Multiplicative-innovation synergies: tests in technological acquisitions

Abstract

Technological innovations enjoy synergies that vary in their speed and magnitude of impact, depending upon whether they are additive or multiplicative in nature. Additive-innovation synergies build incrementally on familiar technologies (as is reflected in the technologies built upon within their patents’ respective antecedents) and the duration of their effect is shorter-lived. Multiplicative-innovation synergies arise from combining greater proportions of diverse technologies and their effects have longer duration. The most-effective organizational-learning processes accompanying exposure to exotic technology streams via technological acquisition will occur if firms have properly invested in adaptive capacity to synthesize inventions using the unfamiliar knowledge. In the first tests of innovation synergies on firm performance, we find that technological novelty in patent content improves return on assets for firms that consistently invested in R&D. Using patent-content scores to characterize whether inventors have integrated greater proportions of exotic technological antecedents into their inventions (or not), we test the impact of innovation synergies on firms’ performance after technological acquisitions. Diversification posture (which could be an alternative explanation for performance differences) is negatively-correlated with innovation synergies in our results.

Appendix: Mathematical notation for calculating backward-dispersion patent-citation scores

Calculations of V-scores for a focal patent were made in a spreadsheet matrix that juxtaposed each Derwent technology-class code (i _n , o _m ) awarded to the focal patent with itself and all other cited Derwent technology-class codes in order to generate the dyad frequencies (p _j ) appearing as probabilities in the cells that were created by the intersection of the matrix rows—which represented all core- as well as non-core Derwent Codes appearing in the backward-cited (or antecedent) patents—with the matrix columns which represented only the Derwent technology-class codes that were awarded to the focal patent. The dyad frequencies (p _j ) are the probability of the intersecting Derwent Codes occurring together in a particular year (and were obtained by searching the Derwent International Patents website). The dyad frequencies in each row were averaged to create the average probabilities (a _i , a _o ).

The frequency with which the Derwent technology class code in each row was cited (f _k ) was divided by the total count of codes cited (F) to create its frequency factor (ff _k ), which was multiplied by the row’s average probability (a _i , a _o ) to produce a weighting (W _k ). The weightings were summed to produce a Core Score (W _i ) reflecting the focal patent’s granted claims and Non-Core Score (W _o ) reflecting all other possible technology-class codes. These were combined to produce a Raw Innovation Score (R) which is equal to the Core- and Non-Core Scores (ΣW _k ). The Raw Score (R) was multiplied by the ratio of non-core frequency counts (Σf _o ) to core frequency counts (Σf _i ) to create the focal patent’s V-score.

$$ \begin{aligned} V = R \times [\Sigma f_{o} /\Sigma f_{i} ] & = V{\text{-}}score,\;{\text{the}}\;{Raw}\;{Innovation}\;{Score}\;{\text{times}}\;{\text{a}}\;{\text{ratio}}\;{\text{of}}\;{\text{the}}\;{\text{count}}\;{\text{of}}\;outside{\text{-}}the{\text{-}}core\; \\ & \quad {\text{technology}}{\text{-}}{\text{class}}\;{\text{codes}}\;{\text{divided}}\;{\text{by}}\;{\text{the}}\;{\text{count}}\;{\text{of}}\;inside{\text{-}}the{\text{-}}core\;{\text{technology}}{\text{-}}{\text{class}}\;{\text{codes}} \\ \end{aligned} $$

where,

• i _n  = Core technology-class codes of backward citations for Patent where the number of Core codes = 1, 2, 3, …, n.

• o _m  = Non-core technology-class codes of backward citations for Patent where number of Non-Core codes = 1, 2, 3, …, m.

• f _k  = Frequency with which a Core technology-class code _i (or Non-Core technology class code _o ) occurred in backward citations of Patent, which is the count of each technology-class code appearing in its backward citations where k = 1, 2, …, n, n+1, … , n+m.

• F = Σf _k  = [Σf _i  + Σf _o ] = the sum of the count of all technology-class codes.

• ff _k  = f _k /F = the frequency factor for one technology-class code.

Assume an $n \times \left( {n + m} \right)$ matrix for searching probability p _j that dyads occur in technology class codes of a focal patent’s backward citations for i _n  × i _n , i _n  × o _m and o _m  × o _m where j = n × (n + m) and p _j is the dyad weighting for a particular core technology-class code_i or non-core technology-class code_o appearing with itself or another backward-cited technology-class code defined as $i_{1} , \ldots ,i_{n } \times i_{1} , \ldots ,i_{n} , o_{1} , \ldots ,o_{m}$. (Twenty reference tables were created to reflect the annual dyad probability with which each combination of technology-class codes occurred together in a patent for each year.) Thus,

$$\begin{aligned} a_{i} ,a_{o} = [\Sigma p_{j} /i_{n} ] & = {\text{Average}}\;{\text{dyad}}\;{\text{weighting}}\;{\text{for}}\;{\text{each}}\;inside{\text{-}}the{\text{-}}core\;{\text{technology - class code}}\; \\ & \quad (i_{1} + \cdots + i_{n} )\;{\text{and}}\;{\text{for}}\;{\text{each}}\;outside{\text{-}}the{\text{-}}core\left( {{\text{or}}\;non{\text{-}}core} \right)\;{\text{technology-class}}\;{\text{code}} \\ & \quad {\text{(}}o_{1} {\text{ + }} \cdots {\text{ + }}o_{m} {\text{)}},\;{\text{the}}\;{\text{sum}}\;{\text{of}}\;{\text{each}}\;{\text{row}}\;{\text{of}}\;{\text{weightings}}\;{\text{divided}}\;{\text{by}}\;{\text{the}}\; \\ & \quad {\text{number}}\;{\text{of}}\;{\text{core}}\;{\text{technology-class}}\;{\text{codes}}\;{\text{that}}\;{\text{there}}\;{\text{are}}. \\ \end{aligned}$$

$$ \begin{aligned} W_{k} = a_{i} ,{\text{ }}a_{o} \times ff_{k} & = {\text{the}}\;{\text{weighted}}\;{\text{score}}\;{\text{for}}\;{\text{a}}\;core\;{\text{technology-class}}\;{\text{code}}_{i} \;{\text{or}}\;{\text{for}}\;{\text{a}} \\ & \quad {\text{non-core}}\;{\text{technology-class}}\;{\text{code}}_{o} \\ \end{aligned}$$

$$R = \Sigma W_{k} = {\it{Raw}}\;{\it{Innovation}}\;{\it{Score}},\;{\text{the}}\;{\text{sum}}\;{\text{of}}\;{\text{all}}\;{\text{weighted}}\;{\text{scores}} = \Sigma W_{i} + \Sigma W_{o}$$

Thus the V-score is

$$ V = \underbrace {{\left[ {\left[ {\sum\limits_{k = 1}^{{n_{i} }} {f_{i} } } \right] + \left[ {\sum\limits_{k = 1}^{{m_{o} }} {f_{o} } } \right]} \right] \times \left[ {\left[ {\sum\limits_{j = 1}^{{n_{i} }} {p_{ij} /i_{n} } } \right] + \left[ {\sum\limits_{j = 1}^{{m_{o} }} {p_{oj} /o_{m} } } \right]} \right]}}_{R} \times \left[ {\sum\limits_{o = 1}^{m} {f_{o} } /\sum\limits_{i = 1}^{n} {f_{i} } } \right] $$

where the Raw Innovation Score, R, captures technological diversity times technological distance and [Σf _o /Σf _i ] represents degree of novelty for each patented invention.