selected technology? Does the learning rate remain constant over time, or does it change over the modeling period? Do costs always decline, or might they also increase and if so, why or how? Because there are still no definitive answers to such questions, it is important to recognize that these are sources of uncertainty that can significantly influence the results of energy-economic models. In this paper we explore the nature of these uncertainties.

In the second section, we briefly review the origins of technology experience curves used most widely for modeling and forecasting. In the third section we survey alternative functional forms of an experience curve and the theoretical and empirical basis for these formulations and the choice of explanatory variables. In the fourth section, we focus on uncertainties in the shape of experience curves, especially as they apply to environmental technologies in the early stages of commercialization. Finally, in the fifth section we summarize and discuss the implications of these uncertainties for large-scale integrated assessments and energy-economic modeling.

In 1936, the aeronautical engineer Thomas P. Wright published a landmark paper in which he observed that the average direct man-hours required to manufacture a given model of Boeing aircraft dropped systematically with each unit produced [11]. Wright captured this phenomenon with an equation representing what he termed a “progress curve”:

(Equation 1)

where *Y* is the estimated average direct man-hours per unit for *x* units; *a* is the direct man-hours needed to manufacture the first unit; and *b (b<0)* is a parametric constant. Wright demonstrated that the labor input, *Y,* dropped by 20 percent for every doubling of cumulative output, *x*—an 80 percent “progress ratio,” where the exponent *b* was −0.32.

Wright’s work remained relatively obscure until it was revisited a decade later by a group of economists at the then recently founded RAND Corporation (a “think tank” created by the U.S. Air Force in 1946 to develop a complete “science of warfare” during the Cold War era). The RAND economists became vitally interested in the application of Wright’s work to the production of war materials—a phenomenon they would eventually call “learning-by-doing.” When later applied to an industry or class of product (rather than to a specific manufacturing process), Wright’s “learning curve” equation became referred to as an “experience curve.”

Subsequent work by the Boston Consulting Group [12] applied Wright’s equation to the relationship between the average unit price and cumulative output of 24 selected industrial products. Since then, this formulation (Equation 1) has been adopted in empirical studies to characterize learning phenomena in a wide range of sectors [13-15], including manufacturing [16], ship production [17, 18], consumer products [19], energy supply technologies [20-28], fuel technology [29-34], energy demand technologies [35], and environmental control technologies [36-38].

Equation 1 can be re-written as:

(Equation 2)

Today, this log-linear form of the experience curve remains the most popular equation used to represent the expected cost improvements of a technology. Studies of conventional and renewable energy systems also have employed this equation to calculate technology progress ratios based on cumulative installed capacity [20, 39-41]. Any nonlinearities in the underlying empirical data are most often ignored, however, and only the “best fit” progress ratio (the value of 2^{−b} in Equation 1) or learning rate (the value of one minus the progress ratio) is typically reported. On this basis, Dutton and Thomas [42] surveyed 100 empirical and theoretical studies of progress functions in industrial engineering, economics and management. Reported progress ratios generally fell in the range of 60% to 94% (i.e., learning rates of 6% to 40%). However, studies showing price *increases* were not included in their analysis. For energy-related technologies, McDonald and Schrattenholzer [43] found a range of learning rates varying from 14% to 34% with a median value of 16%. In all energy-related studies, the cumulative installed capacity of a technology is most commonly used as the independent variable and the reported progress ratio typically applies to a period *after* the technology is commercialized.