Graphical analysis of agricultural research spillover potential

This paper introduces two important extensions to the uncentered correlation metric, the commonly used metric proposed by Jaffe [1986. “Technological Opportunity and Spillovers of R & D: Evidence From Firms’ Patents, Profits, and Market Value.” The American Economic Review 76 (5): 984–1001] for analyzing research spillovers across firms or countries. First, it is shown that the Jaffe metric can be displayed graphically using the biplot, a graphical display of a two-dimensional approximation to any multidimensional matrix. Second, it is illustrated that since the data used to produce the Jaffe metric are constrained within the simplex (i.e. shares add up to one), then a theoretically superior metric satisfying the basic axioms of technological proximity measures in this sample space is the Aitchison distance measure, a metric based on log-ratios of shares. The findings of the paper using agricultural research and development spillover potential for Southern African countries show that the Jaffe metric overestimates the technological proximity across countries as compared to the proposed Aitchison measure.