By Owen Westfold
Technology disruptions are often driven by exponentially falling costs. This, in itself, is not all that surprising: when production costs fall low enough, the price of a disruptive product can outcompete incumbent products, while also maximizing profitability. This is happening right now with electric vehicles.
Among all technologies which exhibit this pattern of exponential cost decline, one of the most consequential is surely the integrated circuit, known to most people as computer chips or semiconductors. Moore's Law is the well-known observation by Intel cofounder Gordon Moore that the number of transistors on an integrated circuit doubles roughly every two years. Since both the cost and capabilities of a circuit depend linearly on its density, this observation can be recast as an exponential decline in the cost of a unit of processing power or storage.
Moore’s Law for semiconductors
For convenience, let's use the term Moore's Law to refer to this general pattern of exponential cost decline for some fixed unit of performance. So, a technology that follows Moore's Law is one with an exponentially declining cost curve. The metric of performance and the rate of decline will, of course, vary depending on the technology in question.
Without Moore's Law for semiconductors, we would all still be living in a technological paradigm belonging to the 1950s. Solar, wind, and batteries depend on semiconductors in crucial ways, and the fact that these technologies are all moving down their own exponential cost curves is driving the disruption of the fuel-based energy system. These examples, along with many others, show that Moore's Law is at the heart of technological progress in the modern age.
The cost curves for solar, wind, and batteries
The importance of Moore's Law motivates the following fundamental questions:
The second question is especially important, since Moore's Law is an essential tool for making predictions about future costs, and hence predicting disruptions themselves.
In this post, we will explore the first question, leaving the second question to a future installment.
Moore's Law can in part be explained as a self-reinforcing phenomenon. As Moore himself wrote in 1996:
“More than anything, once something like this gets established, it becomes more or less a self-fulfilling prophecy. The Semiconductor Industry Association puts out a technology road map, which continues this generation every three years. Everyone in the industry recognizes that if you don't stay on essentially that curve they will fall behind. So it sort of drives itself.”
In this view, the industry's shared belief in Moore's Law helps form its expectations about future progress and competition, which in turn leads to an intense collective effort to innovate. It is, in reality, the fruits of this effort which bring about the declines in cost predicted by Moore’s Law.
This explanation is compelling, but it leaves unanswered the question of how a self-reinforcing process like this begins in the first place. Furthermore, how well does this explanation apply to semiconductor advancements in the 21st century, or, for that matter, to other technologies such as solar, wind, and batteries?
Even though the above explanation of Moore’s Law may seem lacking in some respects, it is inarguable that this level of effort is an important factor in why costs come down over time. This intuition is captured in the concept of the experience curve. In this model, cost is modeled as a function of cumulative production, which is taken as a proxy for manufacturing 'experience'. Wright's Law is the observation, originally made by American engineer Theodore Wright in the context of aircraft manufacturing, that for every doubling of cumulative production, the cost decreases by a certain fixed percentage known as the learning rate. Equivalently, the logarithm of the cost depends linearly on the logarithm of the cumulative production.
Experience curve for solar PV modules
A conceptual advantage of Wright's Law over Moore's Law is that it really does explain technological progress since, unlike time, experience is plausible as an explanatory variable. On the other hand, for most (elastic) products, models based on Wright's Law are complicated by reverse causation—a decrease in price will cause demand to go up, which leads in turn to increased production. Furthermore, improvements in productivity do not necessarily arise from increased experience, as is the case with knowledge spillover from a second industry.
In practice, Moore's Law and Wright's Law are hard to tell apart. This is because for most technologies which obey Wright's Law, cumulative production grows exponentially with time; a quick calculation then shows that Moore's Law is also satisfied. In this situation, both models give the same pointwise forecasts, and estimating the error inherent in these forecasts leads to similar results.
To disentangle Moore's Law from Wright's Law, a clever experiment by researchers at the Institute for New Economic Thinking at Oxford analyzed U.S. military production data from World War II. The fact that demand for military equipment was determined solely by battlefield requirements makes this data atypical. The usual causal link from cost to production was not present, and cumulative production did not follow an exponential trend. They found that about half of the decline in cost could be explained by an increase in cumulative production, while the other half was explained by other unspecified time-dependent factors. This leads to the following conclusions:
Reflecting further on the second point, it is clear that the relationship between Moore's Law and Wright's Law is somewhat subtle. From a theoretical perspective, the two-way causality between experience (as measured by cumulative production) and technological progress (as measured by cost) suggests that we should view the process of technological innovation and disruption as a complex system. Although this notion is difficult to formalize mathematically, a complex system can nevertheless be thought of as a network that evolves over time. The nodes of this network include all the variables of interest, including cumulative production and cost, while the directed edges encode (somehow) all the causal relationships between these variables.
The experience curve and the cost curve fit into this picture in different ways:
Part of the complex system representing a disruption
Implementing such a model in the context of an actual problem would be very cumbersome, if not impossible. For practical purposes, if all we want is to make predictions about future costs, then we must choose between Moore's Law and Wright's Law, and in general, Moore's Law—the language of cost curves—is the more convenient tool. This is especially so if we want to include error estimation in the analysis. The reliability of Moore's Law for making predictions will be discussed in the next installment.