Quantitative empirical trends in technical performance

Technological improvement trends such as Moore's law and experience curves have been widely used to understand how technologies change over time and to forecast the future through extrapolation. Such studies can also potentially provide a deeper understanding of R&D management and strategic issues associated with technical change. However, such uses of technical performance trends require further consideration of the relationships among possible independent variables — in particular between time and possible effort variables such as cumulative production, R&D spending, and patent production. The paper addresses this issue by analyzing performance trends and patent output over time for 28 technological domains. In addition to patent output, production and revenue data are analyzed for the integrated circuits domain. The key findings are: 1. Sahal's equation is verified for additional effort variables (for patents and revenue in addition to cumulative production where it was first developed). 2. Sahal's equation is quite accurate when all three relationships — (a) an exponential between performance and time, (b) an exponential between effort and time, (c) a power law between performance and the effort variable — have good data fits (r 2 > 0.7). 3. The power law and effort exponents determined are dependent upon the choice of effort variable but the time dependent exponent is not. 4. All 28 domains have high quality fits (r 2 > 0.7) between the log of performance and time whereas 9 domains have very low quality (r 2 < 0.5) for power law fits with patents as the effort variable. 5. Even with the highest quality fits (r 2 > 0.9), the exponential relationship is not perfect and it is thus best to consider these relationships as the foundation upon which more complex (but nearly exponential) relationships are based. Overall, the results are interpreted as indicating that Moore's law is a better description of longer-term technological change when the performance data come from various designs whereas experience curves may be more relevant when a singular design in a given factory is considered.