Mapping Firms' Locations in Technological Space: A Topological Analysis of Patent Statistics

TL;DR

This paper introduces a topological data analysis method to map and analyze firms' innovation trajectories in high-dimensional technological space, revealing that firms with unique innovation paths tend to perform better.

Contribution

The paper develops a novel TDA-based approach to characterize firms' inventive activities and demonstrates its effectiveness over traditional methods like PCA and clustering.

Findings

Firms with unique 'flares' in the topological map outperform others.

The method captures heterogeneity in firms' innovation trajectories.

Results remain significant after controlling for various firm characteristics.

Abstract

Where do firms innovate? Mapping their locations and directions in technological space is challenging due to its high dimensionality. We propose a new method to characterize firms' inventive activities via topological data analysis (TDA) that represents high-dimensional data in a shape graph. Applying this method to 333 major firms' patents in 1976--2005 reveals substantial heterogeneity: some firms remain undifferentiated; others develop unique portfolios. Firms with unique trajectories, which we define and measure graph-theoretically as "flares" in the Mapper graph, perform better. This association is statistically and economically significant, and continues to hold after we control for portfolio size, firm survivorship, industry classification, and firm fixed effects. By contrast, existing techniques -- such as principal component analysis (PCA) and Jaffe's (1989) clustering method -- struggle to track these firm-level dynamics.