This study has two aims – to deepen the understanding of the phenomenon of rapid business growth and to explore and discuss how new analytical tools, such as machine learning (ML) and time series clustering, can be used to analyze business populations. The report, which is a methodological report, is part of the framework project "Are Sweden and the EU a favorable environment for fast-growing companies".

The concept of fast-growing companies attracts significant attention from researchers, private actors, policymakers, and international organizations in many countries. In practice, most countries have some form of policy to support fast-growing and potentially fast-growing companies.

Although much attention has been paid to understanding the drivers behind rapid growth, the results are often contradictory. Additionally, there is a need for further investigation into how companies grow, especially as empirical tools now provide us with deeper insights into the nuances of growth trajectories. With advances in empirical tools and techniques, we can now explore not only the factors that drive growth but also the potential patterns, stages, and dynamics that characterize such growth.

The study employs machine learning technique dynamic time series clustering, specifically the Dynamic Time Warping (DTW) algorithm, to identify growth patterns among 37 861 Swedish companies over the period 2010-2020. The DTW technique, which is relatively unexploited in economic research, allows for a flexible comparison of growth trajectories that differ in starting points, speeds, or growth stages. This methodology offers new insight into growth processes by identifying various growth trajectories, trends, and phases, effectively illustrating the varied growth patterns experienced by Swedish companies. In this report, we make a preliminary exploratory attempt to employ machine learning techniques to analyze the connection between firms' growth trajectories and fast-growing episodes, based on Swedish data.

As far as we know, it is the first study of its kind in a Swedish context Two distinct growth patterns emerge among the companies: "Scalers," which show a tendency towards frequent rapid growth episodes over time, and "Mixers," characterized by a mix of rapid growth and more stable periods. Scalers are particularly prone to repeat rapid growth episodes, which may indicate a potential for long-term expansion.

The results indicate that rapid growth has a strong and positive correlation with preceding changes in labor productivity. However, companies that have previously experienced at least one rapid growth episode are more likely to experience a negative change in their productivity levels. We also find that companies in the first cluster (scalers) have a higher likelihood of rapid growth episodes compared to mixers. Older and larger companies tend to have a lower likelihood of such episodes, while a more highly educated workforce and larger capital investments increase the likelihood of rapid growth. It is of great importance for effective economic policy that authorities understand rapid company growth and that they can embrace new methodologies in this area. Currently, our knowledge of the practical applicability of these methods to predict growth trajectories and facilitate the selection process for company support is highly limited. Exactly which methods and what role machine learning should play in future economic strategies should be determined only after their capabilities have been evaluated in comparison to more traditional methods.

By combining dynamic time series clustering with traditional regression analysis, the report aims to provide a deeper understanding of the complex mechanisms behind rapid growth and explore how these processes may differ between clusters. The results suggest that while cluster membership is a crucial factor in identifying potential high-growth episodes, the impact of residual factors (such as changes in labor productivity, capital and human capital investments, company characteristics, and strategic decisions) on growth is comparably consistent across both clusters, indicating the presence of the same underlying processes for rapid growth regardless of cluster membership. In other words, cluster membership captures something that we cannot identify with other variables from the literature, making it an interesting area for further development.