Geography Reference
In-Depth Information
100
Diferential between close and
u
nc
onnec
ted collaborators
Diferential between close
and far collaborators
10
Diferential betw
een
f
a
r a
nd unconne
c
t
ed
c
oll
abo
rat
o
rs
1
Interdependence (
k
)
Note:
The line labeled 'dif erential between close and unconnected collaborators' shows, as a function of
k
, how many times more likely a citation is in a dyad of patents whose inventors cannot reach one another
through the collaboration network (path length < 4) relative to a dyad whose inventors are unconnected
in the network. When
k
= 0.45, for instance, a citation is 48 times more likely. The other two lines provide
the same information for pairs of actors who are close versus far (path length between 4 and ∞) in the
collaboration network and for pairs of actors who are far versus unconnected. The i gure is based on model 4
of Table 15.2 for inventors from dif erent organizations, with all variables other than
k
and the collaboration
network indicators set to their mean values.
Figure 15
.
2
Citation multiplier for proximate versus distant actors in the collaboration
network as a function of interdependence
between close pairs and unconnected pairs arises when the focal patent displays moderate
interdependence. The same is true of the dif erence between close and far pairs. Figure
15.2 also shows that the citation dif erence between far and unconnected inventors -
while consistent with our hypothesis and statistically signii cant - is much, much smaller.
This suggests that for access to knowledge, the value of a social connection to the source
drops of rapidly with the number of intervening intermediaries, echoing the i ndings of
Singh (2005).
Figure 15.3 shows, as a function of interdependence, how many times greater the
probability of citation is between geographically proximate actors than between geo-
graphically distant actors. It does likewise for pairs of inventors in the same organization
versus pairs in dif erent organizations. In both cases, the benei ts of social proximity rise
and then fall with
k
, peaking when the source knowledge displays moderate interdepend-
ence. This provides graphical ai rmation of our hypothesis. In both Figures 15.2 and
15.3, the peak dif erences fall within the range of actual
k
in our data - in fact, within one
standard deviation above the mean.
In addition to being signii cant, the ef ects associated with our hypothesis can have
substantial economic import. For source knowledge that is simple (
k
~ 0), an inventor
