Table 3 presents the estimates of the a and (3, parameters in several different ways. The top panel simply reproduces the a estimates presented in Appendix B, but arrays them in matrix form. The second panel presents the estimated values (with standard errors) in terms of (1/(3,), which has years as units and is equal to the lag at which the citation frequency reaches its maximum value. The bottom panel presents estimated values (with standard errors) for aP2/(Pi)2, which is the integral of the citation function from t=0 to infinity. This is an estimate of the expected number of citations that a single patent will receive from a set of patents consisting of one random patent per year forever. Thus the middle panel of the table measures the “speed” of citation diffusion and the bottom panel measures the overall intensity of citation.

Several features of these matrices are worth noting. Looking first at the a’s, the diagonal elements strongly dominate both the rows and columns of the matrix. What this means is that there is a strong pattern of geographic localization, in the sense that the domestic citation function is shifted upward. This is true for all countries, and it is true whether one compares the domestic citations to citations received from other countries (across the rows) or citations made to other countries (down the columns).

The other notable feature of the top panel of Table 3 is the symmetry of the matrix. For example, a for Germany citing U.S. and for U.S. citing Germany are the two lowest numbers in the matrix. Conversely, the two highest non-diagonal numbers in the a table are for Germany citing Japan and Japan citing Germany. Although these differences among the off-diagonal elements are not as large as the localization effect of domestic citation, it suggests that inter-country knowledge flows are typically bi-directional, with relatively large or small flows in one direction being associated with similar flows in the other direction.