Knowledge Spillovers and Spatial Concentration ofHigh Skill-Intensive Production: The Chilean Case

Hisamitsu Saito
Obihiro University of Agriculture and Veterinary Medicine
saitoh@obihiro.ac.jp

Munisamy Gopinath
Oregon State University
m.gopinath@oregonstate.edu

Abstract: Knowledge spillovers are an important source of economic growth. This study
identifies a mechanism through which knowledge spillovers occur among plants in the Chilean
manufacturing industry. A plant-level production function is estimated with the absorptivecapacity hypothesis, i.e. employment of skilled workers is a key channel through whichknowledge is transmitted across plants. Results show that a plant’s productivity increases with
its skill intensity, which is measured by the share of skilled workers in total employment. We
also find that a plant’s skill intensity is positively correlated with its capital stock, raw
productivity, regional knowledge stock and regional population. Our results suggest that anincrease in regional knowledge stock is the most effective policy to improve a plant’s
productivity. However, policies which encourage a plant to employ high skill-intensive
production also enhance its productivity.
Key words: Knowledge spillovers; Plant’s productivity; Skill intensity.
JEL codes: R11, O18, O15

Knowledge Spillovers and Spatial Concentration ofHigh Skill-Intensive Production: The Chilean Case

1. Introduction
The accumulation of knowledge, a non-rival and partially non-excludable good, is a key
determinant of economic growth of nations (Barro and Sala-i-Martin 2003; Romer 1990; Lucas
1988). Not surprisingly, many empirical studies have found that the emergence of multi-purpose
technologies, e.g. computers, and the increased globalization have raised the knowledge- or skillintensity of production processes (Berman et al. 1994; Feenstra and Hanson 1997).1 However,
the growth and trade literature often assume that the resulting economic gains apply uniformly
across firms or regions of a country. In fact, wide disparities exist in the level and types of
economic activity among firms or regions within a country (Bernard and Jensen 1997;
Henderson et al. 2001). In light of regional and firm heterogeneity, factors contributing to highskill-intensive production and its spatial concentration (e.g. Silicon Valley in the United States or
Bangalore in India) have received substantial empirical attention (Audretsch and Feldman 1996;
Audretsch and Feldman 2004).
In this study, we focus on factors raising plants’ skill-intensity of production in thecontext of a developing economy. The distinguishing feature of developing countries is theirrecent urbanization accompanied by rapid accumulation of skilled workers in cities (Henderson
1986; Henderson et al. 2001). In explaining the above phenomenon, Henderson (1986) finds that(i) high skill-intensive industries tend to locate in large cities and (ii) labor demand is biased
toward skilled worker when city size increases. A factor causing skill bias in labor demand iscities’ specialization in high skill-intensive production by outsourcing less skill-intensive
processes. In addition to the outsourcing, knowledge spillovers are considered to be a key source1

of the skill bias of labor demand in large cities. The objective of this study is to identify themechanism behind the accumulation of high-skill intensive production in specific regions byfocusing on the partial non-excludability of knowledge, i.e. spillovers, as a causal factor. A
better understanding of the underlying process is necessary in the search for regional polices toencourage high skill-intensive production.
Evidence of knowledge spillovers’ contribution to economic growth has been found at
the national and industry levels, but the majority of studies rely on a wage hedonic equation to
examine the existence of spillovers (Ciccone and Peri, 2006; Moretti, 2004b; Moretti 2004c;
Rauch, 1993; Acemoglu and Angrist, 2000). An exception here is the work by Moretti (2004a),
whose production-function estimates show that U.S. manufacturing plants’ productivity
increases by 0.6-0.7 percent as the share of college graduates in a region increases by one percent.
Nevertheless, issues such as the mechanism by which spillovers occur and benefit plants, andwhether or not every plant can equally benefit from spillovers have received limited attention in
the literature. Clarifying the spillover mechanism will help identify the type of plants which
benefit from spillovers. Such economic analysis can then guide effective policies to augment
knowledge spillovers, which eventually contributes to regional economic development.
We draw on the absorptive-capacity hypothesis of Cohen and Levinthal (1989) to identify
the mechanism by which knowledge spillovers enhance plants’ productivity. The absorptivecapacity hypothesis argues that firms must invest in research and development in order to accessnew knowledge created by either other firms or the public sector. Firm-level evidence on theabsorptive-capacity hypothesis can be found in Arora and Gambardella (1994) and Cockburn andHenderson (1998). We extend the notion of absorptive capacity to the case of skilled workers,
meaning such workers’ presence is a key channel by which knowledge is transmitted across2

firms or plants (Malecki 1997; Schmidt 2005). Malecki (1997) argues that technologicalcapability embodied in skilled workers is necessary for firms to evaluate new external
technologies. Furthermore, Audretsch and Feldman (1996) find empirical evidence at theindustry level that high skill-intensive industries are likely to agglomerate because they tend tobenefit more from spillovers than low skill-intensive industries.
Chile provides an interesting case study of spatial patterns of skill-intensive production.
South American countries are considered to be the most urbanized in the developing world(United Nations 2008). Chile is not an exception since its population and skilled workers arehighly concentrated in a few regions. Figure 1 shows the 1998-2003 average number of skilledworkers employed in the manufacturing industry by county. The geographical distribution ofskilled worker is not uniform within Chile, whose northern and central counties tend to have ahigher concentration of skilled workers relative to others. This skewed geographical distributionof skilled worker leads to agglomeration of plants employing high skill-intensive production,
which in turn should attract skilled workers to the region, leading to further accumulation ofskilled workers. Figure 2 shows the kernel density estimates for plants’ skill intensity, defined as
the share of skilled workers in total workers, in counties whose regional skill intensity is above(below) the third (first) quartile of the distribution. From figure 2, it is apparent that high skillintensive plants appear to concentrate in counties with a large share of skilled workers.
In the following, we first outline how a plant-level production function can be extended
to incorporate absorptive capacity. Then, we detail the estimation and testing of plant-levelproduction functions with and without such capacity. The estimates of the plant-level production
function allows us to quantify the effect of regional and plant characteristics (e.g. regional3

knowledge stock, capital stock) on a plant’s choice of skill intensity. Finally, we numericallyevaluate the relative contribution of regional and plant characteristics to a plant’s productivity.

2. Conceptual and Empirical Framework
2.1. A Plant-Level Production Function with Absorptive Capacity
To see how the absorptive-capacity hypothesis contributes to the agglomeration of high skillintensive production, consider the following production function of a plant:(1)

Y  A  Ls   Lu  ,where Y, Ls and Lu are output, skilled and unskilled worker, respectively,   0 and   0 are
parameters characterizing the production function and A represents productivity from spillovers(externalities) defined as follows:(2)A  e S ,where  is a parameter, S measures regional knowledge stock accessible to a plant and 
measures plant’s skill intensity, i.e.,   Ls  Ls  Lu  . If   0 , then A Ls  0 and 2 A Ls 2  0 , implying that A increases with the employment of skilled workers but at adecreasing rate (Cohen and Levinthal 1989). Equation (2) shows two channels through which A
can be improved. The first channel is, of course, to increase regional knowledge stock, S.
Besides this, the effect of spillovers becomes large by increasing plant’s skill intensity,  , asplants can absorb external knowledge more efficiently. Given equation (1) and (2), consider thefollowing profit maximization by a representative plant:maxe S  Ls   Lu   ws Ls  wu Lu
s u


(3)



L ,L

 SLs

 e L  L  Ls   Lu   ws Ls  wu Lu ,
s

u





4

which yields the following first order conditions:



2



2



2



2

(4)

e S Ls  1 Lu   Ls  Lu    SLs Lu  ws  Ls  Lu   0 and(5)e S Ls  Lu 1   Ls  Lu    SLs Lu  wu  Ls  Lu   0,

where ws and wu are wage rate of skilled and unskilled worker with output price as thenumeraire, respectively. Then, the ratio of skilled to unskilled worker is obtained by solving
equation (4) and (5) for Ls Lu :(6)

Ls B  B 2  4

,
Lu
2

where B      S .2 Finally, differentiating equation (6) with respect to regional knowledge
stock, S, we have:

(7)

 
 Ls Lu B 1 
 0.
2

 2
S
B

4




Equation (7) shows that a plant would employ more skilled workers in a region whereknowledge stock is abundant. Also, note that when   0 , i.e. the case where absorptivecapacity hypothesis does not hold, the right hand side of equation (7) is zero and the ratio ofskilled to unskilled worker is not affected by regional knowledge stock.

2.2. Estimation of a Plant-Level Production Function with Knowledge Spillovers
To test the existence of knowledge spillovers and identify the channel through which spillovers
affect plant-level productivity, we extend equation (1) and (2) to an empirical setting andconsider the following Cobb-Douglas production function:

5

(8)

ln Yijrt  0  1 ln Lsijrt  2 ln Luijrt  3 ln M ijrt  4 ln Eijrt  5 ln Kijrt  6 Sijrt  7ijrt Sijrt
 8 ln MPrt  d j  d R  dt  ijrt   ijrt ,where Yijrt , Lsijrt , Luijrt , M ijrt , Eijrt and Kijrt represent output, skilled worker, unskilled worker,
material, energy and capital of plant i belonging to 2-digit industry j in the r-th region at period t.
R denotes the province to which r-th region belongs (Levinsohn and Petrin 2003).3 Fixed effects

d j , d R and d t denote 2-digit industry, provincial and year dummies, respectively. The variable
Sijrt measures regional knowledge stock accessible to a plant, which is measured by the distanceweighted share of skilled workers in total workforce:(9)L  L    L d 
S L  L    L d   L  L    L
s
jrt

ijrt

s
jrt

s
ijrt

qr

s
ijrt

s
jqt

qr

rq

u
jrt

s
jqt

rq

u
ijrt

qr

u
jqt

d rq 

,where Lsjrt and Lujrt are respectively the number of skilled and unskilled workers in industry j in
the r-th region at time t. We subtract own plant’s skilled (skilled and unskilled) workers when
computing the numerator (denominator). As a region used in this study is an administrative
geographical unit, economic interaction among plants may not be complete within a region.
Rather, knowledge stock in any other region ( q  r ) affects the productivity of plants in the r-th
region with its effect decaying as distance between the two regions increases (Lopez-Bazo et al.
2004). Hence, in equation (9), we include skilled and unskilled workers in region q  rweighted by d rq , the great-circle distance between region r (base) and q in kilometers (Crozet etal. 2004). Note Sijrt approaches one (zero) as skilled (unskilled) workers are abundant in thesurrounding regions.
In equation (8), Sijrt is scaled by our measure of the absorptive capacity, ijrt , which isthe share of skilled workers to total workers of plant i (equation 2). If  7 is positive and6significant, high skill-intensive plants gain more from knowledge spillovers than others and theabsorptive-capacity hypothesis is empirically supported. On the contrary, if the absorptivecapacity hypothesis is not valid and every plant, regardless of its skill intensity, benefits fromspillovers, then  6 would be positive and significant. Finally, MPrt is the distance-weighted
regional population:(10)

 Popqt MPrt  Poprt   q  r ,
 d 
 rq 

where, Poprt denotes population in r-th region at period t. The new economic-geography
literature has well documented the productivity-enhancement effect of agglomeration economies,
which are externalities arising from ease of input- and output-market access (Baldwin et al.
2003; Fujita et al. 1999). Equation (10) provides a distance-weighted measure to take into
account of the effect from surrounding regions.
The plant’s raw productivity, ijrt , is defined as plant- and time-specific productivity
shock and  ijrt is an i.i.d. disturbance term (Levinsohn and Petrin 2003). A plant’s productivity
shock is not observable to us, but it may pose a problem in the consistent estimation of theparameters of equation (8) (Levinsohn and Petrin 2003; Olley and Pakes 1996). For example, aplant realizing a positive productivity shock may respond by using more workers or material(intermediate) inputs to increase its output. As ijrt is likely correlated with conventional input
use, ordinary least squares (OLS) estimation of equation (8) where the productivity shock, ijrt ,is added to the i.i.d. disturbance,  ijrt , would result in inconsistent parameter estimates of the
production function.

7

To correct this problem, we employ the Levinsohn and Petrin’s (2003) approach. Given
plants’ predetermined capital stock and locational attributes, Sijrt , plants first realize theirproductivity level and then, choose the level of conventional inputs (Fernandes 2007; Yasar andMorrison 2007). For this purpose, we assume that material (intermediate) input use is amonotonic function of productivity:(11)

ln M ijrt  m ijrt ,ln Kijrt , Sijrt ,ln MPrt  .

Then, we can invert equation (11) and express the productivity shock as a function of material
input, capital stock and locational attributes:(12)

ijrt    ln M ijrt ,ln Kijrt , Sijrt ,ln MPrt  .

By substituting (12) into (8):(13)

ln Yijrt  1 ln Lsijrt   2 ln Luijrt   4 ln Eijrt  7ijrt Sijrt  d j  d R  dt  ln M ijrt , ln Kijrt , Sijrt , ln MPrt    ijrt ,where:(14)  ln M ijrt , ln Kijrt , Sijrt , ln MPrt   0  3 ln M ijrt  5 ln Kijrt  6 Sijrt  8 ln MPrt  ln M ijrt , ln Kijrt , Sijrt , ln MPrt  .

Since  ijrt is assumed to be independent of Ls , Lu and E, we can consistently estimate 1 ,  2 , 4 and  7 by approximating    with a second-order polynomial and using OLS.
Following Levinsohn and Petrin (2003), we proceed to a second stage, where theproductivity shock follows a first-order Markov process, to identify  3 ,  5 ,  6 and  8 . That is,
production function, equation (8), at period t  1 is written as:(15)

ln Yijrt 1  1 ln Lsijrt 1   2 ln Luijrt 1  3 ln M ijrt 1   4 ln Eijrt 1  5 ln Kijrt 1  6 Sijrt 1 7ijrt 1Sijrt 1  8 ln MPrt 1  d j  d R  dt 1  g ijrt    ijrt 1  ijrt 1.
8

where, ijrt 1 is an innovation. From equation (14), we can express plant’s productivity as
follows:(16)

0  ijrt  ˆ   3 ln M ijrt  5 ln Kijrt  6 Sijrt  8 ln MPrt .

Given ˆ1 , ˆ2 , ˆ4 , ˆ7 and irt from the equation (16), we can consistently estimate  3 ,  5 ,  6
and  8 by approximating g   with a third-order polynomial and using nonlinear instrumentalvariables estimator. Instrumental variables estimator is preferred because  ijrt 1  ijrt 1 iscorrelated with ln M ijrt 1 . We use ˆ  ln M ijrt ,ln Kijrt , Sijrt ,ln MPrt  , ln Kijrt 1 , ln Kijrt , ln Mijrt ,ln Eijrt , Sijrt 1 and ln MPrt 1 as instruments. Given the multiple steps in the estimation, thestandard error of parameter estimates is obtained using bootstrapping procedures.4

2.3. Plants’ Skill Intensity and Regional Knowledge Stock
Having illustrated a technological framework to capture knowledge spillovers in plant’s
productivity, we now turn our attention to the role of such spillovers in enhancing plants’ skill
intensity. Recall that if the estimate of  7 is positive and significant, then high skill-intensive
plants can benefit more from spillovers than other plants. Therefore, plants are willing toemploy more skilled workers than unskilled workers as shown in equation (7) if they locate in aregion with a large knowledge stock. In this section, we evaluate how much knowledge
spillovers contribute to raising a plant’s skill intensity. Levinsohn and Petrin (2003) show thatthe log of conventional inputs’ level (e.g. material inputs) is a function of predetermined capital,plant’s raw productivity and locational attributes (equation 11). Similarly, other conventional
inputs such as skilled and unskilled worker are determined as follows:

9

(17)

ln Lsijrt  Ls ijrt ,ln Kijrt , Sijrt ,ln MPrt  and(18)

ln Luijrt  Lu ijrt ,ln Kijrt , Sijrt ,ln MPrt  .

To focus on the direct effect of these variables on demand for each type of workers, we employ afirst-order approximation of equation (17) and (18) (Olley and Pakes 1996). By subtracting thespecified first-order approximation of equation (18) from (17), we have:(19)

Lsijrtwrts
ln u  1   2 ln u  3 Sijrt   4 ln MPrt  5ijrt  6 ln Kijrt  d j  d R  dt  ijrt ,
Lijrt
wrt

where vijrt is the i.i.d. disturbance. The wage rates for skilled and unskilled worker, wrts and wrtu
respectively, are indexed by region and time. Plant’s raw productivity, ωijrt, is obtained fromequation (16).
If ease of input- and output-market access in a large city leads to outsourcing of less skillintensive processes and the specialization in high skill-intensive production as Henderson (1986)
argues, regional market size and plant’s skill intensity should be positively correlated. Moreover,recent contributions to the new economic geography literature show that high-ability workers
self-select into an area with large population (Combes et al. 2008). Thus, a region with a large
share of skilled worker is also likely to have a large population. Therefore, controlling forregional population, MPrt, in equation (19) mitigates a potential simultaneity problem between
regional market size and regional skill intensity. Next, we anticipate that plants in a region witha large knowledge stock, where supply of skilled worker is relatively abundant, might employ
more skilled workers because of their low relative wage. In other words, high skill-intensive
production in a region with a large knowledge stock might be the consequence of low relative
wage for skilled workers rather than spillovers. To control the wage effect on plant’s skill
intensity, relative wage is included in the estimation of equation (19). Finally, industry fixed10effects will control for the difference in skill intensity observed at the industry level, which also
explains the agglomeration of high skill-intensive production in cities (Henderson, 1986).
It is likely that a shock to a plant’s relative labor demand may also affect the regional
knowledge stock. For example, a positive shock on a plant’s relative labor demand may attract
skilled workers and increase a region’s share of skilled workers. Moreover, a high skill-intensive
plant may locate in a relatively high skill-intensive region. Thus, regional knowledge stock, S,
must be instrumented when estimating equation (19). We employ the average years of educationof workers in a previous year as the instrument (see section 4.2.). Finally, equation (17) and (18)do not assume path dependency of absorptive capacity. Plants need to be continuously highskill-intensive to maximize the benefit from spillovers (Schmidt 2005). In other words, highskill-intensive plants at previous periods should employ a large number of skilled workers in thecurrent period to keep their high capacity for absorbing external knowledge. Hence, we checkfor path dependency in plants’ relative skill intensity by adding the lagged plant’s skill intensity,

t 1 , to the right hand side of equation (19). The presence of the lagged plant’s skill intensity inequation (19) also helps mitigate the possible endogeneity problem arising from the selfselection of a high skill-intensive plant into a relatively high skill-intensive region.

2.4. Evaluation of Spillovers’ Effect on Plant’s Productivity
The above two subsections show that plants increase their skill intensity to benefit fromspillovers in a region with a large knowledge stock. Thus, an increase in plant’s productivity
from spillovers can be decomposed into direct and indirect effect, the latter arising fromincreasing plant’s skill intensity, as follows:5

11

(20)

 ln A    6 S   7 S  ln S ln SS   6   7  7 S ln S ln S   6   7  S   3  7 1    S 2 ,where the first term of the third line of equation (20) measures the direct effect, while the second
term represents the indirect effect. Furthermore, other explanatory variables in equation (19), i.e.,
plant’s capital stock, raw productivity, eω, regional population and relative wage, also affectplant’s productivity from spillovers through increasing or decreasing plant’s skill intensity(equation 19):(21)

 ln A    6 S   7 S  ln K ln K 7 S ln K  5  7 1    S ,Equation (21) shows the effect of a plant’s capital stock on its productivity from spillovers, A.
Effects of plant’s raw productivity, regional population and relative wage on A can be obtainedin a way similar to that of equation (21).

3. Chilean Data
We use data from the annual Chilean Manufacturing Census from 1998 to 2003 collected by
National Statistics Institute (INE). Plants with at least 10 employees are surveyed in the Census,
with information on plant location at three administrative levels: macro-region, province andcounty. We use each of the 342 counties as a geographical unit (region) to assure enoughvariation in data and to take account of geographical distribution of plants within a macro-region
or a province, which is obscured if we use macro-region or province as a geographical unit.

12

However, since county is a small administrative geographical unit, interregional spillovers arelikely to exist and therefore, we need to take into account of economic conditions in otherregions (equation 9 and 10).
Six variables are constructed to estimate the plant-level production function: skilledworker, unskilled worker, materials, energy, capital and output.6 The unit of worker is thenumber of workers, while other variables are in Chilean Peso. We use deflators (base year 1996)
from the Chilean National Accounts to convert the latter variables into constant Chilean Peso.
As a measure of regional knowledge stock, we use the distance-weighted share of skilled worker,
SSKL1 (equation 9). Since skilled workers are crucial to R&D and development of new products(Malecki, 1997) and are more educated than unskilled workers (see Appendix B), it is plausible
to assume that a region with a large share of skilled worker has a large regional knowledge stock.
However, as figure 1 shows, economic activity in Chile concentrate in the Santiago Metropolitan
macro-region, which accounts for 40 percent of the national population. The large number ofworkers in the Santiago macro-region may have a huge impact in constructing regional skill
intensity, SSKL1, even in regions far from the Santiago macro-region. To check if this affects theresults, we construct another variable, SSKL2. In constructing SSKL2 in r-th county, we only use
data from counties within the macro-region to which r-th county belongs. In addition, anotheralternative measure of regional knowledge stock in r-th county, SSKL3, is constructed using datafrom r-th county only, i.e., we do not assume any interregional spillovers. Similarly, threealternative measures of MPrt are constructed from Population Projections, INE. MP1 is the
distance-weighted county population, MP2 is the distance-weighted county population within amacro-region and MP3 is county population. Finally, county wages for skilled (unskilled)worker used in the estimation of equation (19) are obtained by dividing the total wage bill for13skilled (unskilled) workers of all plants in a county by the total number of skilled (unskilled)workers. Summary statistics on each of the variables used in this study are presented in table 1.
In addition to mean and standard deviation of variables, the mean of coefficient of variation ofeach variable across plants or county-isic pairs for each year and the mean of coefficient ofvariation across time for each plant or county-ISIC pair are presented to see how much thevariation in each variable is attributed to cross-sectional and time-series variations. Note that
regional characteristics such as regional skill intensity, SSKL, and regional population, MP, show
small variance across time, implying time persistence in those variables.

4. Results
4.1. Production Function Estimates
We first discuss the estimates of the plant-level production function estimated under theassumption of absorptive capacity. Table 2 shows the parameter estimates of the production
function in equation (8) for the Chilean manufacturing industry. Column (1) shows the result of
the estimation with the distance-weighted share of skilled worker, SSKL1, the first of the threemeasures of regional knowledge stock. The results with the distance-weighted share of skilledworker within a macro-region, SSKL2, and the share of skilled worker in a county, SSKL3, areshown in column (2) and (3), respectively. Estimated parameters on conventional inputs –skilled
and unskilled workers, materials, energy and capital- are positive and statistically significant inevery specification. Similar to plant-level studies of other countries, e.g., Henderson (2003),
Chilean manufacturing plants show high intensity of material inputs in production. Returns toscale, which is defined as the sum of coefficients on conventional inputs, is in the range of 1.021.03 and the null hypothesis that technology exhibits constant returns to scale is not rejected.

14

Our specification of absorptive capacity appears to well fit the data since the parameteron  S is positive and statistically significant for all specifications. On the contrary, theparameter on S is not statistically significant. This result is consistent with the argument thathigh skill-intensity is necessary for a plant to utilize new knowledge created by other plants in
the industry presumably through the interaction among skilled workers, i.e., absorptive capacity(Cockburn and Henderson, 1998; Cohen and Levinthal, 1989). In other words, we find evidence
that the presence of high-skilled workers serves as an important channel through whichknowledge is transmitted across plants. Multiplying the parameter from column (1), the basemodel, by plants’ average skill intensity (0.32) and average regional skill intensity (0.46), we
find elasticity of productivity of an average plant with respect to the share of skilled worker in aregion (and surrounding regions) is 0.05. Alternatively, elasticity of plant’s productivity withrespect to the share of skilled worker in a region varies between 0-0.16 depending on the plant’s
skill intensity. In evaluating Moretti’s (2004a) result at its sample mean, we know that theelasticity of the U.S. firms’ productivity with respect to the share of university graduates is 0.100.13. Hence, the magnitude of the spillover elasticity in our study is comparable to the one inMoretti (2004a). However, unlike Moretti’s (2004a) study, our results suggest that high skillintensive plants benefit more from knowledge spillovers. Finally, the parameter on regional
population, MP, is not statistically significant in all three specifications.

4.2. Plant’s Skill Intensity Estimates
In this subsection, we report estimated results on plants’ choice of their skill intensity. The
instruments considered for the regional knowledge stock, S, in the estimation of equation (19) are
the average years of education of workers in industry j in r-th county from the 1992 Housing and15

Population Census and a human capital index (Regional Competitiveness Report, Chilean
Ministry of Economy, various issues). We choose these instruments because educational level at
a previous period is correlated with current educational level of workers, i.e. regional knowledge
stock, as long as they continue to work in the same industry and region. However, the proposed
instruments do not include the educational level of newly employed workers and hence, are notcorrelated with a current shock to plant’s relative labor demand.7 To check the relevance of
these instruments, we employ the Cragg-Donald Wald F statistic presented at the bottom of table
3. The Cragg-Donald Wald F statistic exceeds the critical value for 10 percent maximal IV size
distortion when using the 1992 average years of education of workers in industry j in r-th county
as the instrument for S (Stock and Yogo 2005).8
Column (1), (3) and (5) of table 3 show results from the estimation of equation (19) withthe distance-weighted share of skilled worker, SSKL1, the distance-weighted share of skilledworker within a macro-region, SSKL2, and the share of skilled worker in a county, SSKL3,
respectively. The estimated parameter on the share of skilled worker in a region (andsurrounding regions) is positive and significant for each specification. Thus, after controlling for
the wage effect, the greater the knowledge stock of a region, the higher is the skill-intensity ofplants. In other words, plants raise their skill intensity to benefit from spillovers in a region
where skilled workers are abundant. Furthermore, the parameter on regional population, MP, issignificant for all specifications, implying that plants tend to adopt high skill-intensive
production in regions with a large population. In terms of plant’s characteristics, both plant’s
raw productivity and the capital stock increase plant’s skill intensity. This is consistent with
Pavcnik’s (2003) finding that capital is a complement to skilled workers. Prior literature alsosuggests that high-productivity plants tend to invest in R&D and innovation activity, which16requires relatively more skilled workers. For example, using Chilean manufacturing plant-level
data, Alvarez and Robertson (2004) find a positive relationship between investment intechnology and plant size, which is also positively correlated with the productivity level(Jovanovic 1982).
The above results confirm positive correlation between plant’s skill intensity and regional
knowledge stock. We next check path dependency of absorptive capacity by including thelagged plant’s skill intensity, t 1 , in equation (19). Column (2), (4) and (6) of table 3 present
the estimation results, where we find that the coefficient on the lagged plant’s skill intensity is
positive and significant in each specification. In addition, except the result in column (6), thecase where no interregional spillovers are assumed, the coefficient on regional skill intensity
remains positive and significant. Thus, after controlling path dependency of absorptive capacity,
we observe plants tend to employ more skilled workers in a region where the knowledge stock islarge. Finally, the coefficient on relative wage is negative and significant, implying that plants
employ more skilled workers in a region where relative wage of skilled worker is low, i.e., thesupply of skilled labor is relatively abundant.

4.3. Regional Knowledge Stock and Plant’s Productivity
From the results in previous subsections, we find that high skill-intensive plants benefit morefrom knowledge spillovers. Hence, plants employ more skilled workers to obtain larger benefits
from spillovers in a region with a large knowledge stock. Accordingly, the effect of regional
knowledge stock on plant’s productivity enhancement due to spillovers is decomposed into a
direct and indirect effect, the latter taking place through increasing plant’s skill intensity(equation 20). Following equation (20) and (21), we evaluate both direct and indirect effects

17

numerically at the sample mean with estimation results in column (2), (4) and (6) of table 3. The
results are presented in the column labeled “Elasticity” in table 4. The second, fourth and sixth
columns are respectively the result obtained from the estimates with the distance-weighted shareof skilled worker (SSKL1), the distance-weighted share of skilled worker within a macro-region(SSKL2) and the share of skilled worker in a county (SSKL3).
In general, the direct effect of an increase in regional knowledge stock has the largest
positive impact on overall plant’s productivity from spillovers followed by the indirect effect of
an increase in regional knowledge stock. Sum of direct and indirect effect of an increase inregional knowledge stock is 0.09, 0.09 and 0.03 from the second, fourth and sixth column,
respectively. Thus, as the share of skilled worker in a region (and surrounding regions) increases
by one percent, plant’s overall productivity from spillovers increases by 0.03-0.09 percent. Lallet al. (2004) estimation of a plant-level production function using Indian data shows that theelasticity of localization economies (externalities arising from the agglomeration of the same
industry) ranges between 0.04-0.10 depending on the industry. Hence, after controlling for theindirect effect, the elasticity of knowledge spillovers for the average plant in Chile is numericallycomparable to the result obtained in the case of India. Note however that our study differs fromprevious studies in clarifying the spillover mechanism. Our results clearly show knowledge
spillovers under absorptive capacity hypothesis are important in explaining the skill-biased labordemand in developing countries. In other words, in order to enhance knowledge spillovers,
plants in a region with a large knowledge stock must raise their absorptive capacity, i.e. employ
more skilled workers.
We also compute the change in plant’s overall productivity from spillovers due to anincrease in explanatory variables such as S and K, from median to 90th percentile value.9 Results

18

are presented in the column labeled “% change in productivity” in table 4. Again, direct andindirect effects from an increase in regional knowledge stock have the largest impact on plant’s
productivity followed by that of regional population and capital stock. Overall productivity of aplant locating in a region where the SSKL is at the 90th percentile is 6.11-12.25 percent higher thanoverall productivity of a plant locating in a region with the median level of SSKL. Next, overall
productivity of a plant locating in a region where the MP is at the 90th percentile is 0.28-1.80
percent higher than the overall productivity of a plant locating in a region with median level of
MP. Finally, overall productivity of a plant with the capital stock at the 90th percentile is 0.341.02 percent higher than the overall productivity of a plant with median level of the capital stock.
Since spillover benefits become large for plants with a high capacity for absorbing
external knowledge, plants tend to employ more skilled workers to further increase theirproductivity. The above results indicate that this indirect effect is an important channel toenhance plant’s productivity because an increase in productivity through this indirect effect isquantitatively comparable to an increase through direct effect.

5. Summary and Conclusions
Recent rapid urbanization in developing countries accompanies accumulation of skilled workers
in urban areas. In this study, we examined knowledge spillovers as a source of geographicalconcentration of high skill-intensive production in Chile. Empirical applications of endogenous
growth theory to developed countries suggest knowledge spillovers are an important source ofeconomic growth, but few studies have focused on developing economies. Moreover, themechanism by which knowledge spreads across firms or plants has received limited empiricalattention in both developed- and developing-country studies. To address this gap in the literature,19

we extended the absorptive-capacity hypothesis, i.e. own investment in skills is required toutilize knowledge created by other firms, to a plant-level setting. We anticipated that high skillintensive plants benefit more from spillovers than their low-skill counterparts, which lead toconcentration of high skill-intensive plants in a region where the knowledge stock is abundant.
To test the absorptive-capacity hypothesis, we first estimated a plant-level production
function incorporating knowledge spillovers. We draw on recent approaches to estimating plantlevel production functions, which account for the correlation between unobserved plant’s
productivity and conventional input use. Our estimates of the production function showedstatistical support for the absorptive-capacity hypothesis in Chilean manufacturing industries, i.e.
high skill-intensive plants benefit from spillovers. In other words, plants’ heterogeneity in termsof skill intensity matters for knowledge spillovers in developing countries. Moreover, theeconomic significance of knowledge spillovers to manufacturing plants’ productivity in Chile iscomparable to that found in developed countries.
Since plants are expected to employ more skilled worker than unskilled worker in aregion with a large knowledge stock, we next evaluated how much of plants’ skill intensity
increased in response to an increase in regional knowledge stock. We found that plant’s skill
intensity was positively correlated with the knowledge stock of a region, regional population,
plant’s raw productivity and the capital stock, but was negatively correlated with the relative
wage of skilled workers. Finally, an increase in overall plant’s productivity from spillovers was
decomposed into a direct and indirect effect, the latter arising from increasing plants’ skill
intensity. We also evaluated the effect of plants’ capital stock, raw productivity, regional
population and relative wage on overall plant’s productivity from spillovers through changing its
skill intensity. Results showed that regional knowledge stock contributed the most to overall

20

plant’s productivity enhancement, but the indirect effect through plants’ capital stock andrelative wages had a comparable magnitude.
Knowledge spillovers contribute to the agglomeration of high skill-intensive production
in developing countries as high capacity to absorb external knowledge is necessary to maximize
benefits from spillovers, leading to a large demand for skilled workers in cities. Our results
show that educating local population is effective in the context of regional development since itraises the regional knowledge stock, the source of knowledge spillovers, and at the same time, it
increases the supply of human-capital which helps plants to employ skilled worker at a low wage.
Also, a policy which encourages plants to increase their skill intensity is a good instrument forregional development.

21

References
Acemoglu, D. and J. Angrist. (2000). “How Large are Human-Capital Externalities? Evidence
from Compulsory Schooling Laws.” NBER Macroeconomics Annual. 15: 9-59.
Alvarez, R. and R. Robertson. (2004). “Exposure to Foreign Markets and Plant Level Innovation:
Evidence from Chile and Mexico.” Journal of International Trade and Economic
Development. 13: 57–87.
Arora, A. and A. Gambardella. (1994). “Evaluating Technological Information and Utilizing It:
Scientific Knowledge, Technological Capability, and External Linkages in
Biotechnology.” Journal of Economic Behavior and Organization. 24: 91-114.
Audretsch, D. and M. Feldman. (1996). “R&D Spillovers and the Geography of Innovation and
Production.” American Economic Review. 86: 630-640.
Audretsch, D. and M. Feldman. (2004). “Knowledge Spillovers and the Geography ofInnovation.” in J.V. Henderson and J.F. Thisse, eds., Handbook of Regional and Urban
Economics, Volume 4. Elsevier. Amsterdam.
Baldwin, R., Forslid, R., Martin, P., Ottaviano, G.I.P. and F. Robert-Nicoud. (2003). Economic
Geography and Public Policy. Princeton University Press. Princeton, NJ.
Barro, R and X. Sala-i-Martin. (2003). Economic Growth. MIT Press. Cambridge, MA.
Berman, E., Bound, J. and Z. Griliches. (1994). “Changes in the Demand for Skilled Labor
within U.S. Manufacturing: Evidence from the Annual Survey of Manufactures.”
Quarterly Journal of Economics. 109: 367-397.
Bernard, A. and J.B. Jensen. (1997). “Exporters, Skill Upgrading, and the Wage Gap.” Journalof International Economics. 42: 3-31.
Ciccone, A. and G. Peri. (2006). “Identifying Human-Capital Externalities: Theory with22

Applications.” Review of Economic Studies. 73: 381–412.
Cockburn, I. and R. Henderson. (1998). “Absorptive Capacity, Coauthoring Behavior, and theOrganization of Research in Drug Discovery.” Journal of Industrial Economics. 46: 157182.
Cohen, W. and D. Levinthal. (1989). “Innovation and Learning: The Two Faces of R&D.”
Economic Journal. 99: 569-596.
Combes, P.P., Duranton, G. and L. Gobillon. (2008). “Spatial Wage Disparities: Sorting
Matters!” Journal of Urban Economics. 63: 723-742.
Crozet, M., Mayer, T. and J. Mucchielli. (2004). “How Do Firms Agglomerate? A Study of FDI
in France.” Regional Science and Urban Economics. 34: 27-54.
Feenstra, R. and G. Hanson. (1997). “Foreign Direct Investment and Relative Wages:
Evidence from Mexico’s Maquiladoras.” Journal of International Economics. 42: 371393.
Fernandes, A. (2007). “Trade Policy, Trade Volumes and Plant-Level Productivity in Colombian
Manufacturing Industries.” Journal of International Economics. 71: 52-71.
Fujita, M., Krugman, P. and A.J. Venables. (1999). The Spatial Economy: Cities, Regions, andInternational Trade. MIT Press. Cambridge, MA.
Henderson, J.V. (1986). “Urbanization in a Developing Country: City Size and Population
Composition.” Journal of Development Economics. 22: 269-293.
Henderson, J.V. (2003). “Marshall’s Scale Economies.” Journal of Urban Economics. 53: 1-28.
Henderson, J.V., Shalizi, Z. and A.J. Venables. (2001). “Geography and Development.” Journalof Economic Geography. 1: 81-105.
Jovanovic, B. (1982). “Selection and the Evolution of Industry.” Econometrica. 50: 649-670.

23

Lall, S., Shalizi, Z. and U. Deichmann. (2004). “Agglomeration Economies and Productivity inIndian Industry.” Journal of Development Economics. 73: 643-673.
Levinsohn, J. and A. Petrin. (2003). “Estimating Production Functions Using Inputs to Control
for Unobservables.” Review of Economic Studies. 70: 317-341.
Liu, L. (1991). “Entry-Exit and Productivity Changes: An Empirical Analysis of Efficiency
Frontiers.” Ph.D. Thesis, University of Michigan.
Lopez-Bazo, E., Vaya, E. and M. Artis. (2004). “Regional Externalities and Growth: Evidence
from European Regions.” Journal of Regional Science. 44: 43-73.
Lucas, R.E. (1988). “On the Mechanics of Economic Development.” Journal of Monetary
Economics. 22: 3-42.
Malecki, E. (1997). Technology and Economic Development: The Dynamics of Local, Regionaland National Competitiveness. Second Edition. Addison Wesley Longman. Essex,
England.
Moretti, E. (2004a). “Workers’ Education, Spillovers, and Productivity: Evidence from PlantLevel Production Functions.” American Economic Review. 94: 656-690.
Moretti, E. (2004b). “Estimating the Social Return to Higher Education: Evidence from
Longitudinal and Repeated Cross-Section Data.” Journal of Econometrics. 121: 175212.
Moretti, E. (2004c). “Human-Capital Externalities in Cities.” in J.V. Henderson and J.F. Thisse,eds., Handbook of Regional and Urban Economics, Volume 4. Elsevier. Amsterdam.
Olley, S. and A. Pakes. (1996). “The Dynamics of Productivity in the Telecommunications
Equipment Industry.” Econometrica. 64: 1263-1298.

24

Pavcnik, N. (2003). “What Explains Skill Upgrading in Less Developed Countries?” Journal of
Development Economics. 71: 311-328.
Rauch, J.E. (1993). “Productivity Gains from Geographic Concentration of Human-Capital:
Evidence from the Cities.” Journal of Urban Economics. 34: 380-400.
Romer, P. (1990). “Endogenous Technological Change.” Journal of Political Economy. 98: S71102.
Schmidt, T. (2005). “Absorptive Capacity - One Size Fits All?: A Firm-Level Analysis of
Absorptive Capacity for Different Kinds of Knowledge.” Centre for European Economic
Research Discussion Paper. No. 05-072.
Stock J.H. and M. Yogo. (2005). “Testing for weak instruments in linear IV regression.” in
D.W.K. Andrews and J.H. Stock, eds., Identification and Inference for Econometric
Models: Essays in Honor of Thomas Rothenberg. Cambridge University Press.
Cambridge.
United Nations. (2008). World Urbanization Prospects: The 2007 Revision. United Nations
Publication. New York, NY.
Yasar, M. and C.J. Morrison. (2007). “International Linkages and Productivity at the Plant
Level: Foreign Direct Investment, Exports, Imports and Licensing.” Journal ofInternational Economics. 71: 373-388.

25

Table 1: Summary Statistics

VariableUnit

CV acrossCV across
Time

Mean

Std. Dev.

Plants/Counties

Constant peso

3.45

13.25

3.82

0.24

Number

23.09

66.36

2.86

0.34

Unskilled worker (L )Number

50.62

104.122.06

0.32

Material (M/1,000,000)

Constant peso

1.98

8.69

4.25

0.31

Energy (E/1,000,000)

Constant peso

0.09

0.55

6.27

0.33

Capital (K/1,000,000)

Constant peso

1.67

7.18

4.27

0.20

Index, 0-1

0.32

0.24

0.76

0.33

Index, 0-1

0.46

0.19

0.41

0.13

Index, 0-1

0.45

0.26

0.57

0.28

Index, 0-1

0.40

0.29

0.72

0.40

Number170.83204.761.20

0.02

Number

126.30203.081.61

0.02

Number

45.37

70.65

1.56

0.02

Output (Y/1,000,000)s

Skilled worker (L )uShare of skilled worker of a plant (η)
Distance-weighted share of skilled worker
in a county (SSKL1)
Distance-weighted share of skilled worker
within a macro-region in a county (SSKL2)
Share of skilled worker in a county (SSKL3)
Distance-weighted county population(MP1/1,000)
Distance-weighted county population
within a macro-region (MP2/1,000)
County population (MP3/1,000)

Relative wage for skilled worker (ws/wu)
Constant peso
2.41
3.56
0.84
0.28
Note: CV across plants/counties measures the coefficient of variation of each variable across plants or county-isicpairs for each year. Then, obtained coefficients are averaged over years. Similarly, CV across time measures thevariation across time for each plant or county-isic pair. Then, obtained coefficients are averaged over plants orcounty-isic pairs. For MP1, MP2 and MP3, variation is measured across counties as they are invariant acrossindustries.
Source: INE, Chilean Manufacturing Census, Various Years.
INE, Population Projections, Various Years.

26

Table 2: Parameter Estimates of the Production Function

Variable
lnLs
lnLu
lnM
lnE
lnK
SSKL1
ηSSKL1(1)0.089***(0.008)0.125***(0.009)0.631***(0.045)0.069***(0.005)0.113***(0.024)-0.170(0.178)0.350***(0.101)SSKL2(2)0.090***(0.007)0.125***(0.008)0.638***(0.039)0.068***(0.005)0.108***(0.022)-0.140(0.139)0.342***(0.097)

ηSSKL2
SSKL3-0.118(0.083)0.181***(0.068)ηSSKL3lnMP1-0.005(0.039)

lnMP2

0.000
(0.028)lnMP3Returns to Scale(β2+β3+β4+β5+β6)
Observations(3)
0.098***(0.006)
0.114***(0.007)0.616***(0.050)0.070***(0.005)0.124***(0.026)1.027(0.026)
14202

1.029
(0.022)
14103

0.001
(0.024)1.021(0.029)12629

Note: *** indicates statistical significance at the 1%. Value inparenthesis is the bootstrapped standard error based on 200
iterations. Dependent variable is the log of output.

27

Table 3: Parameter Estimates of the Plants’ Skill Intensity Model

Variableln(ws/wu)
SSKL1

(1)
-0.055(0.059)5.643***(1.231)

(2)

(3)
***

-0.136(0.054)2.546**(1.130)

SSKL2

(4)
*

-0.010(0.070)-0.114(0.062)5.748***(1.318)2.687**(1.151)

SSKL3
lnMP1

0.117***(0.042)0.068*(0.040)lnK
ηt-1
Constant
Cragg-Donald Wald F
Observations-5.133***(0.526)193.94119730-0.122(0.088)-0.166*(0.087)2.597**(1.108)1.249(1.065)0.067***(0.022)0.191*(0.104)0.010*(0.006)0.026(0.018)0.141(0.092)0.012**(0.005)3.013***(0.042)-2.999***(0.280)33.07113043

0.052*(0.032)lnMP30.233***(0.070)0.020***(0.005)(6)

0.067*(0.037)

lnMP2

ω

(5)

0.144**(0.064)0.017***(0.005)3.060***(0.034)-4.099***(0.481)135.30414341

0.167**(0.076)0.020***(0.006)-4.289***(0.438)100.59019623

0.118*(0.067)0.017***(0.005)3.047***(0.036)-3.850***(0.382)73.91714264-3.152***(0.303)52.04417903

Note: *, ** and *** indicate statistical significance at the 10%, 5% and 1%, respectively. Value in parenthesis is thestandard error. Dependent variable is the log of the ratio of skilled to unskilled worker.

28

Table 4: Elasticity of Productivity and Change in Productivity due to Increase in
Explanatory Variables from Median to 90th percentile Value% change in
Variable% change in% change inElasticity productivity Elasticity productivity Elasticity productivity

Direct effectDistance-weighted share of skilled worker ina county (SSKL1)
Distance-weighted share of skilled worker
within a macro-region in a county (SSKL2)

0.050

3.843
0.049

6.685

Share of skilled worker in a county (SSKL3)

0.023

4.560

0.008

1.549

0.000

0.282

Indirect effect through increasing plant's skill intensity
Distance-weighted share of skilled worker ina county (SSKL1)
Distance-weighted share of skilled worker
within a macro-region in a county (SSKL2)

0.040

3.048
0.041

5.569

Share of skilled worker in a county (SSKL3)
Distance-weighted county population(MP1/1,000)
Distance-weighted county population withina macro-region (MP2/1,000)

0.002

1.101
0.002

1.803

County population (MP3/1,000)
Capital (K)Plant's raw productivity (eω)
suRelative wage of skilled worker (w / w )

0.001

1.020

0.001

1.024

0.000

0.340

0.005

0.040

0.004

0.030

0.002

0.008

-0.005-0.288-0.004-0.234-0.003-0.159Note: In evaluating equation (20),  6 is set to zero as it is insignificant in the production function estimates.

29

3,000
2,000
1,000
500
100
50

Figure 1: Average of Plants’ Skill Intensity in Chilean Counties(Unit: Number of Skilled Worker)

30

4.0

Density

3.0

2.0

1.0

0.0
0.0

0.2

0.4

0.6

0.8

1.0

Plant's skill intensity
Counties whose skill intensity is above the third quartile
Counties whose skill intensity is below the first quartile

Figure 2: Kernel Density Estimates for Plants’ Skill Intensity in Counties
Whose Skill Intensity is above (below) the Third (First) Quartile31

Appendix A: Derivation of Equation (20)In this appendix, we show how the third line of equation (20) is derived. First of all, thederivative of plant’s skill intensity with respect to the log of regional knowledge stock is
obtained as follows:  ln L  L  L  ln S  ln  ln S


(A1)

s

s

 ln 1  Lu Ls  ln S  1  L L 
u

s 1

u



1

 1  Lu Ls  ln SLs
 Lu Ls  ln  L L S  suusL  L  ln L LS ln S
s

u 1

Ls Lu
  s  3  S
L  Lu Ls  3 1    S .

The derivative of the log of the ratio of skilled to unskilled worker in the fourth line is  3 fromequation (19). The fifth line is obtained by using this parameter. Substituting equation (A1) into
the second line of equation (20) yields the third line of equation (20). Also, the third line ofequation (21) is obtained in a similar way.

32

Appendix B: Construction of Plant-Level Variables
Output is defined as the sum of revenue, sales of electricity and value of self-produced capital
goods. Inventory is adjusted in the construction of output. Material is the sum of raw materials’
value, goods purchased for resale and the cost of work by third parties. Energy is the sum ofpurchase values of electricity, water and fuel. Output and input variables in values are converted
to constant price by using price deflator (base year 1996) from the Chilean National Accounts,
which is available on the Central Bank of Chile’s webpage. Output is deflated by the deflator forgross output, while material and energy are deflated using the deflator for intermediate goods.
Skilled (unskilled) worker comprises of workers reported as white (blue) collar in the
Chilean Manufacturing Census. White-collar workers include executives, administrative, whitecollar production employees, while blue-collar workers include both blue-collar production andnonproduction employees (e.g. clerks, secretaries). Although Manufacturing Census does notprovide data on worker’s education, 2002 Housing and Population Census provides data on
worker’s occupation (ISCO-88) and years of education. Average years of education for first skill
level (elementary occupations), second skill level (clerks, craft workers and plant and machine
operators and assemblers), third skill level (technicians and associate professionals) and forthskill level (managers and professionals) are 7.8, 9.9, 13.7 and15.2 years, respectively.
Following Liu (1991), capital stock is constructed by the perpetual inventory method
assuming a depreciation rate of 5 percent for building, 10 percent for machinery and 20 percent
for vehicles. Both capital stock and investment are deflated by the deflator for the gross fixed
capital formation. However, as the deflator for the gross fixed capital formation for the foodprocessing industry is not available in the Chilean National Account, we use deflator for thewhole manufacturing industry. Also, note that the deflator is only available at national level.

33

Therefore, we control for the regional and industrial difference in output prices and otherunobservable regional and industrial heterogeneity with provincial and industrial dummies in the
production function.

34

Endnotes
1

The most common measure of skill intensity is the share of educated workers (high-school

diploma, college degree or nonproduction workers) in total employment (Feenstra and Hanson
1997; Moretti 2004a).
2

For analytical simplicity, we substituted ws wu  1 in deriving equation (1).

3

In the Chilean case, there are 51 provinces and 342 counties (regions).

4

For details on bootstrapping procedures, refer to Levinsohn and Petrin (2003).

5

See Appendix A for the derivation of the third line of equation (20), which does not include

subscripts for ease of exposition.
6

Refer to Liu (1991) and Appendix B for details on the construction of plant-level variables.

7

We use the distance-weighted average years of education in a county, the distance-weighted

average years of education within a macro-region in a county and the average years of education
in a county as an instrument for SSKL1, SSKL2 and SSKL3, respectively.
8

The critical value is 16.38 for 10 percent from Stock and Yogo (2005).

9

We use the 90th percentile value instead of the maximum value to avoid misrepresenting change

in variables caused by outliers.

35