Tsukuba Economics Working Papers
No. 2010-010

Localized knowledge spillovers and patent citations:
A distance-based approachby
Yasusada Murata, Ryo Nakajima, Ryosuke Okamoto, and Ryuichi Tamura
January 2011

UNIVERSITY OF TSUKUBA
Department of Economics
1-1-1 Tennodai
Tsukuba, Ibaraki 305-8571
JAPANLocalized knowledge spillovers and patent citations:
A distance-based approach∗Yasusada Murata† Ryo Nakajima‡ Ryosuke Okamoto§ Ryuichi Tamura¶January, 2011

Abstract
We develop a new approach to localized knowledge spillovers by incorporating theconcept of control patents (Jaffe, Trajtenberg and Henderson 1993) into the distancebased test of localization (Duranton and Overman, 2005). Using microgeographic data,
we identify localization distance while allowing for cross-boundary spillovers, unlike theexisting literature where the extent of localized knowledge spillovers is detected at thestate or metropolitan statistical area level. We revisit the recent debate by Thompson
and Fox-Kean (2005) and Henderson, Jaffe and Trajtenberg (2005) on the existence of
localized knowledge spillovers, and find solid evidence supporting localization, even whenfiner controls are used.
Keywords: localized knowledge spillovers; distance-based tests; microgeographic data;
K-density; patent citations; control patents
JEL classifications: O31; R12∗

We are very grateful to Gilles Duranton and Peter Thompson for detailed comments and suggestions on

earlier drafts of this paper. We have also benefited from comments and suggestions by William Kerr, Jungmin
Lee, as well as other participants at various conferences and workshops.
†
Advanced Research Institute for the Sciences and Humanities, Nihon University (murata.yasusada@nihonu.ac.jp).
‡
Department of Economics, Yokohama National University (rn231@ynu.ac.jp).
§
National Graduate Institute for Policy Studies (rokamoto@grips.ac.jp).
¶
Graduate School of Humanities and Social Sciences, University of Tsukuba (tamura@dpipe.tsukuba.ac.jp).

11

Introduction

Ever since Marshall (1920), it is widely recognized that knowledge spillovers are one of thethree major determinants of industry agglomeration. Of the three determinants given in
his classic book, intellectual spillovers are harder to identify than trade in goods and laborpooling (Ellison, Glaeser and Kerr, 2010). Nonetheless, Jaffe, Trajtenberg and Henderson(1993) developed a matching rate method to test localized knowledge spillovers as evidenced
by patent citations. By controlling for the preexisting geographic concentration of production,
they found evidence supporting localized knowledge spillovers at the state and metropolitan
statistical area (MSA) levels. However, their finding was recently challenged by Thompson
and Fox-Kean (2005). The major difference between these two studies lies in the selection ofcontrol patents. In Jaffe, Trajtenberg and Henderson (1993), control and citing patents sharea technology class at the three-digit level, whereas in Thompson and Fox-Kean (2005), bothpatents share a finer technology subclass at the six-digit level.1 The latter authors further
restricted to control patents that have any subclass code in common with originating patents,and found no evidence supporting localized knowledge spillovers at the state and MSA levels.
The existence of localized knowledge spillovers is, thus, still inconclusive (Henderson, Jaffe
and Trajtenberg, 2005).
Are states and MSAs relevant spatial units for testing localized knowledge spillovers? Thereis no a priori reason for the extent of knowledge spillovers to be limited by administrative
boundaries. The matching rate approach, taken by Jaffe, Trajtenberg and Henderson (1993)
and Thompson and Fox-Kean (2005), however, is silent on this issue because it allocatesinventors to states and MSAs while abstracting from where those aggregated spatial units arelocated on the map. Put differently, their approach makes the distance from Boston, MA, to
New Haven, CT, equivalent to that of Boston, MA, to Los Angeles, CA.2 To capture possible
cross-boundary knowledge spillovers, we conduct distance-based tests of localization that havebeen recently developed by Duranton and Overman (2005). Their basic idea is to generate
the distribution of distances between pairs of establishments in an industry and to compare
it with that of hypothetical industries, in which establishments are randomly allocated acrossexisting establishment sites, in order to assess the significance of departures from randomness.
We apply the distance-based approach to test whether knowledge spillovers, as evidenced
1

These case-control methods have been applied to detect localized knowledge spillovers in numerous contexts

for almost two decades. See Almeida (1996) for an early application to the U.S. semiconductor industry. Morerecent contributions include Agrawal, Kapur and McHale (2008) and Agrawal, Cockburn and Rosell (2010),
in which they explored innovation in company towns and the role of ethnicity in knowledge flows.
2
It should also be noted that spatial units often differ in population and area, so that spatial aggregations
tend to mix different spatial scales. For instance, localization tests at the state level involve comparisons between Rhode Island and California, whose area is more than 150 times as large. Furthermore, such aggregation
often leads to spurious correlations across aggregated variables, which is known as the Modifiable Areal Unit
Problem (MAUP).

2

by patent citations, are localized, and examine to what extent they are localized (if they are).
In doing so, we consider which technology classes are localized, and identify the class-specificlocalization distance.3 Our key idea is to use citation distances, computed from inventors’
addresses at the census place level, instead of distances between establishments in Durantonand Overman (2005). We generate the distribution of citation distances by allowing for the factthat citing–cited relationships are unidirectional, unlike the establishment data. Our novelty
lies in incorporating the concept of control patents and the construction of counterfactuals
in a consistent way. This can be done by randomly drawing counterfactual citations, as inDuranton and Overman (2005), while controlling for the existing geographic concentration oftechnological activities, as in Jaffe, Trajtenberg and Henderson (1993) and Thompson andFox-Kean (2005). We finally detect localized knowledge spillovers by comparing the actualand counterfactual distributions of citation distances. We thus build a new bridge between
these two different strands of literature. To our knowledge, there has so far been no attempt
to apply the distance-based method to citing–cited relationships.
Our main results can be summarized as follows. First, distance matters. Our distancebased tests find that, even when we use six-digit controls, knowledge spillovers are localized
significantly for about one-third of all 360 technology classes in question. This is in sharp
contrast to Thompson and Fox-Kean (2005) who used six-digit controls and found no evidence
supporting localized knowledge spillovers at the state and MSA levels. In the three-digit case,more than 70% of 384 technology classes in question exhibit localization, thus confirming theresult by Jaffe, Trajtenberg and Henderson (1993). We further show that, in both cases, themajority of technology classes displaying localization are localized at least once within 200
km, which corresponds roughly to the distance between Boston and New Haven, for example.
We also find that more than 95% of all technology classes exhibiting localization are localized
within 1200 km, which constitutes an upper bound of knowledge spillovers.
Second, heterogeneity across technology classes also matters. In particular, our six-digit
analysis reveals that, while about one-third of technology classes exhibit localization, morethan 10% of technology classes display dispersion. This, together with the six-digit resultin Thompson and Fox-Kean (2005), implies that aggregating different technology classes canoffset the tendency toward localization even when a substantial number of technology classes
display localization at the disaggregate level.
The biases from aggregating spatial units and technology classes are shown to be substantial. To explore the difference between the matching rate and distance-based approaches indetecting localized knowledge spillovers, we conduct class-specific matching rate tests, andcompare the number of localized classes with the corresponding number generated by our
distance-based tests. It turns out that, although the numbers are roughly the same for the3

As shown in Ellison and Glaeser (1997) and Duranton and Overman (2005), the degree of industry local-

ization is known to differ across industries. Thus, we would quite naturally expect that the extent of knowledge
spillovers can also differ across technology classes, and we show that this is indeed the case.

3

three-digit case, the matching rate tests underestimate the number of localized classes for thesix-digit case. Indeed, the matching rate tests fail to detect localized knowledge spillovers formore than 60% of the technology classes that exhibit localization by the distance-based tests.
Hence, our analysis, which allows for distance and heterogeneity across technology classes,
has rich implications for knowledge cluster policies: relevant technology classes must be chosen, i.e., classes that display significant localization should be carefully selected; and crossboundary knowledge spillovers need to be taken into account, i.e., inventors who benefit frompositive knowledge externalities must be clustered in a borderless manner. Our analysis further
suggests that the timing of policies must also be determined accurately because the numberof localized technology classes and the associated localization distances can change over time.
The rest of the paper is organized as follows. Section 2 describes data and methodology.
Section 3 reports our main results. Section 4 concludes.

2

Data and Methodology

This section describes data and methodology. Unlike the conventional matching rate tests atthe state and MSA levels, we need to combine patent citations data and microgeographic datato conduct distance-based tests. Concerning methodology, we first identify control patents,
as in Jaffe, Trajtenberg and Henderson (1993) and Thompson and Fox-Kean (2005), to control for the existing geographic distribution of technological activities. We then constructcounterfactuals, as in Duranton and Overman (2005), while using the case-control methods.
The counterfactual citations thus obtained, with which we compare the actual citations todetect localized knowledge spillovers, share common features between the matching rate andthe distance-based tests. Hence, we can make a direct comparison between these two tests for
localization.

2.1

Patents and Patent Citations

Our data are based on the NBER U.S. Patent Citations Data File, which is described indetail by Hall, Jaffe and Trajtenberg (2001). This data set covers all patent applications
between 1963 and 1999 and those granted by 1999, as well as citing–cited relationships forpatents granted between 1975 and 1999. For each patent, the list of inventors, addresses ofinventors, and the technological category are recorded, along with other information such as
year of application, assignees, and the type of assignees. The detailed information of patentapplication month and patent class (three-digit) and subclass (six-digit) codes is supplemented
with the United States Patent and Trademark Office (USPTO) Patent BIB database.4
We begin with 142, 245 U.S. nongovernmental patents that were granted between January1975 and December 1979. The sampling period is chosen to be comparable to those of previous
4

We use the patent classification as of December 31, 1999.

4

studies. We identify patents as “U.S.” if the country of the assignee is the United States. We
observe that 115, 905 (81.5%) of them were cited at least once by other U.S. patents, and wecall them the originating patents. We then identify the citing patents that cited the originating
patents by examining all patents that were granted between January 1975 and December 1999.
We further exclude “self-citations”. A citing patent is classified as self-citing (i) if it had thesame assignee as the originating patent that it cited; or (ii) if it was invented by the same
inventor as the originating patent that it cited.5 To distinguish unique inventors, we use
the computerized matching procedure (CMP) proposed by Trajtenberg, Shiff and Melamed(2006).6 The CMP uses not only the name of inventors recorded in the patents, but also
patent citations, and inventors’ addresses, while allowing for possible errors in names. We findthat 15.0% of citing patents are classified as self-citations. After excluding self-citations, we
obtain 647, 983 citing patents.

2.2

Geographic Information

Our distance-based approach to localized knowledge spillovers requires microgeographic data,
namely the locations at which inventions were created. In this paper, we identify the locationof each invention at the census place level. The U.S. Census Bureau defines a place as aconcentration of population. There are 23, 789 places in the 1990 census, which we use below.7
They are much more finely delineated than counties (there are 3, 141 counties), but not as
small as zip code areas (there are 29, 470 zip code areas).8 Figure 1 shows the boundary mapof census places for the contiguous U.S. area.
Insert Figure 1
To be more specific, restricting patent inventors who reside in the contiguous U.S. area,
we first match the address of each inventor to the 1990 census place by their names. If thename match fails, we locate it via the populated place provided by the U.S. Geographic Names
Information System (GNIS). We match the inventor’s address with the GNIS populated place,
Jaffe, Trajtenberg and Henderson (1993) and Thompson and Fox-Kean (2005) regard only the former
as self-citations. Our criterion (ii) rules out spurious knowledge spillovers associated with inventor mobility.
5

Furthermore, in response to the comments by Henderson, Jaffe and Trajtenberg (2005), we exclude control
patents that share the same inventors or the same assignees with the originating patents.
6
See Nakajima, Tamura and Hanaki (2010) for the implementation detail of the CMP.
7
In the 1990 census, there are two major types of places: census designated places (CDPs); and incorporated
places. These data can be obtained from 1990 U.S. Gazetteer Files.
8
We could use zip code areas. The NBER U.S. Patent Citations Data File, however, reports zip codes for
only 15.4% of all U.S. patent records. As the NBER Data File reports cities for almost all cases, we could
relate cities to zip codes. Yet, it is often the case that a city has several to dozens of zip codes. Also, thearea for each zip code as of 1990, which is needed to compute its internal distance below, is not available.
We therefore decided to link cities with census places whose relationships are uniquely determined and whose
areas as of 1990 are readily available.

5which is more finely delineated than the census place, and then find the census place that isnearest to the identified GNIS populated place by using their spatial coordination information.
This procedure allows us to identify the 18, 139 census places for 97.0% of all inventors in thesample. The average of within-area distances for census places is 1.70 km, which is far smaller
than those for counties (22.60 km), Consolidated Metropolitan Statistical Areas (CMSAs)(59.93 km), and states (197.93 km).9

2.3

Control Patents and Counterfactuals

Since industries generally tend to agglomerate with one another, the mere geographic coincidence of originating and citing patents does not provide solid support for localized knowledge
spillovers. For example, in the semiconductor industry, many citations are concentrated in
Silicon Valley. This need not imply localized knowledge externalities. It may just reflect thefact that a disproportionate fraction of firms of the related technological area is located inthat region. Hence, to test localized knowledge spillovers, we must control for the existing
geographic distribution of technological activities.
To this end, we use control patents, proposed by Jaffe, Trajtenberg and Henderson (1993)
and Thompson and Fox-Kean (2005), which satisfy the following two conditions. First, control
patents should belong to the same technological area as the citing patent under consideration.
Jaffe, Trajtenberg and Henderson (1993) selected a control patent at the three-digit level,
whereas Thompson and Fox-Kean (2005) constructed a finer control at the six-digit level. The
latter also claimed that a control should match not only with the citing patent but also with theoriginating patent. In what follows, emphasizing their difference in technology classification,
we refer to the controls of Jaffe, Trajtenberg and Henderson (1993) as the three-digit controls,and call those of Thompson and Fox-Kean (2005) the six-digit controls. Second, a control
patent should be in the same cohort as the citing patent. Jaffe, Trajtenberg and Henderson(1993) chose a control patent whose application date is within a one-month window on eitherside of the citing patent’s application date. Similarly, Thompson and Fox-Kean (2005) set theapplication date of a control patent within plus-or-minus six month around that of the citing
patent. Following these studies, we use one-month and six-month windows for the three-digit
and six-digit controls, respectively.10
Insert Table 1

9These distances are computed by the formula derived by Kendall and Moran (1963), which is presented

in Section 2.5.
10
There is one minor difference between their and our control patents. We use a fixed application date window
within which control patents are searched, while Thompson and Fox-Kean (2005) enlarge it in incremental
steps from a one-month window, then a three-month window, and, if necessary, a six-month window until thecontrol patent is found for each citing patent.

6

Table 1 presents the sample sizes. The first column shows the total numbers of the originating and citing patents. These numbers include patents with and without controls. In thesecond and third columns, the numbers of originating and citing patents having at least one
control are reported. It should be noted that citing patents do not always have controls, and,even if they do, the control is not necessarily unique for each citing patent. As shown, 60.20%
of the citing patents have three-digit controls. The rate of the citing patents having six-digit
controls is lower, at 18.65%. The citing patents with no controls assigned (and their originating patents) are dropped out of the samples.11 As a result, 92.64% of the originating patents
remain “in-sample” for the three-digit controls, and the corresponding number is 51.04% for
the six-digit controls. In the analysis that follows, we use these in-sample patents.
Once the relevant control patents are identified, we can construct counterfactuals withwhich we compare the actual citations. For each citation, we define an admissible patent set
by collecting the citing and control patents, either three or six digit, so that the admissible
patent set consists of the patents that either actually cited or could have cited the originating
patent. We then allocate a counterfactual citation between the originating patent and a patentthat is randomly drawn from the corresponding admissible patent set.12 In what follows, we
propose tests that nonparametrically balance the actual and counterfactual citations subject
to the same technological and temporal profiles, and attribute the remaining difference in
geographic distributions to the localization of knowledge spillovers, which is unrelated to thepreexisting concentration of technological activities.

2.4

The Matching Rate Approach

The main idea of the matching rate approach, invented by Jaffe, Trajtenberg and Henderson(1993) and refined by Thompson and Fox-Kean (2005), is to compute the geographic matchingrate of the actual citations, and compare it with that of counterfactual citations. Following
the previous studies, we define the matching rate of the actual citations as the proportion of
the citing patents whose geographic units such as states and CMSAs are matched with thoseof the originating patents. We analogously define the matching rate of the counterfactual
citations by matching geographic units between an originating patent and a patent that is
randomly drawn from the corresponding admissible patent set. Thompson and Fox-Kean(2005) propose a similar random sampling method to construct the matching rate of theWe also drop technology classes in which originating patents are distributed across less than 10 census
places. This selection of patents is required because we estimate the density of distances for each technology
class in the subsequent analysis, and a sufficient number of location points are needed to obtain well-behaved
11

estimated density functions. See Section 3.2 for more exposition.
12
It should be noted that, in the six-digit case, we use the admissible patent set that consists only of theciting and control patents belonging to the same technology class as the corresponding originating patent.
This is a logical consequence of the additional restriction in the six-digit case that originating-citing-control
triads of patents must share at least one patent subclass in common.

7

counterfactual citations. They randomly select a patent from the admissible patent set once
for each citation. By contrast, we resample patents many times from the admissible patent set,and consider a simulated distribution of the counterfactual matching rate. We now describe
the procedure of our matching rate test in detail.
Let pc be the population probability that a citing patent is in the same geographic unit
as the originating patent, and let pr be the corresponding probability for a randomly drawn
patent from the admissible patent set. We test the null hypothesis H0 : pc = pr (no localized
knowledge spillovers) against the alternative hypothesis H1 : pc > pr (significant localized
knowledge spillovers). Let p̂c be the matching rate of the actual citations that we observe inthe data. Under the null hypothesis, it is not statistically different from a realization of thecounterfactual matching rate, which we denote by p̂r . We thus reject the null hypothesis of
no localized knowledge spillovers if the p-value, Prob(p̂c ≤ p̂r ), is less than 5%.
o

We first construct the observed matching rate p̂c as follows. Let {oi }ni=1 be the set oforiginating patents, where no is the number of originating patents. The set of the patentscithat cite oi is defined as {cij }nj=1 , where nci is the number of citing patents. We computethe number of location matches, mci , between the originating patent oi and the citing patents
ci{cij }nj=1 . The total number of location matches divided by the total number of citations gives! o! o
the observed matching rate p̂c = ni=1 mci / ni=1 nci .
We then construct the distribution of the counterfactual matching rate p̂r by the following

Monte Carlo simulation. For each citing patent cij , we identify the admissible patent set Rijthat consists of the citing patent itself and the associated control patents. Suppose that werun 1000 simulations. In the k-th simulation, for each citing patent cij , we randomly select ahypothetical patent rkij from the admissible patent set Rij . We then calculate the number ofilocation matches, mri
k , between the originating patent o and the randomly chosen hypothet-

ical patents {rkij }nj=1 . The total number of location matches divided by the total number of! o!no cihypothetical citations gives the counterfactual matching rate p̂rk = ni=1 mrik/i=1 n , whereci

the total number of hypothetical citations equals that of actual citations. The Monte Carloprocess allows us to obtain the simulated distribution of the matching rate {p̂rk }1000
k=1 . We finallycompute the p-value of the matching rate test by using the standard percentile method.

Although the matching rate test is straightforward, one should be careful for multiple
inventors per patent. To determine whether or not a pair of citing and cited patents falls into
the same geographic unit, we use the following two matching methods. Consider, for eachciting-cited relationship, all possible pairs of an inventor of the citing patent and an inventorof the cited patent. The locations of the citing and cited patents are then matched (i) if the
majority of all possible inventor pairs fall into the same geographic unit (median matching); or(ii) if at least one pair of inventors falls into the same geographic unit (minimum matching).
These matching methods are in accord with those used in previous studies. For example,
Jaffe, Trajtenberg and Henderson (1993) employ a similar method as our median matching.
Thompson and Fox-Kean (2005) mention the minimum matching as an alternative to their8random matching.

2.5

The K-density Approach

As mentioned in the Introduction, the extent of knowledge spillovers is unlikely to be limited
by administrative boundaries. The matching rate approach that we have taken in the previous subsection, however, cannot address this issue because it abstracts from where CMSAs
and states are located in the United States. To capture possible cross-boundary knowledge
spillovers, we rely on distance-based tests of localization that were recently developed by Duranton and Overman (2005). Their basic idea is to generate the distribution of distances
between pairs of establishments in an industry and to compare it with that of hypotheticalindustries, in which establishments are randomly allocated across existing establishment sites,in order to assess the significance of departures from randomness.
We apply Duranton and Overman’s approach to test whether knowledge spillovers, asevidenced by patent citations, are localized, and examine to what extent they are localized (ifthey are). As before, we allocate a counterfactual citation between the originating patent anda patent drawn randomly from the corresponding admissible patent set. Unlike the matchingrate approach, however, we compare the distribution of distances between the originating andciting patents with the counterfactual distribution generated by the randomization. We thenconsider the deviation from randomness as evidence of localized knowledge spillovers. Our
distance-based test uses the same counterfactuals as the matching rate test, so that we canmake a direct comparison between these two tests for localization. We thus build a new bridge
between the two strands of literature, which are the matching rate test of localized knowledge
spillovers and the distance-based test of industry localization.
Such an attempt, however, poses two main difficulties that we need to deal with. First,
unlike establishments whose locations are usually uniquely determined, patents can have multiple addresses because their inventors are not necessarily unique. We thus compute, for eachcitation relationship, all possible distances between the inventors of the originating patent andthose of the citing patent, and focus on their median or minimum distance. The distance computation is in line with the median or minimum matching method of the matching rate tests,
respectively, as presented above. We do the same for the counterfactual citation relationship.
Second, because of the data limitation, the location of each inventor is identified at thecensus place level. Although census places are narrowly delineated compared with counties
and states, they are not spatial points. This poses a “zero distance” problem, i.e., even when
the actual distance between the originating and citing inventors is not zero, it is measured to
be zero if they happen to live in the same census place. To address this problem, we consider
spatial interaction between the two inventors within the same census place. Assuming thateach census place is a circle, it is readily verified that the distance between the two randomly"
chosen points in a census place with area S is given by [128/(45π)] S/π (Kendall and Moran,
91963). We use this correction for the distance between the two inventors who are in the same
census place, instead of regarding the distance as to be zero.
It is also noted that, unlike the previous studies on patent citations, we analyze the localization distance that is specific to each patent class. Because the degree of localization
is known to differ across industries (e.g., Ellison and Glaeser, 1997; Duranton and Overman,
2005), it seems natural to expect that the extent of localized knowledge spillovers can also
differ across patent classes. As we show later, this is indeed the case.
We now describe the detailed procedure of our distance-based test of localized knowledge
spillovers. Let A be the set of all technology classes, categorized at the patent class level. We
noAdenote by {oiA }i=1
the set of originating patents for technology class A ∈ A , where noA is thenciA
number of originating patents. The set of patents that cite oiA is denoted by {cijA }j=1 , wherenci
A is the number of citing patents. The number of citations originating from technology class!noA ci
A is then given by NA = i=1
nA . We finally denote by dij
A the great-circle distance between
patents oiA and cij
A , which, as mentioned above, is given by either the minimum or median

distance from the inventors of the originating patent to those of the citing patent. Following
Duranton and Overman (2005), the kernel density (henceforth K-density) estimator of citation
distance for technology class A at any point d iso

# A (d) =
K

ci

nA nA
$
$

1
f
2hNA i=1 j=1%

d − dij
A
h

&

,

(1)

where f is a Gaussian kernel function and h is the bandwidth set as in Silverman (1986).
Note that, expression (1) reflects the fact that, unlike Duranton and Overman (2005), we
consider unidirectional relationships from the inventors of originating patents to those of citing
patents.13
Concerning counterfactuals, we run 1000 Monte Carlo simulations.14 The construction ofcounterfactuals is the same as that of the matching rate test. For each citing patent cij
A , weij
identify the admissible patent set RA
that consists of the citing patent itself and the associatedij
control patents. In each simulation, we randomly draw a hypothetical patent rAk
from theijadmissible patent set RA
for each citing patent cij
A to estimate the counterfactual K-density
ij
for the distribution of distances from originating patents oiA to hypothetical patents rAk, usinga formula similar to (1). After 1000 simulation runs, we rank the counterfactual densities at
each 10 km in ascending order and select the 5-th and the 95-th percentiles to obtain a lower
5% and an upper 5% confidence interval that we denote K A (d) and K A (d), respectively.
Detecting localization based on K A (d) and K A (d), however, only allows us to make local
statements at a given distance. Unfortunately, this does not lead to statements about the13

As in Duranton and Overman (2005), we adopt the reflection method in Silverman (1986) to deal withboundary problems associated with the fact that distances cannot be negative.
14
We also repeated our simulations 2000, 5000, and 10, 000 times for several technology classes, and obtained
very similar results.

10

global citation patterns of a technology class because even a technology class with randomly
distributed citations will exhibit dispersion or localization with a high probability. Indeed, byconstruction, there is a 5% probability that a technology class displays localization for eachdistance, so that the probability for this to occur at least once across all distances is quite
high.
Therefore, we finally define the global confidence bands that we use to detect localized
knowledge spillovers. Let d¯A be the maximum distance for technology class A under consideration.15 We look for the identical upper and lower local confidence intervals such that,when we consider them across all distances between 0 and d¯A km, only 5% of our randomly
generated K-densities hit them. Let K A (d) be the upper global confidence band of technology# A (d) > K A (d) for at least one d ∈ [0, d¯A ], this technology class is said toclass A. When K

exhibit global localization at a 5% confidence level. Conversely, the lower global confidenceband of technology class A, K A (d), is such that it is hit by 5% of the randomly generated
K-densities that are not localized. A technology class is then said to exhibit global dispersion# A (d) < K (d) for at least one d ∈ [0, d¯A ] and the technolat a 5% confidence level when KAogy class does not exhibit global localization. The definition of global dispersion requires noglobal localization because otherwise dispersion at large distances could be a consequence of
localization at smaller distances, given that our densities must sum to one by construction.
Hence, we define'(# A (d) − K A (d), 0
ΓA (d) ≡ max K

as an index of global localization, and'()# A (d), 0 if ! ΓA (d) = 0
max K A (d) − KdΨA (d) ≡0
otherwise
as an index of global dispersion.
Insert Figure 2
Figures 2(a)–(b) illustrate K-densities (solid) and global confidence bands (dotted) for two
patent classes, namely butchering (452) and amusement devices: toys (446), respectively. The
former exhibits global localization while the latter is globally dispersed.

3

Results

The purpose of this section is fourfold. Using the matching rate tests at the aggregate level, we
first replicate the same qualitative features as those of Jaffe, Trajtenberg and Henderson (1993)
and Thompson and Fox-Kean (2005), despite some differences in data and methodology. We
Following Duranton and Overman (2005), we define the maximum distance as the median of all distancesof all possible counterfactual citations for technology class A.
15

11

then turn to our K-density tests, and show that a substantial number of technology classes
display localization, even when control patents are selected at the six-digit level. We further
explore in details why the discrepancy arises between these two tests by comparing our classspecific distance-based tests with the matching rate tests at the disaggregate level. We finallyderive some policy implications from our findings.

3.1

The Matching Rate Tests

Table 2 reports the results of the matching rate tests for the state, CMSA and county levels.16
Following Jaffe, Trajtenberg and Henderson (1993) and Thompson and Fox-Kean (2005), thematching rate tests are implemented at the aggregate level encompassing all technology classes.
Using controls at the three- and six-digit levels, we compare the observed matching rate withthe average of the counterfactual matching rates for each geographic unit. The standard errorsof the counterfactual matching rates are computed by simulation with 1000 replications.
Insert Table 2
In the case of the three-digit controls, the observed matching rates are significantly higher
than the counterfactual ones for all spatial scales, although the matching rates become smaller
for finer geographic units. We reject the null hypothesis of no localized knowledge spillovers
at a 5% significance level, and, thus, find solid evidence of localized knowledge spillovers.
By contrast, the null hypothesis is not rejected for the six-digit controls, which suggests noevidence of localized knowledge spillovers. These results share the same qualitative features
as those of Jaffe, Trajtenberg and Henderson (1993) and Thompson and Fox-Kean (2005),
although our data construction and methodology are somewhat different from theirs.

3.2

The K-density Tests

We now describe the results of the K-density tests. We introduce some notations. For atechnology class A ∈ A , knowledge spillovers are said to exhibit localization at distance d if

ΓA (d) > 0, whereas they are said to exhibit dispersion at distance d if ΨA (d) > 0. We define!
a technology class A as having localized knowledge spillovers if ΓA ≡ d ΓA (d) > 0, and as!
having dispersed knowledge spillovers if ΨA ≡ d ΨA (d) > 0. Finally, we use L1 = {A ∈A |ΓA > 0} and D1 = {A ∈ A |ΨA > 0} to denote the sets of technology classes displaying
localized and dispersed knowledge spillovers, respectively.

Table 3 presents the main results. As we consider both the minimum and median distances,
as well as the three- and six-digit controls, there are four possibilities. First, concerning thethree-digit case, we find localized knowledge spillovers for the majority of technology classes,with about 70% being localized for both the median and minimum distances. These results
16

As in Thompson and Fox-Kean (2005), we use 16 CMSAs as defined in 1981 by excluding Puerto Rico.

12

are in line with those obtained by Jaffe, Trajtenberg and Henderson (1993). Turning to thesix-digit controls, more than 30% of technology classes exhibit localized knowledge spillovers
regardless of whether we use the median or minimum distance. Although fewer classes exhibit
localization in the six-digit case, we obtain solid evidence for localized knowledge spillovers.
This is surprising given that Thompson and Fox-Kean (2005) find no evidence supporting
localization at the state and CMSA levels. The matching rate tests that we have presented
above also report no localization for the six-digit controls.
Insert Table 3
To investigate more closely the scope of knowledge spillovers, let L1 (d) = {A ∈ A |ΓA (d) >0} and D1 (d) = {A ∈ A |ΨA (d) > 0} be the sets of technology classes that exhibit localizationand dispersion, respectively. Figure 3 illustrates the distributions of |L1 (d)| and |D1 (d)| forthe three- and six-digit controls. In each case, there is no substantial difference between the

median (solid) and the minimum (dotted) distance methods. We see that the number of
localized technology classes is greater at smaller distances for both the three- and six-digit
controls. The degree of localization decreases as the distance from the originating patents
increases, thus suggesting that knowledge spillovers decay with distance. Interestingly, thisis consistent with the assumption that is made in the recent theory of spatial development(Desmet and Rossi-Hansberg, 2009). By contrast, there is no clear pattern for dispersed
knowledge spillovers, although we observe some significant dispersion across various distances.
Such dispersion of citing inventors may arise, for instance, when the benefits of their poolingis dominated by the costs of their poaching from firms’ perspectives (Combes and Duranton,2006).
Insert Figure 3
We can delineate a boundary within which knowledge spillovers are localized. Figure 4
shows the percentages of technology classes displaying localization at least once within distance d. As shown, there are substantial differences between the three- and six-digit cases.
However, no matter which control is used, more than half of the technology classes displaying
localized knowledge spillovers are localized at least once within about 200 km, which corresponds roughly to the distance between Boston and New Haven. We can also consider 1200
km as an upper bound of the extent of knowledge spillovers because more than 95% of all
localized classes are localized by this distance, regardless of which controls are used.
Insert Figure 4
We further examine heterogeneity in the patterns of knowledge spillovers across technology
classes. Figure 5 illustrates the distributions of ΓA and ΨA for the median distance casebecause the results are fairly robust regardless of the choice between the median and theminimum distances.17 Both distributions are skewed substantially with the localization and
17

The results of the minimum distance method are available upon request from the authors.

13

dispersion indices being close to zero, while there are several technology classes displaying
highly localized or dispersed knowledge spillovers. Interestingly, for the three-digit controls,
the fraction of localized technology classes outweighs substantially that of dispersed technology
classes. By contrast, in the six-digit case, the corresponding difference between the localized
and dispersed technology classes is not so large.
Insert Figure 5
Finally, Table 4 presents the top 20 technology classes with highest degrees of localization,measured by ΓA , for the median distance case. The rankings for the three- and six-digit
controls are roughly similar, in that five out of the top 20 localized classes overlap between
the three- and six-digit cases.18 Table 4 also shows that knowledge spillovers are highly
localized in “traditional” industries such as: agriculture, husbandry and food (Patent Class452); furniture and house fixtures (256); earth working and wells (166 and 405); and appareland textile industries (2, 36, and 112), where the categories are given by Hall, Jaffe andTrajtenberg (2001). We also find significant localization of knowledge spillovers for manymechanical industries (Patent Classes 192, 221, 239, 254, 296, 301, 303, 411, 440, 492 and508), in particular, transportation mechanical industries (296 and 301).
Insert Table 4

3.3

Comparison

We have shown that, unlike the matching rate tests, the K-density tests provide solid evidence
for localized knowledge spillovers, even for the six-digit controls. We now explore the differences, as well as the similarities, in detecting localization between these two approaches. In
particular, we argue, in what follows, that the matching rate tests using the six-digit controls
underestimate localization of knowledge spillovers because of the following two “aggregation”
problems.
The first problem is “technological aggregation”. As shown above, the K-density tests
reveal considerable heterogeneity across technology classes in whether knowledge spillovers
are localized or dispersed. This is particularly so, in the six-digit case, where the distributionsof ΓA and ΨA are roughly similar. Accordingly, if these heterogeneous classes are pooled, as
in the conventional matching rate tests, both localization and dispersion can be cancelled out
with each other, and, thus, may leave no evidence of localization at the aggregate level.
To confirm this idea, we implement class-specific matching rate tests. Specifically, we
test the hypothesis of no localized knowledge spillovers at the 5% significance level for eachtechnology class. Let L1 = {A ∈ A |pcA > prA } denote the set of technology classes that exhibit
In fact, the rank correlation coefficient between the three- and six-digit controls is computed as ρ = 0.36,
and the null hypothesis of no correlation is rejected at the 1% significance level.
18

14

localization by the class-specific matching rate tests, where pc and pr depend on technology
class A. Table 5 shows that, when the three-digit controls are used, localized knowledge
spillovers are detected for 270 or 266 technology classes, depending on whether the spatial
units are states or CMSAs. Interestingly, these numbers are fairly close to the 275 localizedclasses, obtained from the K-density tests in Table 3.19 Hence, we conclude that the matchingrate and the K-density tests detect roughly the same number of localized technology classes
for the three-digit controls.
However, for the six-digit controls, the matching rate and the K-density tests substantially differ in detecting the number of localized technology classes. Indeed, the class-specificmatching rate tests identify localization for a smaller fraction of technology classes than do
the K-density tests. More concretely, only 47 to 69 technology classes display localization in
the former tests, depending on the spatial units, whereas more than 100 technology classes
are shown to be localized in the latter tests. Yet, even in the class-specific matching rate,
the percentages of technology classes with localized knowledge spillovers remain in the range
between 13% and 20%. Hence, we find evidence that knowledge spillovers are localized fornonnegligible, though not overwhelming, technology classes, even in the six-digit case.
Insert Table 5
The second problem of the conventional matching rate tests is “geographic aggregation”.
The matching rate tests ex ante allocate inventors to spatial units such as states and CMSAs.
As Duranton and Overman (2005) pointed out, this aggregation treats administrative units
symmetrically, so that inventors in neighboring spatial units are treated in exactly the same
way as inventors at the opposite ends of a country. This creates a downward bias when dealing
with localized knowledge spillovers that cross an administrative boundary. The distance-based
tests have an advantage in that they do not overlook such cross-border knowledge flows.
To investigate this possibility, we again focus on the discrepancy between the matchingrate and the K-density tests for the six-digit controls. We first implement the matching rate
tests for the two groups of technology classes, that is, the set of localized technology classes
by the K-density tests, L1 = {A ∈ A |ΓA > 0}, and the set of nonlocalized technology classes,

L0 = {A ∈ A |ΓA = 0}. We then define L10 = {A ∈ A |pcA = prA and ΓA > 0} as the set oftechnology classes where the K-density tests detect significant localization, while the matchingrate tests do not. Thus, it follows that L10 ⊆ L1 . Similarly, we define L01 = {A ∈ A |pcA >prA and ΓA = 0} ⊆ L0 .

Table 6 provides the results. First, looking at the results of |L10 | in the first and second

rows, a large number of technology classes that are detected as localized by the K-density tests
are not identified as localized by the matching rate tests. We thus find that the matching rate
Table 5 shows the results for the median matching case. The results for the minimum matching case are
qualitatively similar, and, thus, are omitted. They are available upon request from the authors.
19

15

tests underestimate localized knowledge spillovers. The number of underestimated technology
classes ranges from 67 to 89, depending on the spatial units. These biases are substantial since
the percentage of underestimated classes is as high as 61% to 62% at the state and CMSA
levels, respectively, and it amounts to 81% at the county level. Moving to the results of |L01 |in the third and fourth rows, a number of technology classes that are not detected as localized
by the K-density tests are identified as localized by the matching rate tests. This implies
that the matching rate tests can also overestimate localized knowledge spillovers. However,the numbers of underestimated localized classes, |L10 |, much outweigh those of overestimatedlocalized classes, |L01 |. We see that the difference ranges from 40 to 62, which explains thedifference between |L1 | in Table 3 and |L1 | in Table 5 for the six-digit controls.
Insert Table 6
We finally investigate where we observe the downward biases of the matching rate tests
using the six-digit controls in detecting localized knowledge spillovers. Figure 6 plots |L10 (d)|for each distance d, where L10 (d) = {A ∈ A |pcA = prA and ΓA (d) > 0}. We first notice that the

downward biases tend to be most substantial around 200 km or 500 km, depending on whether
we focus on counties or on CMSAs and states. For example, the county-level matching rate
tests fail to detect about 40 technology classes as having no localized knowledge spillovers at
200 km. This underestimation is inherent in their construction. The matching rate tests cannot
discern, by their definitions, knowledge spillovers that travel longer than their predeterminedadministrative boundaries. For example, given that the average of within-area distances for
the U.S. states is 197.9 km, localized knowledge spillovers whose scope significantly exceedsthat distance are unlikely to be captured by the state-level matching rate test. In this light,
the matching rate tests with smaller spatial units, which have the smaller average of withinarea distances, tend to more severely underestimate localized knowledge spillovers that canbe detected by the K-density tests.
Insert Figure 6
In summary, the existing matching rate tests systematically understate localized knowledge spillovers, as evidenced by patent citations. We explain this by two aggregation problems,
which are technological and geographic aggregations. If we control for heterogeneity in localization and dispersion by disaggregating technology classes, the matching rate tests provide
evidence of localized knowledge spillovers for a fraction of technology classes. Yet, they still
fail to identify a substantial number of localized technology classes that are detected by the
distance-based K-density tests. Our analysis also suggests that the matching rate tests withsmaller administrative units tend to exacerbate the underestimation problem. In view ofthis, the geographic aggregation problem with the matching rate tests cannot be resolved,
even when taking smaller administrative units such as counties. Rather, in that case, thedownward biases become more substantial.
16

3.4

Policy implications

Our K-density tests find solid evidence supporting localization, regardless of whether we
use the three- or six-digit controls. Since we allow for distance and heterogeneity acrosstechnology classes, our findings shed new light on cluster policies. First, policy makers needto select the “right” technology classes, i.e., those displaying significant localized knowledge
spillovers. Second, for each “right” technology class, the “right” scope, i.e., the distance within
which the technology class exhibits localization, must also be selected in a borderless manner.
Since the majority of technology classes that display localization are localized within 200 km,
knowledge cluster policies can generally be made within this distance in order to enhanceknowledge externalities.
However, this is not the end of the story. The combination of the “right” technology classand the “right” scope at one time does not necessarily ensure a successful cluster policy atother times. For instance, the father of Silicon Valley, Frederick Terman, could not replicate“Silicon Valley East” in New Jersey several years later. The reason why such an attempt, led
by Bell Laboratories, was in vain, may be that they failed to choose “right” time, as pointed
out by Findlay (1992) and Leslie and Kargon (1996). This experience suggests that “right”
technology classes and “right” scopes may change over time.
To explore this issue, we restrict ourselves to the citing patents granted in two sub-periods,
1985-1989 and 1995-1999. Interestingly, Figure 7 illustrates that, as time goes by, the numberof localized technology classes, |L1 (d)|, gets smaller in shorter distances while it gets larger inlonger distances. This feature is common to the three- and six-digit cases, although it is lessclear in the latter case. We further show that, in both cases, the distances within which the
majority of technology classes displaying localization are localized can increase up to 500 km
in the latter period. It should be noted, however, that the larger the cluster size the more
likely to be higher the commuting costs and land rents. Accordingly, such large-scale cluster
policies are unlikely to be justified by the cost-benefit analysis that encompasses not only
positive knowledge externalities but also negative congestion externalities, as emphasized by
Duranton et al. (2010). Hence, we may conclude that policy makers must also care about the“right” time to implement cluster policies.
Insert Figure 7

4

Conclusion

We propose a distance-based approach to localized knowledge spillovers and revisit the recent
debate by Thompson and Fox-Kean (2005) and Henderson, Jaffe and Trajtenberg (2005)
on the existence of localized knowledge spillovers. Our concern has been two aggregation
problems, namely technological and geographic aggregations, both of which are ignored in that17

literature. Overcoming these two problems, our distance-based tests have found solid evidence
supporting localized knowledge spillovers for a substantial number of technology classes, evenwhen the finer six-digit controls are used. At the same time, nonnegligible technology classes
exhibit dispersion, thus implying considerable heterogeneity across classes. We show that theclass-specific matching rate tests for the six-digit controls understate the number of localized
technology classes that are detected by the distance-based tests. These aggregation biases may
thus explain why the matching rate tests, implemented by Thompson and Fox-Kean (2005),
could not find any significant evidence for intranational knowledge spillovers.
Our distance-based tests have found that the number of localized technology classes forthe six-digit controls is smaller than that for the three-digit controls. However, as argued
by Henderson, Jaffe and Trajtenberg (2005), finer controls need not be better because they
can induce the sample selection problem. Our six- and three-digit results thus provide thepossible shares of localized technology classes, with the range being between 30% and 70%.
Furthermore, we show that, in either case, the localization of knowledge spillovers attenuateswith distance. We thus conclude that substantial numbers of technology classes display localized knowledge spillovers at the intranational level, regardless of whether we use the three- or
six-digit controls.
To compare our distance-based tests with the conventional matching rate tests such as
Jaffe, Trajtenberg and Henderson (1993) and Thompson and Fox-Kean (2005), we have relied
on typical case-control methods by specifying the technology level at which control patents are
selected. It is worth noting, however, that Thompson (2006) developed an alternative methodthat does not involve such case controls. Using more recent data that can distinguish citations
added by inventors from those added by examiners, Thompson (2006) showed that inventor
citations are more likely to match the state or CMSA of their originating patents than examiner
citations. Given our result that the matching rate tests are subject to the two aggregation
problems, that alternative approach may be biased as well. Our distance-based method canbe modified to address such an issue by testing for the localization of inventor added citations
relative to the counterfactual geographic distribution of examiner added citations.
Our findings from class-specific distance-based tests have several implications for cluster
policies. First, policy makers need to select the “right” technology classes. Second, for each“right” technology class, the “right” scope must also be taken into account. Since the majorityof technology classes that display localization are localized within 200 km, knowledge cluster
policies can generally be made within this distance in order to enhance knowledge externalities.
As administrative boundaries need not limit knowledge spillovers, such policies would require
coordination among adjacent administrative units. Last, policy makers must also care about
the “right” time to implement cluster policies because the “right” technology classes and the“right” scopes can change over time. Although we have mainly focused on cross-boundary
knowledge spillovers to illustrate the biases generated by the matching rate tests, our K-density
tests can also be applied to localized knowledge clusters in smaller scales. This direction is18

independently explored by Kerr and Kominers (2010).20
Finally, our distance-based measure of localized knowledge spillovers can be used to explore
the determinants of industry agglomeration. Some studies (e.g., Rosenthal and Strange, 2001;
Ellison, Glaeser and Kerr, 2010) already attempted to include proxies for the importance ofknowledge spillovers, which are constructed more directly from patent data, into their regression analysis. However, we are not aware of any study that incorporates a measure of localized
knowledge spillovers for explaining industry agglomeration. Using such a localization measure
would lead to a better understanding of the relationship between industry agglomeration andknowledge spillovers.

We became aware of their project after the first draft of our paper was completed. Kerr and Kominers(2010) apply a similar distance-based method to patent data. However, there is one notable difference. Their
20

K-density tests detect localization by comparing pairwise distances among inventors in a technology with thoseobtained from 1000 random draws of U.S. inventors of a similar size to that technology, as have been done by
Duranton and Overman (2005) in the context of establishment agglomeration. Hence, their K-density tests
abstract from the concept of control patents and explicit citing–cited relationships, both of which are at theheart of our tests.

19

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proximity influence knowledge flows? Evidence from patent data.” Journal of Urban Economics, 64: 258–268.
Agrawal, Ajay, Iain Cockburn, and Carlos Rosell. 2010. “Not Invented Here? Innovation in company towns.” Journal of Urban Economics, 67: 78–89.
Almeida, Paul. 1996. “Knowledge sourcing by foreign multinationals: Patent citation analysis in the U.S. semiconductor industry.” Strategic Management Journal, 17: 155–165.
Combes, Pierre-Philippe, and Gilles Duranton. 2006. “Labour pooling, labour poaching, and spatial clustering.” Regional Science and Urban Economics, 36: 1–28.
Desmet, Klaus, and Esteban Rossi-Hansberg. 2009. “Spatial development.” Working
Paper 2009-18, Instituto Madrileño de Estudios Avanzados.
Duranton, Gilles, and Henry Overman. 2005. “Testing for localization using microgeographic data.” Review of Economic Studies, 72: 1077–1106.
Duranton, Gilles, Martin Philippe, Thierry Mayer, and Florian Mayneris. 2010.
The Economics of Clusters: Lessons from the French Experience. Oxford University Press.
Ellison, Glenn D., and Edward L. Glaeser. 1997. “Geographic concentration of in US
manufacturing industries: A dartboard approach.” Journal of Political Economy, 105: 889–
927.
Ellison, Glenn D., Edward L. Glaeser, and William R. Kerr. 2010. “What causes
industry agglomeration? Evidence from coagglomeration patterns.” American Economic
Review, 100: 1195–1213.
Findlay, John M. 1992. Magic lands: Western cityscapes and American culture after 1940.
Berkeley:University of California Press.
Hall, Bronwyn, Adam Jaffe, and Manuel Trajtenberg. 2001. “The NBER patent citation data file: Lessons, insights and methodological tools.” NBER Working Paper #8498.
Henderson, Rebecca, Adam Jaffe, and Manuel Trajtenberg. 2005. “Patent citations
and the geography of knowledge spillovers: A reassessment: comment.” American Economic
Review, 95: 461–464.
Jaffe, Adam, Manuel Trajtenberg, and Rebecca Henderson. 1993. “Geographic localization of knowledge spillovers as evidenced by patent citations.” Quarterly Journal of
Economics, 108: 577–598.
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Kendall, M.G., and P.A.P. Moran. 1963. Geometrical Probability. London:Charles Griffin& Company Limited.
Kerr, William R., and Scott Duke Kominers. 2010. “Agglomerative forces and cluster
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Leslie, Stuart W., and Robert H. Kargon. 1996. “Selling Silicon Valley: Frederick Terman’s model for regional advantage.” Business History Review, 70: 435–472.
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21

Table 1: Sample Patent Sizes
Total

3-digit

6-digitOriginatings

115,905

107,561

59,168Percent
Citings
Percent(100.00)
647,983(100.00)(92.64)
390,104(60.20)(51.04)
120,876(18.65)Controls—

33,472,826

941,532

Table 2: Matching Rate Test Results
3-digit Control
Median Minimum

6-digit Control
Median Minimum

State

Observed Rate (%)

12.53*

13.54*

13.38

14.31

CMSA

Counterfactual Rate (%)
Std. Error
Observed Rate (%)

9.33(0.04)
9.24*

10.16(0.04)
10.29*

13.45(0.07)
10.12

14.49(0.06)
11.18

Counterfactual Rate (%)
Std. Error

6.54(0.03)

7.32(0.03)

10.33(0.06)

11.37(0.06)

Observed Rate (%)
Counterfactual Rate (%)
Std. Error

4.08*
2.54
(0.02)

5.27*
3.31(0.02)

4.34
4.63(0.04)

5.62
5.88(0.05)CountyNotes: ∗ denotes statistically significant at 5% level.

Table 3: K-density Test Results
3-digit Control
MedianMinimum
All Classes |A |Localized Classes |L1 |Non-localized Classes |L0 |Dispersed Classes |D1 ||L1 |/|A | × 100 (percent)6-digit Control
MedianMinimum

384

384

360

360

275
109
39

273
111
40

109
251
41

109
251
51

(71.61%)(71.09%)(30.27%)(30.28%)22

Table 4: Top 20 Localized Technology Classes
Class ID

Patent Class Name

ΓA

3-digit controls
405 Hydraulic and Earth Engineering
452 Butchering
36
Boots, Shoes, and Leggings
223 Apparel Apparatus
606 Surgery
367 Communications, Electrical: Acoustic Wave Systems and Devices
296 Land Vehicles: Bodies and Tops
285 Pipe Joints or Couplings
492 Roll or Roller
181 Acoustics
30
Cutlery
501 Compositions: Ceramic
411 Expanded, Threaded, Driven, Headed, Tool-Deformed, or LockedThreaded Fastener
254 Implements or Apparatus for Applying Pushing or Pulling Force
256 Fences
239 Fluid Sprinkling, Spraying, and Diffusing
290 Prime-Mover Dynamo Plants
303 Fluid-Pressure and Analogous Brake Systems
192 Clutches and Power-Stop Control
112 Sewing
6-digit controls
256 Fences
221 Article Dispensing
248 Supports
433 Dentistry
222 Dispensing
137 Fluid Handling
141 Fluent Material Handling, with Receiver or Receiver Coacting Means
296 Land Vehicles: Bodies and Tops
301 Land Vehicles: Wheels and Axles
405 Hydraulic and Earth Engineering
440 Marine Propulsion
411 Expanded, Threaded, Driven, Headed, Tool-Deformed, or LockedThreaded Fastener
166 Wells
285 Pipe Joints or Couplings
508 Solid Anti-Friction Devices, Materials Therefor, Lubricant or Separate Compositions for Moving Solid Surfaces, and Miscellaneous Mineral Oil Compositions
2
Apparel
261 Gas and Liquid Contact Apparatus
198 Conveyors: Power-Driven
218 High-Voltage Switches with Arc Preventing or Extinguishing Devices
118 Coating Apparatus

23

0.02010.01550.01530.01450.01430.01350.01220.01060.01030.01000.00980.00950.00890.00880.00870.00820.00810.00780.00780.00770.00700.00380.00300.00290.00250.00240.00230.00230.00230.00220.00220.00220.00220.00220.00210.00200.00190.00190.00190.0018Overlapped
!

!
!

!

!

!

!
!
!

!

Table 5: Matching Rate Test Results for Disaggregated Technology Classes
3-digit controls
All Classes |A |Localized Classes |L1 |Non-localized Classes |L0 ||L1 |/|A | × 100 (percent)6-digit controls

State

CMSA

County

State

CMSA

County

384
270

384
266

384
247

360
68

360
69

360
47

114
(70.31%)

118(69.27%)137(64.32%)292(18.89%)291(19.17%)313(13.06%)

Table 6: Matching Rate Tests Conditional on K-density Tests for Six-digit Controls
State|L10 |: pcA = prA and ΓA > 0|L10 |/|L1 | × 100 (percent)|L01 |: pcA > prA and ΓA = 0|L01 |/|L0 | × 100 (percent)CMSACounty67

68

89(61.47%)26(10.36%)(62.39%)28(11.16%)(81.65%)27(10.76%)24

25
Figure 1: Census Places as of 1990












































































   

(a) Butchering (452)(b) Amusement Devices: Toys (446)Figure 2: K-density and Global Confidence Bands for Two Illustrative Patent Classes

26










































































(b) six-digit controls: |L1 (d)|









(a) three-digit controls: |L1 (d)|


































(c) three-digit controls: |D1 (d)|(d) six-digit controls: |D1 (d)|Figure 3: Distance Distribution of the Numbers of Technology Classes

27

































































(a) three-digit controls(b) six-digit controls

Figure 4: Percentage of Localized Technology Classes within Each Distance

28
















































































































(b) six-digit controls: ΓA









(a) three-digit controls: ΓA























(c) three-digit controls: ΨA(d) six-digit controls: ΨA

Figure 5: Distributions of Localization and Dispersion Indices

29


































Figure 6: Distance Distribution of |L10 (d)| for Six-digit Controls

30









































































(b) six-digit controls: |L1 (d)|









(a) three-digit controls: |L1 (d)|
















































(c) three-digit controls: Percentage of lo- (d) six-digit controls: Percentage of localcalized classes
ized classes

Figure 7: Changes in Localization Distances31