Marshallian Externalities in Innovation

Journal of Economic Growth, 4: 39–54 (March 1999)c© 1999 Kluwer Academic Publishers, Boston.

Marshallian Externalities in Innovation

MORGAN KELLY

Department of Economics, University College, Dublin 4, Ireland

ANYA HAGEMAN

Department of Agricultural Resource and Managerial Economics, Cornell University, Ithaca, NY 14850, USA

A quality ladder model is used to test for Marshallian externalities in innovation. The model predicts that, in theabsence of spillovers, the geographical distribution of research should be the same as that of production. Thishypothesis is strongly rejected: innovation in two-digit industries exhibits strong spatial clustering independentlyof the distribution of employment. We find also, in support of Romer and Lucas, that there are strong spilloversfrom aggregate innovative activity in a region to the research intensity of individual industries. The location of asector’s R&D activity is determined more by the location of other sectors’ innovation than by the location of itsown production.

Keywords:

JEL classification: O3, O4

1. Introduction

The idea of Marshallian externalities as one source of sustained growth has had a deservedlylarge impact on economic theory since the work of Romer (1986) and Lucas (1988). Theempirical performance of such models has not been impressive, however. While thesemodels predict that regions with high concentrations of capital should grow at least as fastas poor areas, at the level of U.S. states, Barro and Sala-i-Martin (1992) find that pooreststates experienced the fastest growth of per capita income, while for U.S. metropolitanareas Glaeser, Kallal, Scheinkman, and Shleifer (1992) find no connection between highconcentration of an industry in a city and its subsequent employment or wage growth. Whilethere is little question that spillovers affect the level of productivity,1 it is unclear at bestwhether these static externalities translate into higher rates of growth.

However, most motivations offered for spillovers focus not on production but on innova-tion and the generation of new knowledge. If innovation and production are geographicallyseparate activities—in particular if firms locate R&D in areas with high concentrationsof skilled workers but situate their routine production in areas with cheaper labor—thenthere is no reason for Marshallian externalities that affect innovation to translate into highergrowth rates.

This article starts therefore by seeing whether there are Marshallian externalities in the

40 KELLY AND HAGEMAN

innovation process. For a simple quality ladder model in framework of Romer (1990),Grossman and Helpman (1991), Aghion and Howitt (1992), and others, we show that R&Dactivity will have the same geographical distribution as production, if there are no spilloversin innovation.

The hypothesis that innovation has the same geographical distribution as production istested using patent data and strongly rejected. We find that innovation clusters strongly,independently of the distribution of employment, with all sectors tending to locate theirR&D in the same regions. In other words, the agglomerative forces considered by Ellisonand Glaeser (1997) that cause different sectors to concentrate production in different regionsare different from those that affect innovation.

If spillovers affect innovation, what form do they take? Following Romer (1986) andLucas (1988), the effect of aggregate innovative activity within a region on the researchintensity of individual sectors is investigated and turns out to be strong. For several sectorsthere is also a strong relationship between their density in a region, as measured by theirshare of manufacturing employment, and their innovative activity.

This article’s relation to the empirical growth literature was mentioned above. In thepatent literature there have been extensive attempts to quantify spillovers arising fromR&D (see Griliches, 1990, and Nadiri, 1993, for extensive surveys), although the concernin this literature is more with calculating rates of return to innovation than looking forgeographical clustering. A notable exception is Jaffe, Trajtenberg, and Henderson (1993),who show how patents are more likely to be cited by firms in the same SMSA than wouldbe expected given the distribution of innovative activity.

2. Innovation Without Spillovers

To start, consider the spatial distribution of innovation in the absence of Marshallian exter-nalities. The model used is a simple quality ladder model of growth of the sort consideredby Aghion and Howitt (1992) and Grossman and Helpman (1991, chap. 4) among others,and is outlined only briefly here.

2.1. Preferences and Technology

There is a representative household with intertemporally separable preferences over a com-pound goodD

U =∫ ∞

0e−ρt log D(t)dt. (1)

Dropping time notation,D is defined on an interval of goods with measure 1

D =(∫ 1

0

(∑g

qg( j )xg( j )

)αd j

) 1α

, (2)

MARSHALLIAN EXTERNALITIES IN INNOVATION 41

where 0< α < 1 andxg( j ) is the amount consumed of thegth generation of goodi . qg( j )is the quality of thegth generation, which isλ times the quality of the previous generation.The individual buys only the generation of the good that offers the lowest price per unit ofquality. Imposing the normalization that total expenditureE = 1, it follows that the interestrate equalsρ. There is a fixed supply of laborL.

It takes one unit of labor to produce each good. The newest generation of each goodis produced by a monopolist. If unconstrained by competition from earlier generations ofgoods, it sets a price to maximize profitsp = w/α wherew is the wage rate. However, ifthis price would allow earlier generations of goods to be produced profitably, it sets a pricep = λw. The constrained case is assumed here. Because all firms charge the same price,expenditure on each good is identical and equal to 1. It follows that the firm earns profitsat rate5 = (1− 1/λ) and has present valueV .

2.2. Innovation

To develop a new generation of a good and become the new monopolist, firms undertakeR&D. If a firm allocatesr units of effort to R&D for an intervaldt, it is successful withprobability r dt : innovation is a memoryless, constant returns to scale process. The in-cumbent is assumed to have no cost advantage and therefore does not innovate to replaceitself. An innovation effort ofr requiresar workers. Facing a total R&D effort ofr , themonopolist will have a lifetime that is exponentially distributed with parameterr . Giventhat shareholders require a returnρ, it follows that the value of the firm satisfies

ρV = 5+ V̇ − rV . (3)

To ensure a finite demand for labor, the payoff to R&D must be bounded:

wa ≥ V (4)

with equality when innovation is positive. Finally, demand for labor, production, and R&Dmust equal its supply

a r + 1

p= L . (5)

If innovation is positive, the economy moves immediately to a steady state with innovationrate

r =(λ− 1

λ

)L

a− ρλ. (6)

Define the number of workers in R&D asR≡ r a. It follows that if L is large, the fractionof workers engaged in R&D is

R

L≈(λ− 1

λ

). (7)


2.3. Geography

The economy is split intoI regions where regioni hasLi workers. Labor is immobilebetween regions, but the monopoly firm can establish plants throughout the economy toemploy these workers. This results in a constant wage across regions and removes theincentive for labor to be mobile. Apart from sizeLi , regions are identical for purposesof innovation. Firms capable of undertaking R&D are distributed uniformly through theeconomy: the number in each region is proportional to its size.

Constant returns to scale imply that location and size of firms in the research sectorare indeterminate across regions. One simple way to obtain a determinate solution is tointroduce a small degree of diminishing returns to each firm’s R&D. If a firm undertakesresearch at intensityr for durationdt, its probability of success isr ξdt whereξ is less thanunity by an infinitesimal amount. This ensures that each firm undertaking R&D operateson the same scale and that each region allocates the same fraction of its labor force toinnovation.

Consider now a sectorj that produces a subset of positive measure of the goods in theeconomy. The sector’s share of regional employmentLi j /Li will vary across regionsi , re-flecting differing geographical endowments or the static, locational externalities mentionedin the introduction. This labor force can be used for production or for R&D. Each regioni has a number of firms capable of undertaking R&D in each sectorj that is proportionalto its sizeLi j . Repeating the earlier analysis, each sectorj devotes a constant share of itsresources in each region to R&D. In other words the geographical distribution of a sector’sinnovation should be the same as that of its employment.

Ri j

Li j≈(λ− 1

λ

). (8)

We wish to test how well this prediction matches the observed distribution of innovativeactivity.

3. Patents as a Measure of Innovation

To evaluate the empirical performance of this model first requires some measure of R&D.2

This article uses corporate patent data to measure the geographical distribution of innovativeactivity across different industries, taking data from the U.S. Department of CommercePATSIC tape. This assigns each successful patent application to the state where the patentingfirm is incorporated and to one or more SIC categories depending on the use to whichthe patent is expected to be put. There are two potential difficulties with this approach.First, patent applications may be an unreliable proxy for innovative activity. Second, theassignment of patents to SIC categories by the patent office may not coincide with theassignment that most researchers would make. These two issues are addressed in turn.

The existence of a positive relationship between patenting and R&D expenditure has beenestablished by a number of microeconomic studies such as Bound, Cummins, Griliches,Hall, and Jaffe (1984) and Pakes and Griliches (1984), while Kortum (1997) considers


Figure 1. R&D expenditure versus patent applications (logs), 1987.

the changing relationship between R&D inputs and patent outputs through time. At anaggregate level, Figure 1 plots total R&D expenditure in each state (data for Delaware andthe District of Columbia were not disclosed), as measured by the NSF survey, against totalcorporate patent applications. Both series are for 1987. Logarithmic axes are used to allowthe majority of points corresponding to states with low patenting to be distinguished fromeach other. A strong relationship between R&D expenditure and patent applications isevident: the linear correlation between these variables is 0.95. While the NSF allocatesR&D expenditure to the state where it occurs, the Patent Office assigns patents to the statewhere the corporation is registered. The close correlation between the two indicates that,with the possible exceptions of Delaware and the District of Columbia, research conductedby firms outside the state where they are incorporated is not a problem when using patentdata to measure innovation.

The reliability of the Patent Office classification of patents by industry is more problematic.The patent office assigns patents to sectors according to their potential use, rather than thesector of their origin. More important, many of the assignments, such as cross-listingautomobile engine patents with the aircraft industry and agricultural chemicals with drugs(cf. Griliches, 1990, p. 1667), are quite idiosyncratic.

This article examines the innovative activity of two-digit industries.3 This makes thedistinction between industry of origin and industry of potential use less problematic thanat the three-digit level and lessens the problem of multiple assignment: while an enginepatent may have potential applications in many different transport sectors, it will have fewerpotential uses in other two-digit sectors.4 Omitting patents assigned to more than one sectordid not cause any of the results reported below to change materially.

The distribution of patenting activity across states and sectors is each illustrated in Fig-ure 2. This gives a biplot (Gabriel, 1971) of the rank of each state in patents per worker for


Figure 2. Biplot of patents per worker by state and sector, 1987.

each of the twelve sectors considered here, where closeness of points indicates similarity.The most noticeable feature of the graph is the closeness of the points corresponding topatents in different sectors: if a state ranks high in patents per worker in one sector, it tendsto rank high in other sectors. It is interesting also that the cluster of states with the highestlevel of research in Figure 1 are all close together in Figure 2, indicating similar patterns ofsectoral innovation.

4. Distribution of Patents

Patents are one measure of the output of the R&D process. However, the quality laddermodel of Section 2 was concerned with inputs to the R&D process. A production functionis needed to link the two. We assume that the number of patents generated in a region isa random variable whose expected value is proportional to the region’s R&D expenditure.Formally, the number of patentsπi j generated in each regioni by sectorj is assumed to bea Poisson process with parameterηj Ri j

Pr(πi j = k) = (ηj Ri j )k exp(−ηj Ri j )

k!(9)

for nonnegative integersk. The parameterη can vary across sectors, allowing the sameR&D expenditure to result in a different number of patents.

Consider now the expected number of patents each region would have generated if allregions had the same employment levelL̃ in every sector and consequently the same numberof firms capable of undertaking R&D. By (8) all regions would have the same employmentin R&D and the same expected number of patents. For every region, we therefore examine


Table 1.Geographical clustering in patents per worker.

Kolmogorov-SmirnovAll States All States

Except DelawareSector and District of Columbia

1 Food and kindred products 0.353 0.3502 Textile mill products 0.630 0.5783 Chemicals and allied products 0.542 0.4634 Petroleum and natural gas 0.569 0.5785 Rubber and miscellaneous plastics products 0.670 0.5266 Stone, clay, glass and concrete products 0.470 0.3997 Primary metals 0.923 0.2898 Fabricated metal products 0.504 0.4719 Machinery, except electrical 0.526 0.491

10 Electrical and electronic machinery 0.644 0.39011 Transportation equipment 0.579 0.51812 Professional and scientific instruments 0.742 0.615

Notes: Kolmogorov-Smirnov statistics for Poisson distribution in patent applications per 10,000workers in each state in 1987. The first column includes all states, the second excludes Delawareand the District of Columbia. 0.01 significance level for K-S statistic: 0.233.

the number of patents it generated, normalized by employment:

π∗i j ≡ πi jL∗

Li j, (10)

whereπ∗i j is rounded to the nearest integer. Given the additivity of Poisson processes,by choosingL∗ sufficiently large the distribution ofπ∗i j can be approximately arbitrarilyclosely by a Poisson process with parameterηj (1− 1/λ)Li j .

The distribution of patent applications perL∗ = 10,000 workers for twelve two-digitsectors in 1987 is examined here.5 Definitions of the sectors are in Table 5 in the appendix.To test the null hypothesis that patents per worker are distributed as a homogeneous Poissonprocess, a Kolmogorov-Smirnov goodness of fit statistic is computed. The results are listedin the first column of Table 1.6

Goodness-of-fit tests typically have low power for samples of the size considered here:it is hard to reject any nonpathological distribution as the one that generated the data. Inthis case, however, the data decisively reject the null hypothesis that patents per worker arerandomly distributed across states. The reason for this significance is apparent in Figure 3,which shows the distribution patents per worker for a typical sector: chemicals.7 Most stateshave few or no patents per worker, California and some Northeastern and Midwestern stateshave a fairly large number, while a handful of states (Delaware, Oklahoma, and Montanahere, all of which have large chemical industries) have a very large number. Innovativeactivity, as measured by patents per worker, exhibits strong spatial clustering.8


Figure 3. Patents per worker, chemicals, 1987.

4.1. Delaware and the District of Columbia

Because patents are assigned to the state where a firm is incorporated, not to the state whereresearch occurs, patent data can exhibit spurious clustering in innovation if many firms areincorporated in a single state. Figure 1 showed that this is not a problem for most states, butomitted Delaware, where most research is by a single firm, and the District of Columbia,where R&D is negligible. Both, however, are assigned large numbers of patents: Delawareis assigned the patents of firms that take advantage of the low cost of becoming incorporatedthere, while D.C. is assigned patents resulting from federal government research.

To see whether the significant clustering in patents per worker is an artefact of the assign-ment of a large number of patents to these two areas with few workers, the second columnof Table 1 computes the same Kolmogorov-Smirnov statistics, omitting Delaware and D.C.Again the null hypothesis that patents per worker are randomly distributed is decisivelyrejected.

4.2. A Dartboard Approach

Following the excellent study of industrial agglomeration by Ellison and Glaeser (1997),it is useful to compute analogues of their measures of clustering,G andγ . While Ellisonand Glaeser compared the distribution of each sector’s employment with aggregate indus-trial employment, our concern here is the difference between each sector’s patenting andemployment. We therefore defineG =∑i (si − xi )

2 (wheresi is statei ’s share of patents


Table 2.Ellison-Glaeser measures of agglomeration.

Sector G γ K-S

1 0.036 0.030 0.6732 0.041 0.035 0.6533 0.038 0.032 0.7554 0.155 0.152 0.8165 0.026 0.020 0.6946 0.022 0.016 0.6737 0.024 0.018 0.6128 0.016 0.010 0.5719 0.023 0.017 0.633

10 0.036 0.030 0.61211 0.026 0.020 0.57112 0.011 0.005 0.510

Notes: Ellison-GlaeserG andγ measures of agglomerationin patents per sector relative to employment. Column 3 is aKolmogorov-Smirnov statistic for the hypothesis that the em-pirical distributions of patent and employment shares are equal.

in a sector andxi is its share of employment in that sector) and define

γ = G− (1−∑i x2i )H

(1−∑i x2i )(1− H)

, (11)

whereH is the Herfindahl index of patents in the sector.Table 2 reports values forG andγ for each of the twelve sectors assuming that each state

employs 10,000 workers in each sector.γ is computed assuming a value ofH of 0.007(equal to the average Herfindahl index for employment in two-digit sectors found by Ellisonand Glaeser): altering this value substantially did not alter the results substantially.

The values ofG andγ range from around 0.005 for scientific instruments to 0.15 forpetroleum products and are similar or lower than those found by Ellison and Glaeser foremployment, who employ a rule of thumb that values below 0.02 are low. To attacha formal statistical meaning to the value ofG, column 3 reports Kolmogorov-Smirnovstatistics for the null that the distributions of employment and patent shares are equal. Thisgives the greatest vertical distance between the two empirical distributions and in all casesis very large, ranging from 0.5 to 0.8, corresponding to a significance level above 0.00001.Similarly, to gauge the magnitude of theγ values, we computed a Monte Carlo distributionof γ assuming that patents per worker were randomly distributed according to a poissonprocess with parameter equal to the mean number of patents in each sector. Running 1,000simulations in each case, the highest estimate ofγ ranged from−0.004 to−0.007. Whilethe Ellison-Glaeser measures of agglomeration are not large in some cases, they are verydifferent from those that would obtain if patents per worker were randomly distributed.


4.3. Incumbent Advantage

Although the results in Table 1 reject the model of Section 2, it is not yet clear whether thenull hypothesis of no spillovers in innovation that is being rejected, or one of the subsidiaryassumptions used to derive (8). Of these, the least plausible is that the incumbents enjoyno cost advantage in innovation and therefore undertake no R&D.

For a model similar to that of Section 2, Barro and Sala-i-Martin (1994) show that anincumbent that enjoys a cost advantage in R&D will undertake all innovation in its sector.In terms of the patent data used here, this would imply strong geographical clustering ininnovation, occurring in the states where the few monopolists making up each two-digitsector are incorporated. To determine whether the clustering is due to spillovers or toincumbent advantage, it is necessary to model and test an explicit spillover mechanism.

Before doing this, however, a simple, informal test can help to distinguish between thealternatives of spillovers and incumbent advantage. As Brezis, Krugman, and Tsiddon(1991) argue, there is less likely to be incumbent advantage in the exploitation of newtechnology, and the model of Section 2 is therefore applicable. To the extent then thatinnovation of new technology is undertaken by smaller firms, there should be a differentdistribution of innovation between large, incumbent monopolist firms and smaller firmsdeveloping new technologies. Defining smaller firms as those that registered five or fewerpatents in a sector in 1987, the distribution of innovation turns out to be almost identical tothat for all firms. For the twelve sectors considered here, the median rank-order correlationbetween the total sample of patents and the size-truncated one is 0.97, and the minimumvalue is 0.92. Computing K-S statistics for this size-truncated sample produced results thatwere substantially identical to those in Table 1.

5. Marshallian Externalities in Innovation

This section tests directly for Marshallian externalities in innovation by attempting to iden-tify the source of such externalities and by seeing how they affect the spatial distribution ofinnovation. The simplest way to introduce Marshallian externalities into the quality laddermodel of Section 2 is to assume that the number of firms in regioni capable of undertakingR&D in sector j is proportional toµi j Li j where the Marshallian externality parameterµi j measures the extent of spillovers in innovating goodj in areai .9 0 ≤ µi j ≤ 1 and∑

i µi j = 1. Each of these firms is assumed to undertake an equal amount of R&D asbefore. Aggregate R&D is determined as in Section 2 but its distribution across regionsinow depends onµi j

Ri j

Li j= (1− 1/λ)µi j . (12)

As in Section 4 it will be assumed that the production function linking research inputs tooutputs of patents is a Poisson process: the number of patents in areai for goods of type


j is a Poisson random variable with parameterηj Ri j . It follows that expected number ofpatents is

E(πi j ) = ηj Ri j . (13)

Taking logs,

log(E(πi j )) = log(ηj (1− 1/λ))+ log(Li j )+ log(µi j ). (14)

To estimate (14), the spillover parametersµi j must be identified. Following Romer (1986)and Lucas (1988) it will be assumed that the relative ability of a region to generate firmsable to innovate in sectorj depends on the total amount of research conducted by all othersectors. Specifically, we suppose that

log(µi j ) = βj log

(∑k 6= j

πik

), (15)

the sum of total patent applications of all other sectors in the region in the same year.Because the department variable in equation (14) is a Poisson distributed count, the

equation must be estimated using a Poisson regression. A familiar problem with thisestimation procedure (cf. Hausman, Hall, and Griliches, 1984; McCullagh and Nelder,1989, pp. 198–200) is that count data are inclined to be overdispersed: the mean of thedependent variable is generally less than its variance, rather than being equal to it as aPoisson process assumes. The standard remedy is used here: it is assumed that for eachsector j , the number of patents in each stateπi j is Poisson distributed with parameterZ,whereZ is a gamma distributed random variable with meanηj Ri j and indexηj Ri j /(1−σ 2).It follows thatπi j is negative binomially distributed with meanηj Ri j and varianceσ 2ηj Ri j .The regression parameters were estimated by maximum likelihood.

As well as a constant, the log of the sector’s labor force and total patent of all othersectors, the following variables were included in the regression. All are in logs. The firstis the average number of employees of firms in the sector. This tests the importance ofincumbent advantage. If all, or most, R&D is undertaken by incumbents, patenting will beconcentrated in states with large firms.

The second is the fraction of the population in 1980 that had four or more years ofcollege to measure the education of each sector’s workforce. Although the derivation of(14) assumed that all workers can be used in production or R&D, in practice this is true onlyfor more highly educated workers. If more patents occur in states with highly educatedworkforces, it might suggest that the model of Section 2 would not be rejected if sectorallabor forceLi j was correctly measured as the total skilled labor force.

Only average education levels for a state, not the educational levels of workers in indi-vidual sectors, are available. However, sectoral wages are strongly correlated with averageeducational levels by state, indicating that a state with a highly educated population hasmore skilled workers in every sector than a less educated state. Finally, each sector’s shareof total manufacturing employment is included to see if the density of firms within a statefacilitates innovation independently of other variables is considered.


Table 3.Median correlations between explanatory vari-ables.

Total Labor College SizeLabor 0.807College 0.244 −0.095Size 0.293 0.680 −0.213Share 0.360 0.784 −0.179 0.778

Note: See Table 4 for definitions of variables.

The median correlation between these explanatory variables across the twelve sectors isgiven in Table 3. There are two areas of strong correlation. First, total patents of othersectors are correlated with the sector’s labor force: larger states tend to generate more patentsand employ more workers than smaller states. Second, sectoral employment, average plantsize, and sectoral share of employment are predictably correlated, each being a function ofthe number of employees in the sector.

Regression results for the twelve sectors in 1987 are given in Table 4. Given the potentialdifficulties discussed above with patent data for Delaware and the District of Columbia,observations for these two regions were omitted when calculating the reported results.Including these two observations did not however lead to any substantial changes in thereported patterns of significance.

The pattern of significance is similar in every sectoral regression: aggregate innovativeactivity as measured by total patents of other sectors is highly significant (except for sector9) while, for half the sectors, employment is insignificant. Among the other variables,human capital is significant for five of the sectors, while size and share of employment areinsignificant in most cases both individually and also jointly. Excluding size and share fromthe regressions did not affect the reported results substantially.

6. Conclusions

This article was based on two propositions. First, Marshallian externalities are more impor-tant for innovation than for production. Second, innovation and production need not occurin the same locations. As a result, Marshallian externalities can have an important effect ongrowth, through their effect on innovation, without necessarily affecting the relative growthof output in different regions. As a consequence, tests of Marshallian externalities thatfocus on the growth of output (seeing whether areas with high wages or high concentrationsof an industry experience the highest growth rates) may miss the most important aspect ofthese externalities, which is their effect on the innovation process.

We therefore started by testing whether there are Marshallian externalities in innovation.We did this first by demonstrating that, in the absence of spillovers, the spatial distributionof innovation would be random. This hypothesis was strongly rejected by two-digit industrydata: innovation shows strong geographical clustering, independently of the distributionof employment. The static externalities and resource endowments that cause production


Table 4.Determinants of innovation.

Sector Total Labor College Size Share σ̂

1 0.796∗∗ 0.116 0.060 −0.178 3.080 1.206(0.310) (0.142) (0.050) (0.900) (2.919) (0.331)

2 0.944∗∗ 0.044 0.051 0.564∗ 3.733 1.718(0.105) (0.086) (0.038) (0.281) (6.110) (0.512)

3 0.780∗∗ 0.258∗ 0.063∗ 0.262 5.018 1.748(0.172) (0.118) (0.033) (0.434) (6.515) (0.368)

4 1.099∗∗ 0.189∗∗ 0.039 1.903 6.647∗∗ 0.931(0.154) (0.079) (0.052) (2.095) (1.767) (0.239)

5 0.679∗∗ 0.247∗ 0.053∗ 0.324 −0.793 2.335(0.189) (0.128) (0.031) (0.505) (7.901) (0.524)

6 0.575∗∗ 0.334∗ 0.069∗∗ 1.579∗ −11.432 3.720(0.162) (0.178) (0.028) (0.906) (7.017) (0.959)

7 0.459∗∗ 0.303∗∗ 0.038 0.660∗ −9.995 3.261(0.105) (0.087) (0.033) (0.004) (9.396) (1.329)

8 0.575∗∗ 0.069 0.036 0.392 6.988 3.247(0.186) (0.073) (0.028) (0.008) (5.165) (0.704)

9 0.148 0.200∗∗ 0.059∗∗ 0.524 −2.403 3.128(0.238) (0.055) (0.026) (0.827) (2.596) (0.646)

10 1.077∗∗ −0.002 0.081∗ 0.067 3.537 1.775(0.285) (0.047) (0.040) (0.262) (3.239) (0.362)

11 0.891∗∗ −0.018 −0.028 0.049 6.518∗ 2.035(0.187) (0.046) (0.035) (0.186) (3.128) (0.452)

12 0.937∗∗ −0.008 0.064 −0.565 11.690 2.362(0.192) (0.145) (0.041) (0.397) (11.943) (0.517)

Notes: Negative binomial regression. Observations for Delaware and the District ofColumbia are excluded. Dependent variable: corporate patent applications by sectorfor each state in 1987. Total: total corporate patent applications of all other sectors(in 1,000s). Labor: employment in sector (in 10,000s). College: fraction of adultpopulation with four or more years of college education. Size: mean number of em-ployees per establishment. Share: sector’s employment as fraction of manufacturingemployment in state. All explanatory variables are in logs.σ̂ : estimated deviance of negative binomial regression.Standard errors in parentheses.∗ denotes significance at 5%, ** denotes significance at 1%.

to concentrate in some locations do not appear to affect innovation. Sectors locate theirresearch not where they are producing but near to where other sectors are also researching.

Can this clustering in innovation be explained by factors other than Marshallian external-


ities? Three alternative hypotheses were examined and rejected. First, we demonstratedthat the clustering in patents per worker was not an artefact of the large number of firms thatregister in Delaware. Second, the distribution of research activity does not simply reflectthe existing distribution of educated workers: the level of human capital in a state was not inmost cases a significant predictor of sectoral patenting. Third, the clustering in innovationdoes not reflect the location of incumbent firms with a cost advantage in R&D: plant sizewas an insignificant or negative predictor of patenting, and the distribution of patentingamong firms with few patents was almost identical to the distribution of all patents. Onthe other hand, it was not possible to reject the hypothesis that a spillover exists from totalinnovation in a region to the innovative activity of other sectors. For slightly more than halfthe sectors, it was also not possible to reject the existence of a spillover from their share ofmanufacturing employment in a state, to their patenting activity.

Because our concern here was with testing for Marshallian externalities in innovation, wedid not examine the impact of innovation on output growth. A natural framework for doingthis is provided by Vernon’s (1966) product cycle paradigm, which has been formalized byGrossman and Helpman (1991, ch. 12), Krugman (1979), Segerstrom (1991), and Stokey(1991) among others. In these models there are two types of goods, new ones that requireskilled workers to be produced and mature ones that can be made by unskilled workers.Skilled and unskilled workers are concentrated in different areas, called the North and theSouth. Growth of Northern regions depends on their success in innovating and comingup with new goods that cannot be imitated by unskilled Southern areas, whereas Southernareas grow by offering low production costs to attract producers of mature goods. A naturalextension of the analysis here would be to partition U.S. regions into areas that innovateand areas that produce mature goods and to examine the factors that determine the growthof each type of region. For this purpose, however, state-level data are likely to be tooaggregated to be useful.

Appendix: Data Sources and Definitions

Number of corporate patents: U.S. Patent and Trademark Office,PATSICtape.

Employment, number of establishments, total manufacturing employment: Bureau ofEconomic Analysis,County Business Patterns.

Fraction of adults with college education, 1980: U.S. Bureau of the Census,Countyand City Data Book. 1983.

Percentage of population with college education, 1990:County and City Extra. 1992.

R&D expenditure: National Science Foundation,Geographic Patterns: R&D in theUnited States. 1989. Table B-45.

Acknowledgments

We would like to thank seminar participants at the SEDC and Dublin Economic Workshopfor useful suggestions, and in particular Oded Galor and an anonymous referee for theircareful and constructive criticisms of the submitted draft. All errors are ours.


Table 5.Definitions of sectors.

Number SIC CODE

1 Food and kindred products 202 Textile mill products 223 Chemicals and allied products 284 Petroleum and natural gas extraction and refining 3,295 Rubber and miscellaneous plastics products 306 Stone, clay, glass, and concrete products 327 Primary metals 33, 3462, 34638 Fabricated metal products 34 (ex 3462, 3463, 348)9 Machinery, except electrical 3510 Electrical and electronic machinery 36, 382511 Transportation equipment 37, 34812 Professional and scientific instruments 38 (ex 3825)

Notes

1. Krugman (1991) finds considerable geographical concentration in virtually all U.S. industries; Ciccone andHall (1993) and Rauch (1991) find significant effects of concentration on productivity; Baxter and King (1991)find a productivity spillover from aggregate to individual output; and Caballero and Lyons (1992) find a largerSolow residual at the two-digit industrial level than at the three-digit one, which they interpret as evidence ofexternal economies. See Cooper and Haltiwanger (1993) for a survey of this literature.

2. A natural measure of inputs devoted to innovation would be a direct measure of spending by firms such asthe biannual National Science Foundation survey of R&D expenditures but strict confidentiality rules restrictit to reporting only aggregate expenditure by all corporations, with data withheld for smaller states. R&Dexpenditure data are readily available in published accounts but only for larger publicly traded firms.

3. Even if a reliable three-digit classification of patents were available, the nondisclosure of employment andwage data for three-digit industries in many states would force us to use two-digit data.

4. In a typical year, more than one-third of patents are assigned to more than one three-digit category, whereasfewer than one-fifth are assigned to more than one two-digit category.

5. The data used are for the forty-eight states and the District of Columbia. In cases where the exact employmentlevel is not disclosed in theCounty Business Patternsbut only the range in which it lies, we use the midpointof the range as the employment level.

6. For samples of the size considered here, standard K-S critical values tabulated for continuous distributions arefairly accurate for discrete distributions such as the Poisson (they are in fact slightly conservative) (cf. Pettittand Stephens, 1977).

7. All other sectors show the same pattern.

8. Similar clustering was found when, following Krugman (1991, app. D), Gini coefficients were computed bylooking at share of patents versus share of employment.

9. In this constant-returns world, if Marshallian externalities caused the cost of innovation or probability of successto vary across regions, all innovation would occur in the single location with highest success probability relativeto cost.

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Marshallian Externalities in Innovation