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Garcilazo 2008

p. 24

“The knowledge spillovers approach occurs at the micro level in innovative units (i.e. R&D departments within firms, universities and research centers) as well as local institutions and individuals. The interaction – with each other and with their external environment through networks – produces the transmission of knowledge in the form of knowledge spillovers.”

p. 36-37

Can we relate the indicator that measures accessibility to markets, specifically the impedance function to spillovers?

Rodriguez pose crescenzi 2006

p. 7-8

In the structure of the empirical model, spillovers are external factors including investment in R&D in neighbouring regions; conditions conducive to the establishment of a regional system of innovation in neighbouring regions; and initial conditions in neighbouring regions (captured by GDP per capita).

Spillovi,t-j = measure of accessibility to extra-regional sources of innovation


p. 11-12

“…spillovers are assessed in terms of their contribution towards the creation of new local knowledge…we develop a measure of ‘accessibility’ to extra-regional innovative activities which we introduce in the analysis by means of a standardized ‘index of accessibility to innovation.’”

Ai = SUMg(rj)f(cij)


Ai = accessibility of region i

rj = activity R to be reached in region j

cij = generalized cost of reaching region j from i


“…the ‘impdance’ is the bilateral trip-time distance between region iand

region j:

f(cij) = wij = (1/dij)/(SUM(1/dij))


dij= average trip-length (in minutes) between region i and j

“…use of trip-length rather than kilometers allows us to take account of

‘different road types, national speed limits, speed constraints in urban and

mountainous areas, sea journeys, border delays (…) as also congestion in

urban areas’ (IRPUD 2000, p.22), which significantly affect real-world


Crescenzi et al

p. 12

Spillover is included in the “modified Cobb-Douglass knowledge production function”–

specifically, in the form of “SpillRD,” which is a vector of neighbouringregions’ innovative efforts

(in terms of R&D expenditures), and “SpillC,” which is a vector of broader socio-institutional

characteristics in neighbouring regions (in terms of structural characteristics, such as, education,

life-long learning, sectorialcomposition, use of resources (unemployment) and demographics).

p. 14-15

It is assumed that inter-territorial spillovers contribute to the creation of new local knowledge.

“SpillRD,” a measure of innovative activities (in terms of R&D expenditure), can be

reached from each region at a cost which increases with distance. For each region the

R&D expenditure recorded in neighbouringregions is weighted by the inverse of

their bilateral distances.


The proxy Spillxi for spillovers from variable xi flowing into region iis

calculated as:

Spillxi = SUM(xj)*((1/dij)/(SUM(1/dij)))

= ((SUM(xj)*dij))/(SUM(dij))


xi = variable under analysis

dij = average trip-length (in minutes)/distance between region i and j

Although road distance provides a more realistic representation of the

real cost of interaction and contacts across space, we do not have that

kind of distance measure for the United States; therefore, we rely on

straight line distances.


p. 21

Spatially-weighted average of neighbouring counties

p. 22

“...empirical analyses of the diffusion of spillovers have highlighted the presence of

very strong distance decay effects in the US – knowledge spillovers, in general, do not

spread beyond a 80 to 110 kms radius from the MSA where they are generated (Varga

2000; Acs 2002)...Greater distance and stronger distance decay effects are...likely to

lead to the creation of self-contained innovative areas in the US, which necessarily

have to rely on their own innovative inputs rather than on spillovers from other


What about “mobility?” Better stated, what about labour mobility and spatial


Audretsch and feldman 1996

p. 630

“As Alfred Marshall (1920) and, later Krugman(1991b) argue, there may be

geographic boundaries to information flows or knowledge spillovers,

particularly tacit knowledge, among the firms in an industry.”

p. 635

“Krugman (1991a) points out that the extent to which the location of production is geographically concentrated will be shaped by transportation costs. Transportation costs [Description and source: Radius of the mean distance shipped in 1967 (Commodity Transport Survey of the United States Census of Transportation for 1967, taken from Weiss (1991)] are inversely related to the mean distance shipped, so that a higher value of transportation costs should be associated with a lower geographic concentration of production.”

Carlino et al 2001

p. 5-6

“We make the assumption that knowledge spillovers depend on the average

value of employment density in location i”

Aggregate Production Function for MSA i:

Yi,t= Ai,t * F(Ki,t, Li,t)


Yi,t = output in location i at time t

Ki,t =capital stock in i at time t

Li, t = labor in i at t

Ai, t = Hicks-neutral productivity that differs across locations


log Ai = ai +bi log Si


Si = knowledge spillover in location i

bi = strength of the spillover in location i

ai = vector reflecting all other productivity factors in location i

[Note: Si is assumed to be external to any individual firm in i, but

internal to the firms’ local economy]


log Ai =ai +bi log (E/N)i


E = total employment in location i

N = land area in i

[Note: employment density = employment / square miles]

Sonn storper 2005

p. 1020

“Some analysts believe that the importance of proximity in knowledge

production will eventually disappear with the continued development

of telecommunications.”

The net local citation percentage (NLCP)was then calculated according to the

following formula:



TLC = total location citation = fractional counts where citing and cited patents

were from the same geographical unit

JTH = Jaffe, Trajtenberg, and Henderson’s control technique = construction of

the control variable, which connects each patent with a ‘control patent'

Fannin 2003
FANNIN (2003)

p. 65-66

“To incorporate knowledge spillovers of regional knowledge

production over space, regional and national weighted patent stock

variables were added to Equation (4.6). Five regional weighted patent

stock variables were calculated based on the distance from the

reference county. Latitude-longitude coordinates from a county’s

geographic centroid were assigned based on the Albers projection from

ArcViewGIS. The Euclidean distance formula was applied to pair wise

comparisons of county coordinates to calculate the centroiddistances

between counties. Each regional patent stock variable measured the

weighted regional patent stock of all counties that fall within the six distance

bands outlined by the regional weighted patent stock variables: 0-30 miles,

30-50 miles, 50-70 miles, 70-90 miles, and 90-120 miles.”


“Given that the regions constructed represent circular bands

measured from the center of the reference county, the

geographic area of each regional band increases for each

region further removed from the reference county… If both

spatial and non-spatial spillovers are large and the spatial

impact decays rapidly with increased distance, one may see a

case where spillovers are large in spatially proximate regions,

decline to a minimum value in a more distant region, and then

begin to grow again in even more distant regions.”

What about ‘temporal’ spillovers?


1.2.7 Spatial Considerations

“Spatially, high-innovation counties tend to be proximate to

metropolitan areas…For instance, some of the greatest

concentrations of high PII are clustered in the New England

states, Silicon Valley, the District of Columbia, St. Paul

Minneapolis, and along the central corridor of Colorado.

The highest innovation scores are not, however, always

confined to the central portions of major cities.”