Beyond the learning curve: factors influencing cost reductions in photovoltaics

Abstract

The extent and timing of cost-reducing improvements in low-carbon energy systems are important sources of uncertainty in future levels of greenhouse-gas emissions. Models that assess the costs of climate change mitigation policy, and energy policy in general, rely heavily on learning curves to include technology dynamics. Historically, no energy technology has changed more dramatically than photovoltaics (PV), the cost of which has declined by a factor of nearly 100 since the 1950s. Which changes were most important in accounting for the cost reductions that have occurred over the past three decades? Are these results consistent with the notion that learning from experience drove technical change? In this paper, empirical data are assembled to populate a simple model identifying the most important factors affecting the cost of PV. The results indicate that learning from experience, the theoretical mechanism used to explain learning curves, only weakly explains change in the most important factors—plant size, module efficiency, and the cost of silicon. Ways in which the consideration of a broader set of influences, such as technical barriers, industry structure, and characteristics of demand, might be used to inform energy technology policy are discussed.

Introduction

The cost of photovoltaics (PV) has declined by a factor of nearly 100 since the 1950s, more than any other energy technology in that period (Wolf, 1974, McDonald and Schrattenholzer, 2001, Maycock, 2002). Markets for PV are expanding rapidly, recently growing at over 40% per year (Maycock, 2005). Future scenarios that include stabilization of greenhouse-gas (GHG) concentrations assume widespread diffusion of PV. In a review of 34 emissions scenarios, Nakicenovic and Riahi (2002) found a median of 22 terawatts (TW) of PV deployed in 2100 for those scenarios that include GHG stabilization. At present however, PV remains a niche electricity source and in the overwhelming majority of situations does not compete economically with conventional sources, such as coal and gas, or even with other renewable sources, such as wind and biomass. The extent to which the technology improves over the next few decades will determine whether PV reaches terawatt scale and makes a meaningful contribution to reducing GHG emissions or remains limited to niche applications.

The learning curve is an important tool for modeling technical change and informing policy decisions related to energy technology. For example, it provides a method for evaluating the cost effectiveness of public policies to support new technologies (Duke and Kammen, 1999) and for weighing public technology investment against environmental damage costs (van der Zwaan and Rabl, 2004). Energy supply models now also use learning curves to endogenate improvements in technology. Prior to the 1990s, technological change was typically included either as an exogenous increase in energy conversion efficiency or ignored (Azar and Dowlatabadi, 1999). Studies in the 1990s began to use the learning curve to treat technology dynamically (Williams and Tarzian, 1993, Grübler et al., 1999) and since then it has become a powerful and widely used model for projecting technological change. Recent work however has cautioned that uncertainties in key parameters may be significant (Wene, 2000), making application of the learning curve to evaluate public policies inappropriate in some cases (Neij et al., 2003). This paper examines some of these concerns. After a review of the advantages and limitations of the learning curve model, the applicability of learning curves to PV is then assessed by constructing a bottom-up cost model and comparing its results to the assumptions behind the learning curve.

Characterizations of technological change have identified patterns in the ways that technologies are invented, improve, and diffuse into society (Schumpeter, 1947). Studies have described the complex nature of the innovation process in which uncertainty is inherent (Freeman, 1994), knowledge flows across sectors are important (Mowery and Rosenberg, 1998), and lags can be long (Rosenberg, 1994). Perhaps because of characteristics such as these, theoretical work on innovation provides only a limited set of methods with which to predict changes in technology. The learning curve model offers an exception.

The learning curve originates from observations that workers in manufacturing plants become more efficient as they produce more units (Wright, 1936, Alchian, 1963, Rapping, 1965). Drawing on the concept of learning in psychological theory, Arrow (1962) formalized a model explaining technical change as a function of learning derived from the accumulation of experiences in production. In its original conception, the learning curve referred to the changes in the productivity of labor which were enabled by the experience of cumulative production within a manufacturing plant. It has since been refined, for example, Bahk and Gort (1993) make the distinction between “labor learning”, “capital learning”, and “organizational learning”. Others developed the experience curve to provide a more general formulation of the concept, including not just labor but all manufacturing costs (Conley, 1970) and aggregating entire industries rather than single plants (Dutton and Thomas, 1984). Though different in scope, each of these concepts is based on Arrow's explanation that “learning-by-doing” provides opportunities for cost reductions and quality improvements. As a result, these concepts are often, and perhaps misleadingly, grouped under the general category of learning curves. An important implication of the experience curve is that increasing accumulated experience in the early stages of a technology is a dominant strategy both for maximizing the profitability of firms and the societal benefits of technology-related public policy (BCG, 1972).

The learning curve model operationalizes the explanatory variable experience using a cumulative measure of production or use. Change in cost typically provides a measure of learning and technological improvement, and represents the dependent variable.¹ Learning curve studies have experimented with a variety of functional forms to describe the relationship between cumulative capacity and cost (Yelle, 1979). The log-linear function is most common perhaps for its simplicity and generally high goodness-of-fit to observed data. The central parameter in the learning curve model is the exponent defining the slope of a power function, which appears as a linear function when plotted on a log–log scale. This parameter is known as the learning coefficient (b) and can be used to calculate the progress ratio (PR) and learning ratio (LR) as shown below where C is unit cost and q represents cumulative output:

$$C_t=C_0{\left(\frac{q_t}{q_0}\right)}^{-b}\text{,}$$

$$\mathrm{PR}=2^{-b}\text{,}$$

$$\mathrm{LR}=(1-\mathrm{PR})\text{.}$$

Several studies have criticized the learning curve model, especially in its more general form as the experience curve. Dutton and Thomas (1984) surveyed 108 learning curve studies and showed a wide variation in learning rates leading them to question the explanatory power of experience. Argote and Epple (1990) explored this variation further and proposed four alternative hypotheses for the observed technical improvements: economies of scale, knowledge spillovers, and two opposing factors, organizational forgetting and employee turnover. Despite such critiques, the application of the learning curve model has persisted without major modifications as a basis for predicting technical change, informing public policy, and guiding firm strategy. Below, the advantages and limitations of using the more general version of the learning curve, the experience curve, for such applications are outlined.

The experience curve provides an appealing model for several reasons. First, availability of the two empirical time series required to build an experience curve—cost and production data—facilitates testing of the model. As a result, a rather large body of empirical studies has emerged to support the model. Compare the simplicity of obtaining cost and production data with the difficulty of quantifying related concepts such as knowledge flows and inventive output. Still, data quality and uncertainty are infrequently explicitly assessed and as shown below can have a large impact on results. Second, earlier studies of the origin of technical improvements, such as in the aircraft industry (Alchian, 1963) and shipbuilding (Rapping, 1965), provide narratives consistent with the theory that firms learn from past experience. Third, studies cite the generally high goodness-of-fit of power functions to empirical data over several years, or even decades, as validation of the model. Fourth, the dynamic aspect of the model—the rate of improvement adjusts to changes in the growth of production—makes the model superior to forecasts that treat change purely as a function of time.² Finally, the reduction of the complex process of innovation to a single parameter, the learning rate, facilitates its inclusion in energy supply and computable general equilibrium models.

The combination of a rich body of empirical literature and the more recent applications of learning curves in predictive models has revealed weaknesses that echo earlier critiques. First, the timing of future cost reductions is highly sensitive not only to changes in the market growth rate but also to small changes in the learning rate. Although, an experience curve $R^2$ value of $>0.95$ is considered a strong validation of the experience curve model, variation in the underlying data can lead to uncertainty about the timing of cost reductions on the scale of decades. Fig. 1 shows experience curves based on the two most comprehensive world surveys of PV prices (Maycock, 2002, Strategies-Unlimited, 2003). The Maycock survey produces a learning rate of 0.26 while the Strategies Unlimited data give 0.17.³ What may appear as a minor difference has a large effect. For example, assuming a steady industry growth rate of 15% per year, consider how long it will take for PV costs to reach a threshold of $0.30/W, an estimate for competitiveness with conventional alternatives. Just the difference in the choice of data set used produces a crossover point of 2039 for the 0.26 learning rate and 2067 for the 0.17 rate, a difference of 28 years. McDonald and Schrattenholzer (2001) show that the range of learning rates for energy technologies in general is even larger. Neij et al. (2003) find that calculations of the cost effectiveness of public policies are very sensitive to such variation. Wene (2000) observes this sensitivity as well and recommends an ongoing process of policy evaluation that continuously incorporates recent data.

Second, the experience curve model gives no way to predict discontinuities in the learning rate. In the case of PV, the experience curve switched to a lower trajectory around 1980. As a result, experience curve-based forecasts of PV in the 1970s predicted faster technological progress than actually occurred (Schaeffer et al., 2004). Discontinuities present special difficulties at early stages in the life of a technology. Early on, only a few data points define the experience curve, while at such times decisions about public support may be most critical.

Third, studies that address uncertainty typically calculate uncertainties in the learning rate using the historical level of variance in the relationship between cost and cumulative capacity. This approach ignores uncertainties and limitations in the progress of the specific technical factors that are important in driving cost reductions (Wene, 2000). For example, constraints on individual factors, such as theoretical efficiency limits, might affect our confidence in the likelihood of future cost reductions.

Fourth, due to their application in planning and forecasting, emphasis has shifted away from learning curves based on employee productivity and plant-level analysis, to experience curves aggregating industries and including all components of operating cost. While the statistical relationships generally remain strong, the conceptual story begins to look stretched as one must make assumptions about the extent to which experience is shared across firms. In the strictest interpretation of the learning-by-doing model applied to entire industries, one must assume that each firm benefits from the collective experience of all. The model assumes homogenous knowledge spillovers among firms.

Fifth, the assumption that experience, as represented by cumulative capacity, is the only determinant of cost reductions ignores the effect of knowledge acquired from other sources, such as from R&D or from other industries. Earlier, Sheshinski (1967) wrestled with the separation of the impact of two competing factors, investment and output. Others have addressed this limitation by incorporating additional factors such as workforce training (Adler and Clark, 1991), R&D (Buonanno et al., 2003, Miketa and Schrattenholzer, 2004), and the interactions between R&D and diffusion (Watanabe et al., 2000). The amount of data required for parameter estimation has so far limited widespread application of these more sophisticated models.

Finally, experience curves ignore changes in quality beyond the single dimension being analyzed (Thompson, 2001).⁴ The dependent variable is limited to cost normalized by a single measure of performance—for example, hours of labor/aircraft, $/W, or $¢$/megabyte. Measures of performance like these ignore changes in quality such as aircraft speed, reliability of power generation, and the compactness of computer memory.

This study seeks to understand the drivers behind technical change in PV by disaggregating historic cost reductions into observable technical factors. The mechanisms linking factors such as cumulative capacity and R&D to technological outcomes, while certainly important, are at present not well understood. Many of the problems mentioned above arise because the experience curve model relies on assumptions about weakly understood phenomena. Rather than making assumptions about the roles that factors like experience, learning, R&D, and spillovers play in reducing costs, a set of observable technical factors are identified whose impact on cost can be directly calculated.

This study includes the period from nascent commercialization, 1975, to 2001. During this 26-year period, there was a factor of 20 cost reduction in the cost of PV modules. Only PV modules are examined and balance-of-system components such as inverters, storage, and supporting structures are excluded.⁵ The focus here is on explaining change in the capital cost of PV modules, rather than on the cost of electricity produced, mainly due to data quality considerations and to be able to exclude influential but exogenous factors such as interest rates. The study is limited to PV modules manufactured from mono-crystalline and poly-crystalline silicon wafers because crystalline silicon has been the overwhelmingly dominant technology for PV over this period. Crystalline silicon PV comprised over 90% of production over this period and its share increased in the second half of the period.⁶ While photovoltaic electricity has been produced from a wide variety of other materials, such as cadmium-telluride and copper-indium-diselenide, during the study period these competing technologies remained in the development stage and were not commercially relevant. The price data used in the study are weighted averages of the two types of silicon crystals. The study uses worldwide data rather than country-level data because over this time period the market for PV became global. Some of the change often attributed to within-country costs is due to the globalization of the industry, rather than learning from that country's experience. Junginger et al. (2005) articulated the need for such an international view and as a result developed a global experience curve for wind power. This study adopts a similarly global view. The scope of this study thus addresses the concerns raised by Schaeffer et al. (2004) regarding the importance of data quality, system boundaries, and sufficient historical time period for assessing experience in energy technologies. Finally, the technological characteristics of PV provide two simplifying aspects that help restrict the influence of potentially confounding factors in the study. First, there has been no significant change in per unit scale in PV panels. PV panels have been sized on the order of one square meter per panel for three decades. Compare this to wind turbines in which the size of individual units has increased by almost two orders of magnitude over the same period (Madsen et al., 2003, Junginger et al., 2005).Second, there are essentially no operation and maintenance costs associated with PV, other than regular cleaning and inverter replacement. This limits the role of “learning-by-using”, which would normally be an important additional factor to consider (Rosenberg, 1982).

The analysis began by identifying factors that changed over time and had some impact on PV costs. Using empirical data, the annual level of these seven factors over the study period, 1975–2001, was compiled and a model to quantify the impact of the change in each factor on module cost developed.