-gas-fired ones), or whose “lumpiness” precludes mass production (e.g., advanced reactor designs such as the high-temperature gas-cooled reactor, or HTGR). For “radical” innovations suitable for mass production (e.g., fuel cells, PVs), a mean expected learning rate of 20 percent is assumed. This figure is the empirical rule of thumb advanced in the literature; for example, it is the median of the sample of 108 learning rates reported in Argote and Epple (1990). The above distinction is based on a taxonomy of empirically analyzed technological learning rates of energy technologies reported in Christiansson (1995) and Neij (1997). Uncertainty ranges around mean expected learning rates are higher for “revolutionary” technologies than for “incremental” ones.

Formally uncertain increasing returns are introduced into the model as follows: we assume that the progress ratio (the negative exponent in a classical learning curve formulation) is uncertain, reflected by a normal distribution around a mean expected value. The expected future costs for technologies with potential for learning effects (as supplied by the technology agents) are thus log-normally distributed, contingent of course upon the realization of the cumulative output growth demanded by the energy-consuming/producing regions. The uncertainty space of the learning curve's progress ratio is again sampled by random draws and deviations from the solution, with mean expected values added to the objective function via the risk function term, as explained above. The main difference, of course, is that, owing to nonconvexity, exploration of this uncertainty space is computationally much more demanding.


Technology spillover effects are also represented in the model, albeit in a rudimentary and simplified way. First, potential spillovers between energy sector technologies and other sectors are not considered (e.g., between aircraft and gas turbines, or spillovers from the semiconductor industry to PVs). For energy sector technologies, we adopt the concept of technology “family” learning: technologies that belong to a generic class of technologies (various gas turbines, different fuel cells, etc.)—irrespective of the primary energy resource used as input fuel—are assumed to be entirely substitutable as targets for technology improvements. This assumption postulates the rather optimistic viewpoint that whatever improvement is achieved for one technology within a technology “family” spills over to the other technologies within that “family.” Thus, technological learning phenomena are treated as generic: improvements in gas-fired combined-cycle technology are assumed also to benefit gas combined cycles that use coal or syngas derived from biomass as fuel. Formally, this is done by adding all installations of technologies within one “family” to the cumulative installations of a combined technological learning curve. Altogether, four such technology “families” exhibiting joint technological learning via spillover effects are considered in the model (see Figure 11.3).


As mentioned, in addition to demand and resource quantity–cost uncertainties, the existence and magnitude of possible increasing returns from technological innovation are a main source of technological uncertainty in our model. Future technology costs can be influenced through different strategies; the outcome of such strategies is, however, uncertain. From the multiple dimensions of technology improvements, we consider only cost reductions that result from alternative research, development, and deployment strategies.

The causality mechanism of technological improvements (cost reductions) in our model is characterized by a twofold complementary relationship: between improvements in disembodied technological knowledge (R&D) and embodied technological knowledge (deployment),5 and between supply (by technology agents) and demand (by regions). This twofold complementarity reflects our understanding of the literature (e.g., Freeman 1994): there are different sources of technological knowledge that are not perfectly substitutable. Increased R&D expenditures might yield improved technology blueprints, but they do not lead to lowered technology costs in the market place in the absence of demand; and no matter how high demand growth is, improved design blueprints will not emerge without R&D. Conversely, technology demand and supply are complementary sources of improved technological knowledge. Learning by doing in manufacturing cannot take place in the absence of technology demand (e.g., realization of corresponding “learning by using” by technology users), and supply and demand interact via prices (traditionally captured via demand elasticities). These distinctions are not important in social planner models,6 but they are important in our multi-actor model (as well as in reality). Moreover, knowledge generation does not proceed in isolation from the economy or society at large. Changes in relative prices, environmental constraints, and even strategic considerations all play an important role and add to the complexity and uncertainty of the environment in which technology choices are made by a multitude of actors.

11.3.5   Resource and environmental constraints

Resource availability and environmental constraints are treated as uncertain. To some degree they represent two sides of the same coin: the uncertainty concerning the level of energy resources that can be extracted from nature and the level of resulting emissions that can be “disposed of” in the environment.

Resource availability and cost assumptions were derived from the “middle ground” Case B scenario described in Nakicenovic et al. (1998a), which we adopt for the mean expected values in our model. Corresponding resource extraction profiles and costs were obtained for the five regions of the model from that scenario [based on Rogner (1997)]. These assumptions ensure convex relationships between the quantity of resources available and their costs,7 which are preferred for ease of numerical solution. As for other salient uncertain variables, here too normal distribution functions are constructed around mean expected values. The resulting uncertainty domain explored by the model is narrower than those explored within the entire range of scenarios of Nakicenovic et al. (1998a) and the IPCC (2000). The reason is that including enormous amounts of unconventional fossil resources at potentially very low costs (e.g., methane clathrates) in the uncertainty space would result in nonconvex resource extraction cost profiles around the mean values of the Case B scenario. Relaxing this simplifying assumption remains an important task for future model improvements.

Future environmental constraints might emerge, influencing technology choices. Such constraints could take the form of either “hard” quantitative limits or emissions taxes. The existence, magnitude, and timing of such emissions taxes can be treated with the approach used to treat technological uncertainty. For the model calculations reported here, we follow assumptions similar to those described in Grübler and Gritsevskyi (1998) and Grübler (1998) for a possible carbon tax. First, we assume a cumulative probability distribution of the occurrence of the emissions tax over the entire time horizon. Starting near zero in 2000, the starting year of our simulations, the cumulative probability distribution rises over time. The illustrative (conservative) distribution function assumed reflects only a 50 percent chance that a carbon tax is ever implemented. The probability of the tax's being introduced rises to 25 percent by 2030, reaching 50 percent toward the end of the model's time horizon. For the magnitude of the tax, we assume a distribution with a very small probability of a high carbon tax level, as represented by a Weibull distribution around a mean value of US$75 per ton carbon (C), with a 99 percent probability that the tax will not exceed US$150 per ton C if it is implemented at all. According to our understanding of the literature, such assumptions do not represent any particularly daunting outlook on possible future environmental constraints.

11.3.6   Computational implementation

Computational model solutions are obtained by applying a sequential optimization procedure to sub-problems that approximate the original problem in two respects. In the most general case, a highly nonlinear stochastic global optimization problem should be solved. Stochastic operators in the objective function are approximated by statistically calculated values using simultaneous random draws, where the dynamically adjusted “polling” size is set according to the required accuracy. Nonconvexities that arise from increasing returns and corresponding cost reductions are handled using an adaptive stochastic search technique. This approach is based on a modified “direct” search algorithm using the Monte Carlo technique, but in this case with a dynamical adjustment of the probability space depending on the results obtained in the previous steps. For sub-problems calculated during the adaptive stochastic search, a linear optimization technique is used. Because the linear optimization problem is rather large (10,000–15,000 variables and 5,000–7,000 constraints), the interior point method with simultaneously solved primary and dual problems was employed. This method has additional benefits, including accuracy and a computation time that is adjusted depending on the ratio of “the best solution obtained so far” to the “low-to-high” approximation for the current sub-problem.

The model is implemented in the Matlab 6.x computational environment using its Optimization and Statistical Toolbox and the advanced optimization toolbox TomLab 3.0. The latter implements a large set of state-of-the-art optimization methods, including the Stanford Optimization Library.

11.4   Model Simulations

11.4.1   Introduction

Below, we discuss a number of quantitative model simulations, the results of which should be considered illustrative rather than definitive. The prime objectives of the model development and simulations reported here were to demonstrate the feasibility of an analytical solution of the proposed model and to gain qualitative insights into its behavior under an increasingly comprehensive treatment of uncertainty. To make the model's behavior transparent and to minimize computing time, for instance, no additional constraints beyond physical balance constraints were employed. Additionally, the use of levelized costs in this model version means that the dynamics of capital stock replacements or capacity under-utilization cannot be represented. These factors need to be borne in mind when judging the “realism” of the model simulations reported here, especially in comparison with other modeling approaches that employ constraints for reproducing base-year energy flows or additional market penetration constraints to avoid “flipflop” model behavior. The tentative model simulations presented here should therefore be viewed as a “work in progress” aimed at elucidating generic dynamic patterns of technological change under uncertainty and uncertain increasing returns in a multiregion, multi-agent model rather than results that can be taken directly “off the shelf” for energy or climate-change policy analysis.

To maintain comparability between model simulations, there are a number of important common assumptions for all model runs. First, energy demand, resource availability, and technology portfolio assumptions are shared by all simulations. The main differences are whether these assumptions are treated as certain or uncertain, whether technologies can exhibit (certain or uncertain) increasing returns to scale, and whether a (certain or uncertain) carbon tax is assumed in the model simulations. The uncertainty space around uncertain variables (demands, convex resource extraction cost curves, technology costs) is represented the same way in all model simulations. The uncertainty domain around each variable is defined as +/– three standard deviations around the mean expected value assuming a normal distribution. For the carbon tax case we assume a non-symmetric Weibull distribution. This reflects our interpretation of the literature that small-probability, high-risk events cannot be excluded from the climate-change problem. Hence, we consider the possibility of a low-probability but extremely high carbon tax level, as reflected in a Weibull distribution that otherwise shares the same variance as the other (normal) uncertainty distribution functions. Technically, all simulations also share the same discount rate (5 percent) and the same time horizon (eight 10-year time steps). Because of end-period truncation effects that diminish the significance of the model results for the last time period, in the subsequent discussion we report results only for the periods up to 2070.

11.4.2   A taxonomy of model simulations

Altogether six main types of model simulations were performed. These are denoted by the letters A to F in Figure 11.2 in the previous section and in Figures 11.4 to 11.7 in this section. In addition, a number of sensitivity runs for particular assumption permutations within scenario clusters were performed. These are denoted by consecutive numbers (2, 3) in combination with the letters of the main scenario clusters. Altogether 14 different scenarios (model runs) are reported in the subsequent sections.

Scenarios in cluster groups A and B embrace the traditional deterministic model framework. Key variables are not assumed to be uncertain; in other words, we assume perfect ex ante foresight. Scenario A represents the traditional social planner perspective; it postulates the existence of a single global social planner that optimizes regional resource allocation under a global (discounted) cost-minimum criterion. Scenario A2 is a sensitivity run assuming an uncertain carbon tax for the social planner, no-uncertainty scenario A. Group B scenarios contrast this scenario with a Pareto-optimal formulation. Scenario B2, where regions have equal weights, is for all practical purposes identical to the social planner perspective of scenario A and serves only as a control scenario calculation. Scenario B3 is equivalent to the main scenario B (Pareto optimum), but in addition assumes an uncertain carbon tax (comparable to scenario A2).

Scenarios in groups C and D systematically introduce additional uncertainties. Scenario C, a kind of initial base case for the subsequent simulations, uses a Pareto-optimal formulation (like the scenarios in group B), but treats energy demand, resource availability, and technology costs as uncertain. No carbon taxes or increasing returns are assumed. Scenario D adds an uncertain carbon tax (see Section 11.3 and discussion below) to Scenario C; the sensitivity run of Scenario D2 assumes a carbon tax with an ex ante known probability of occurrence and a perfectly known value. The difference between scenarios D and D2 illustrates the effect of treating future carbon tax levels as uncertain (assuming an asymmetrical uncertainty distribution, in this case, a Weibull distribution).

Scenarios in group E model the impacts of assuming increasing returns to scale in new energy technologies as a combined result of investments in research, development, and deployment; learning by doing; and learning by using (see Section 11.3). Scenario E (scenario with full uncertainty) assumes uncertainty in both increasing returns and a carbon tax. Scenarios E2 and E3 provide sensitivity runs for this scenario. In scenario E2, increasing returns are treated as certain (i.e., potential future cost reductions as a function of intervening investments are assumed to be perfectly known ex ante). Scenario E3 models uncertain increasing returns in the absence of an uncertain carbon tax.

Finally, scenarios in group F model heterogeneous agents on top of the scenarios in group E. Whereas in the previous scenarios, regions and technology agents all share the same risk function, in scenario group F the risk functions differ. Scenario F assumes (conservatively) only a small dispersion of risk factors. The small-scale, local technology agents (constrained to a maximum of 5 percent market share in each region) are assumed to be high risk takers, whereas the global technology agents (maximum 30 percent market share in any region) are assumed to be risk averse. Regional technology agents are assumed to share the same risk function as the energy-producing/consuming regions, as in the previous scenarios. Scenario F2 assumes that all technology agents are highly risk averse; that is, cost overruns are weighted three times as much as the energy regions. Scenario F3 is identical to scenario F2, except for the absence of the uncertain carbon tax.

Figure 11.4. Overview of Scenarios and Their Global Total Expected Energy Systems Costs (Discounted 5 Percent), in Trillion (1012) US$ for the Model Run Scenarios.

For explanation of individual scenarios, see Figure 11.2 and text. Scenarios assuming a carbon tax are indicated with an asterisk.

Figure 11.4 summarizes the scenarios that form the basis of the subsequent discussion in this section in terms of their global total, discounted expected energy systems costs. Costwise, the greatest differences between scenarios concern assumptions regarding the introduction of a future carbon tax that raises total expected costs (e.g., scenario B2 versus scenario B, or scenarios D and D2 versus scenario C), and assumptions about possible increasing returns to technological innovation that lower total expected costs (e.g., scenario E3 versus scenario C, or scenarios E2 and E versus scenario D). Conversely, cost differences between social planner (A, B2) and Pareto-optimal scenarios (e.g., B), between scenarios of deterministic versus uncertain carbon taxes (D2 versus D), between certain versus uncertain increasing returns (E3 versus E2), and between homogeneous versus heterogeneous risk aversion (scenarios F2 or F versus E) are small. Scenario differences in terms of trade flows, technology portfolios, or emissions will be much larger than this simple comparison of total expected costs might suggest. Nonetheless, the cost differences of the scenarios provide a useful basis for structuring the following discussion into scenario differences under the presence (or absence) of increasing returns or the existence (or absence) of carbon taxes, or a combination of these factors. Before doing so, however, we will address the scenario differences between a social planner and a Pareto-optimal formulation.

Figure 11.5. Energy Trade Flows (Imports of Fossil Fuels, in Gtoe) at the Global Level (Solid Lines) and for the OECD Regions (Dashed Lines) for Two Optimization Scenarios: Social Planner Perspective (Scenario A) and Pareto-Optimal Formulation (Scenario B).

All other salient scenario variables (demand, resource availability, technology costs, absence of environmental constraints) are identical. For comparison, 1998 trade flows for the world (black diamonds) and the OECD (white diamonds) are also shown [based on IEA (2001)].

11.4.3   Social planner versus Pareto optimum

Scenario A embraces the traditional social planner perspective of long-term energy-optimization models.8 Conversely, Scenario B replaces the traditional global optimization with a “negotiated” Pareto optimum among the five energy-consuming/producing regions of the model. As expected, scenario differences are greatest in terms of energy trade flows, particularly in the short to medium term (Figure 11.5).

Short- to medium-term trade flows are substantially lower in the social planner scenario. If there were a single global social planner deciding on energy supply options, supply security concerns and import diversification would not be factored into the global optimization. Instead, regions focus on domestic energy production where they have the highest comparative cost advantages (e.g., coal-based electricity as opposed to imported liquefied natural gas in OECD countries outside Europe and Japan), with trade flows restricted to non-substitutable commodities (e.g., oil in the transport sector) and between regions with high resource extraction cost differences (e.g., Middle East versus North Sea oil). The generally low energy trade flows in scenario A also reflect our use of marginal rather than average extraction costs for the initial, flat part of the upward-sloping regional resource extraction cost curves [increasing resource extraction costs, particularly for oil in the “rest of the world” region and for gas in the “reforming economies” (EEFSU) region]. They also reflect the assumption of partial substitutability between the energy demand categories “liquids” (e.g., oil products) and “grids” (electricity, gas). Recall also that base-year energy flows are not constrained in the scenario calculations reported here.

The Pareto-optimal solution of scenario B is radically different. Short- to medium-term trade flows are much larger, both for the OECD and for the world as a whole. Simulated trade flows are also in much better agreement with actual trade statistics both quantitatively and qualitatively (Figure 11.5). Whereas after 2020, global trade patterns of fossil fuels are quite similar in both scenarios on aggregate, regional differences persist. In particular, fossil fuel imports to the OECD region are much larger in the Pareto-optimal scenario than in the social planner scenario.

The results suggest that, over the long term and at the global level, the differences between a social planner and a Pareto-optimal perspective could be less pronounced than one might expect a priori. Given a limited number of negotiating parties9 and decisive regional differences in the long-term availability of fossil resources, global trade patterns are almost identical between the two approaches. On the one hand, this finding is welcome news for global, long-term energy and emission scenarios, which have almost invariably embraced a global social planner perspective. On the other hand, the results also indicate that short-term and regional trade patterns are very different in the two approaches. This finding cautions against the use of global social planner models in policy analysis of “winners” and “losers” of climate policies, for instance, when identifying the impacts of carbon taxes on future oil export revenues.

11.4.4   Technology choice under uncertainty

To compare the differences in technology choice under various conditions of uncertainty, we first reduce the comparatively high technological complexity of the model results to a manageable number of variables. To that end, Figure 11.6 compares the diffusion of various energy technologies aggregated into three clusters with two technology groups each (i.e., six groups altogether). The technology clusters are differentiated with respect to technological maturity. Within each cluster, we then differentiate between two groups of technologies: fossil-fuel based and non-fossil based. The first cluster aggregates currently available “offthe-shelf” technologies such as conventional coal-fired power plants, gas combined cycles, or conventional nuclear power plants. The second technology cluster comprises fossil and non-fossil technologies that represent incremental improvements over existing technologies or that can be expected to become commercially available in the medium term, such as advanced coal-fired power plants, gas-based fuel cells, wind turbines, or hydrogen from steam reforming of natural gas, etc. Finally, the third cluster represents long-term technology innovations: coal-based fuel cells, non-fossil hydrogen production and end-use technologies, advanced decentralized renewable electricity options (e.g., PVs), or inherently safe advanced reactor designs.

The top left-hand panel in Figure 11.6 shows technology choice without considering any uncertainty at all (Pareto-optimal scenario B). The patterns of technology choice are characterized by total reliance on currently known “off-the-shelf” technologies, which are almost exclusively based on fossil fuels. As such, the scenario mimics perfectly the static technology picture of traditional “business-as-usual” scenarios available in the literature.

More interesting are the patterns that emerge when salient energy systems uncertainties—such as demand, resource availability, or technology costs (scenario C, middle panel, left), or an uncertain carbon tax (scenario D, middle panel, right)—are introduced in the absence of possible increasing returns. Although existing fossil-fuel-based technologies remain dominant over the entire simulation horizon, there is nonetheless a substantial diversification of technology choice, including long-term “third-generation” technology options. Technology diversification and up-front investments in technology options that may have a significant market impact only after 2050 are thus an economically rational hedging strategy in view of uncertainty. The possibility of a carbon tax biases the technology portfolio more in the direction of non-fossil technologies, albeit not exclusively. The general pattern that emerges is that, with additional uncertainties (such as an uncertain carbon tax on top of all other uncertainties), the technology portfolio relies even less on conventional fossil-based energy technologies and becomes even more diversified.

Introducing possible increasing returns to technological innovation yields yet another distinguishing feature of technology choice. The dominance of current, fossil-based technologies disappears entirely. The direction and breadth of diversification in turn are a direct function of the extent to which uncertainty is considered. Making the rather unrealistic assumption that the magnitude of possible increasing returns is known with perfect foresight (scenario E3, bottom panel, left) and assuming no carbon tax reduces technological diversity in favor of rapid diffusion of “third-generation” fossil technologies (e.g., coal-based fuel cells). This focus on a few technologies is a direct result of the hypothetical assumption of no uncertainty and perfect foresight. Under these conditions, there is no economic logic for incurring additional costs10 for diversifying technology portfolios and experimenting in realizing potential increasing returns across a broad front of technology options. The fact that long-term fossil-based technologies are favored in this particular simulation of scenario E3 is not particularly significant, as it is entirely dependent on input assumptions (in this case, initial start-up costs of fossil versus non-fossil “third-generation” technologies). More interesting is the case with full uncertainty (scenario E, bottom panel, right). Here, a much broader diversification takes place, and the presence of an uncertain carbon tax shifts the direction of technology choice in favor of both medium- and long-term non-fossil technologies. As in scenario E3, this swift shift occurs to the detriment of existing technologies (technology group one in Figure 11.6).

Figure 11.6. Global Diffusion of Six Groups of Energy Technologies (in Gtoe) under Different Types of Uncertainty.

Scenarios grouped to the right (gray background) include an uncertain carbon tax; scenarios grouped to the left (white background) exclude a carbon tax. For explanation of scenarios, see Figure 11.2 and text.

Considering that our simplified model does not employ base-year constraints and that it uses levelized costs and optimizes over an entire time horizon spanning many decades, the dynamics of technology “switch-over,” particularly over the short term, are neither plausible nor realistic. As we have shown elsewhere (Grübler and Gritsevskyi 1998), moving toward an explicit representation of capital stock (i.e., also of sunk investments) alleviates this problem of an overly dynamic technology response, especially in the case of potential increasing returns.

Nonetheless, a number of general conclusions can be drawn from the model simulations shown in Figure 11.6. Foremost, while a radical transformation of the energy technology landscape is possible, it requires consideration of all salient uncertainties. Thus, postulating increasing returns, general scenario uncertainty, or carbon taxes alone is not sufficient to move away from a “lock-in” situation of the dominance of current fossil technologies. A combination of all these factors, however, can result in a shift from the current lock-in on fossil technologies and a radical transformation of the technological landscape. Second, radical technological change (i.e., toward “third-generation,” long-term technology options) seems possible only by considering some mechanism of increasing returns on technological innovation, as uncertain as it may be. Third, there is an inherent tradeoff between phenomena of increasing returns and uncertainty: assuming perfect foresight and no uncertainty leads to a pronounced “crowding-out” effect in the technology portfolio. Innovation efforts (investments in R&D and niche market deployments) concentrate on a few technologies in order to maximize learning effects at the lowest possible costs. Conversely, treating the potential benefits from innovation as uncertain requires hedging and technology portfolio strategies that increase diversity but come at additional costs. Finally, independent of the scenario considered, in the model simulations one technology group—fossil-based “incremental” innovations (cluster 2)—systematically has the lowest option value and diffusion potential. Advanced coal-fired power plants, but also gas-based fuel cells (even though they look promising from a medium-term perspective), do not succeed in the model simulations. Whereas this result should not be interpreted as a definitive judgement of the potential merits of these technologies, it does point to yet another trade-off. Ultimately, technology policy will have to move from the easy decision to “let one hundred flowers bloom” to tough choices of whether to further near- to medium-term incremental innovation or concentrate on radical, long-term options. Because in our model we have embraced a time frame that extends many decades into the future, the answer we can report here is predetermined. A definitive answer on the option value of near- versus long-term technology portfolios awaits further methodological improvements in our model—for example, moving from devising an optimal hedging strategy for a single long time horizon to some other decision-making paradigm, such as sequential decision making under a rolling time horizon.

Figure 11.7. Carbon Emissions for Different Scenarios with Varying Degrees of Representation of Uncertainties (Index, 2000=1.0).

Scenarios including a carbon tax are denoted by solid lines; scenarios without a carbon tax, by dashed lines. For an explanation of the scenarios, see Figure 11.2 and text.

11.4.5   Environmental constraints

Figure 11.7 reports the resulting carbon emissions of the various scenarios simulated by the model. Because of unconstrained model simulations, slight scenario differences emerge in the base year.11 To clarify the dynamics of carbon emissions under increasing treatment of uncertainty, Figure 11.7 shows emissions as an index starting at base-year values of one.

The highest, continuously rising carbon emissions result from the scenarios embracing the traditional deterministic modeling framework without uncertainty and static technology (scenarios A and B). In these scenarios, emissions rise threefold by 2070, in line with typical “business-as-usual” scenarios available in the literature that embrace identical modeling perspectives and assumptions. It is interesting to note that moving from a social planner (scenario A) to a Pareto-optimal (scenario B) model formulation has little impact on future carbon emissions. Similarly, the responses of the social planner and Pareto-optimal scenarios to a given carbon tax are almost identical (see scenario A2 versus scenario B3).

Including scenario uncertainties (demands, resource availability, costs), as in scenario C, lowers emissions somewhat, but the continuous upward trends persist. Conversely, adding a carbon tax on top of a deterministic model formulation (scenario B3) yields much lower (but still rising) medium-term emissions, as in the scenario considering uncertainty in the absence of a carbon tax (scenario C). By 2070, however, emissions in both scenarios are of comparable magnitude. Evidently, combining these two uncertainties—even in the absence of possible increasing returns—yields an even more dramatic effect on future carbon emissions. Combining uncertainty in demand, resource availability, and technology cost, as well as a possible carbon tax (scenario D), results in near stabilization of global carbon emissions at levels that are about 50 percent higher than in 2000.

An interesting finding concerns the emissions impacts of treating ceteris paribus the carbon tax as certain (scenario D2) as opposed to treating it as uncertain (scenario D). Were the timing of the introduction and the level of a carbon tax known with certainty (scenario D2), emissions would be higher than in the uncertain tax case (scenario D). The reason for lower emissions in the uncertainty case lies in the model formulation of uncertainty along a Weibull distribution. In other words, the even very low probability of a high carbon tax underlying scenario D (recall that the mean and variance of the uncertain carbon tax are identical, unlike the case with a symmetrical distribution of uncertainty, as in a normal distribution) leads to hedging strategies away from fossil-based technologies that result in higher emission reductions than with a deterministically known carbon tax.

Thus, the type and extent of uncertainty of future environmental limits are as important as ex ante known absolute levels of these limits, as represented, for instance, by carbon tax levels. This observation has important implications for the climate debate. Any discussion of “optimal” levels of future carbon taxes— however defined—cannot be separated from a discussion of the uncertainties influencing such tax levels, and especially from a discussion of the extent and shape of such uncertainties. In other words, the impact on optimal technological hedging strategies in the face of uncertain climate damages will be influenced as much by the absolute magnitude of such damages [be it 1 or 3 percent of future gross domestic product (GDP)], as by the possibility of low-probability, extreme events. Admitting a less than 1 percent chance that climate-change damages could be substantially higher (say, 10 percent of GDP) leads to much higher anticipatory hedging strategies than assuming a “well-behaved” uncertainty distribution (e.g., when a symmetrical distribution of climate damages around a mean value of a GDP loss of 1–2 percent is assumed).

The emissions picture changes dramatically if the possibility of even uncertain increasing returns is added to all other uncertainties. In such a case (scenario E in Figure 11.7), emissions could actually decline below current levels in the long term (post 2040), yielding the lowest cumulative emissions of all scenarios considered. The scenarios of possible increasing returns are also the three cheapest in terms of total discounted energy systems costs (see Figure 11.4), with a significantly lower cost penalty of a carbon tax identical to those in the other scenarios. This result suggests that any discussion of quantifying climate-change externalities—for example, in the form of carbon taxes—cannot be separated from a discussion of the possible increasing returns an induced technological change perspective entails. In the presence of increasing returns, not only is much more technological diversification optimal for a given level of quantification of environmental externalities (a carbon tax), but the emissions reduction impact of any given level of carbon taxes is also substantially higher. However, the conclusions on technological diversification given above also hold for emissions. Any individual measure, be it stimulating increasing returns to technological innovation or quantifying environmental externalities (via taxes), is unlikely to yield the kind of drastic emission reductions that could yield “stabilization of atmospheric concentration of CO2 below dangerous levels” (UNFCC 1992). A combination of all factors might.

11.4.6   Heterogeneous agents

Figure 11.8 illustrates the different patterns of technological choice when heterogeneous agents are represented in the model. To this end, in addition to the assumptions of scenario group E (the scenario with full uncertainty including increasing returns and a possible carbon tax), we assume that the technology agents that supply new energy technologies to the five energy-producing/consuming regions in our model differ from the regional actors in their risk attitudes (i.e., in their risk function). In scenario F, only about one-third of the actors on the market are assumed to differ from the regional actors in their risk function. In scenarios F2 and F3, all of them differ markedly. For illustrative purposes, we assume that the technology agents are three times as risk averse as the regional agents in the presence (scenario F2) or absence (scenario F3) of an uncertain carbon tax.

To simplify the scenario comparison, we focus on scenario differences in energy-conversion technologies (hydrogen production, various electricity-generation technologies, etc.), which we aggregate into nine different clusters (designated by roman numerals in Figure 11.8).12 Scenarios are then ranked on a linear scale based on their cumulative (2000–2070) deployment of these nine energy-conversion technology clusters. Interconnecting the nine technology clusters gives a simple “spider graph” overview of the different technology portfolios of the scenarios.

Interestingly, in the absence of a carbon tax, even introducing the heterogeneous and highly risk-averse behavior of the technology agents (scenario F3 versus scenario D, shown as dashed lines in Figure 11.8) does not lead to a narrower technology portfolio. Scenario F3 even has a slightly more diversified portfolio (cf. the gains in technology clusters VIII and IX) compared with scenario D, which assumes the same risk attitude for all agents in the model. Apparently, the higher risks of the technology agents considered in the global Pareto optimum lead to a higher degree of regional specialization, and hence to a more differentiated technology demand from the regions. At the global level, these regional differences compensate for the otherwise-expected loss in technological variety under heterogeneous and risk-averse behavior of the technology agents.

Conversely, with a carbon tax, even an uncertain one, technological variety seems to be more difficult to maintain with rising risk aversion. Scenario F assumes (only slightly) heterogeneous risk behavior of the technology agents combining risk-averse, risk-taking, and risk-“neutral” (in comparison to the energy-producing/consuming regions) behavior. The scenario shows a portfolio almost identical to that of the comparable scenario E (with homogeneous risk). However, scenario F2, in which the technology agents are three times as risk averse as the energy-producing/consuming regions, experiences a drastic collapse of the richness of the technology portfolio. The “spiderweb” of technology diversification in Figure 11.8 almost collapses to a star-like structure. Scenario F2, for instance, entirely dispenses with the deployment of three technology clusters (II, IV, and VI) that were a prominent part of the technology portfolio in the homogeneous, risk-“neutral” scenario (scenario E). In a high-cost (carbon tax) scenario, increasing the risk aversion of the technology agents thus leads them to focus on fewer technologies as targets of their forward-looking innovation investments. The result is a “crowding out” of technological variety.

Figure 11.8. “Spider Graph” of Technology Portfolio of Nine Clusters of Energy-Conversion Technologies (Denoted Clockwise by Roman Numerals).

The graph plots relative proportions of cumulative market deployment between 2000 and 2070 for scenarios of homogeneous technology agents versus scenarios of heterogeneous technology agents. Scenarios assuming an uncertain carbon tax are denoted by solid lines; scenarios without a tax, by dashed lines. For an explanation of scenarios, see Figure 11.2 and text.

Despite the considerable work that remains to be done on further model testing and sensitivity analysis (not to mention on developing plausible model parameterizations), two conclusions can be drawn at this stage. First, methodologically, a feasible approach has been developed that allows us to represent heterogeneity between different agents acting under deep uncertainty while maintaining the tradition of an optimization framework. Second, policywise, the simulations illustrate the inherent trade-off between maintaining a broad technological portfolio that is optimal in the face of the numerous uncertainties the future inevitably holds and the desire to provide market signals factoring in environmental externalities. Single-purpose policy signals such as a carbon tax ultimately lead to a “crowding-out” effect in narrowing technology portfolios that may be more optimal for facing uncertainties beyond climate change. Technological diversity and a “healthy” heterogeneity between actors appear to go hand in hand. How these two intertwined factors can be nurtured by creative policies remains a key issue for further research.

11.5   Conclusion and Outlook

Owing to the new nature of the model, we do not wish to overemphasize conclusions from the first, illustrative simulation runs reported in this chapter. Rather, we focus here on open research questions and the future agenda for model development.

Nonetheless, two conclusions appear possible at this early stage of the model's life cycle. First, the proposed approach and model formulation of uncertain increasing returns in a multiregion, multi-actor, multi-technology model are feasible and solvable. Even if simplified, the model's representation of the energy system is sufficient for analyzing the most important technological linkages and interdependencies while maintaining a minimum degree of technological (innovation) variety. Second, the model simulations add to earlier results suggesting that radical technological change and long-term reversals of increasing emission trends are only feasible endogenously via a mechanism of increasing returns—even if these returns are uncertain. Incremental or “routine” innovations, or the consideration of various types of uncertainties (including environmental uncertainties), yield individual changes in technology adoption decisions, but no radical technological change or “big hits.” Radical change is possible over the long term, provided the necessary intervening efforts (R&D efforts and niche market deployment of new technologies) are taking place, initiating a stream of continuous improvements and innovations that can translate into increasing returns, albeit with no guarantee of success. As innovation is highly uncertain, such strategies need to be spread over a broad portfolio of technological options rather than directed at winners “picked” prematurely. But as our model simulations indicate, such innovation strategies, even if uncertain, make eminent economic sense.

A number of items remain on the agenda for future research. First and foremost, the model awaits further detailed sensitivity analysis and further scrutiny of the plausibility of both behavior and results. Further work is also required on the model's Pareto-optimal trade formulation, even if it is not at the core of our investigations on technological innovation and dynamics under uncertain increasing returns. The concept of different levels of risk aversion for different agents also has not yet been explored in detail in model simulations and sensitivity tests. Finally, representation of past decisions (i.e., modeling of existing energy systems structures) that limit near- to medium-term decision flexibility also remains an important task for improving both model plausibility and policy relevance.

Concerning methodological extensions, three important unresolved issues remain on the research agenda. First, improvements are needed in the representation of uncertainties. The current model version and calibration unduly “compresses” the uncertainty space to small random variations around mean expected values. Representation of the possibility of large “surprises” with potentially large consequences (e.g., availability of enormous amounts of methane clathrates at competitive costs) awaits definitive methodological and algorithmic solutions. Simply changing the functional form of uncertainty representation—for example, using distribution functions with long tails—might not be sufficient when dealing with possible long-term “surprises,” as low probability combined with discounting might not significantly change the model's behavior.

Second, improvements in the model's oversimplified treatment of the innovation process are required. Inclusion of the extremely high uncertainty of technological invention (i.e., option generation) and better representation of the interplay between embodied and disembodied aspects of technological change and knowledge generation (as well as knowledge depreciation) remain important tasks. We do not adhere to the opinion that disembodied and embodied aspects of technological change are substitutable (no matter how large, R&D efforts can never replace the ultimate test of market applications and substitute for the costly and time-consuming efforts of learning by doing and learning by using). Important lags in knowledge transfer and spillover effects also need to be recognized in more detail. Ultimately, the model will also have to keep track of investments and capital flows that are treated extremely simplistically in the current model version.

Third, the biggest remaining challenge is to allow for some endogenous mechanism of uncertainty reduction and information updating, even if this implies a departure from “once-through” analytical resolutions within an optimization framework. Rolling time windows instead of century-long optimization periods and/or their combination with simulation techniques with informational updating (e.g., on realized technological progress, environmental limits, etc.) need to be explored.

Thus, the tasks ahead are huge. But the challenge is worth the effort. After all, it is only through improved technology that humans can prepare for the numerous contingencies that an uncertain future holds. “Unlike resources found in nature, technology is a man-made resource whose abundance can be continuously increased, and whose importance in determining the world's future is also increasing” (Starr and Rudman 1973:364).


The model presented here builds on earlier work performed at IIASA dealing with stochastic uncertainties in future technology costs (Golodnikov et al. 1995; Grübler and Messner 1996; Messner et al. 1996) the possibility of increasing returns via learning curve effects (Messner 1995, 1997), and treating technological learning curves as stochastic (Grübler and Gritsevskyi 1998; Gritsevskyi and Nakicenovic 2000; and Chapter 10 in this volume). We wish to thank in particular Yuri Ermoliev for his continuous help in clarifying conceptual and mathematical issues as well as for proposing solutions to them. Our IIASA colleagues are to be absolved of blame for the shortcomings of this chapter.


1.   While it is impossible to estimate the relative contributions of embodied and dis-embodied knowledge in the technological knowledge stock as a whole, it is possible to look at least at the relative knowledge acquisition costs, or expenditures. Even in the most R&D-intensive industries, such as the aerospace industry, R&D generally does not exceed 20 percent of sales; the average for the manufacturing industry does not exceed 5 percent (including R&D funded by industry as well as from other sources; see NSF 1998). Development expenditures account for the majority of R&D expenditures (typically about two-thirds in the United States; NSF 1998). Thus, measured by expenditures, disembodied technological change in its purest form (i.e., research) accounts for less than 2 percent on average. This average, however, masks huge differences between sectors and technologies.

2.   The sensitivity of technology choice and diffusion profiles to variations in the discount rate is explored in more detail in Grübler and Messner (1998).

3.   Alternatively, one could consider risk profiles derived from standard utility functions. However, this would require a more comprehensive treatment of heterogeneous agents in our model (e.g., also representing consumers). Choosing empirically based parameter assumptions also represents a formidable challenge.

4.   In a future version of the model, we plan to relax the rather unrealistic assumption that technological learning can go on forever by explicitly including knowledge depreciation. In such an improved model version, learning is assumed to be contingent on a continuously increasing knowledge stock. That is, once installation expansion rates cease to grow, the technology-related knowledge stock begins to depreciate. This assumption reflects the empirical observations reported in Michina (1992, 1999) and Irwin and Klenow (1994).

5.   This technology knowledge stock is represented simply by cumulative expenditures. We recognize the importance of “forgetting by not doing,” but in this first model version we have not included a knowledge-depreciation parameter.

6.   Consequently, learning-curve types of models have been justifiably criticized on the basis that they ignore the important difference between who pays for new technological knowledge (learning) and who benefits (via lowered prices) from it.

7.   This is the reason why we adopted this particular scenario and not the structurally and quantitatively very similar IPCC-B2 scenario. In terms of cumulative “call on resources,” the two scenarios are very similar to each other.

8.   A confirmation sensitivity run of scenario B2 (Pareto optimum with equal weights) yields identical results and thus need not be discussed separately here.

9.   Open research questions concern the stability of the Pareto optimum under a large number of regions/countries and the issue of coalition formation in such a model formulation. Considering the long time horizon of our model and the possibility of increasing returns, it remains doubtful if stable Nash equilibria could be identified under such conditions.

10.  The additional costs of a scenario of uncertain increasing returns compared with those of the certain scenario are US$2.5 trillion (see Figure 11.4), or some 3 percent of the total discounted energy systems costs of the uncertainty scenario.

11.  Differences are greatest for scenarios considering (uncertain) increasing returns.

12.  Given the illustrative nature of these model simulations, we refrain from reporting the hardware equivalents of these nine energy-conversion technology clusters, not least to avoid giving the impression of drawing premature policy conclusions on relative technological merit. Hence, our discussion focuses simply on differences in technology structure or portfolios between the scenarios.


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