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Knowledge Spillovers and TFP Growth Rates
Núria Quella∗
Economics Department, Stony Brook University,
Stony Brook, NY 11794-4384, USA
April 2009
∗E-mail address: nuria.quella@stonybrook.edu, Tel.: +1 631 632 7534; fax: +1 631 632 7516.
I thank Boyan Jovanovic and Sílvio Rendon for useful suggestions, and Dale W. Jorgenson for his
gracious provision of data. I am also indebted to participants in seminars at Banco de México,
ITESM, CIDE, U. de Guanajuato, ITAM, the Midwest Macroeconomic Meetings in St. Louis, the
Society for Economic Dynamics in Vancouver, the Society for Computational Economics in Montréal,
and LACEA-LAMES in México City for helpful comments. The usual disclaimer applies.
Abstract.- In this paper I calibrate unobserved labor-generated knowl-
edge spillovers within and between six large macroeconomic sectors cover-
ing the U.S. civilian economy from 1948 to 1991. Using quality-adjusted
data I show that manufacturing and trade & transportation are the main
source of knowledge flows to the overall economy for the entire period.
However, the productivity slowdown of the early seventies coincides with
trade & transportation taking over manufacturing as the main source and
destination of post-73 knowledge flows. Furthermore, I compute the gap
between the market and the optimal allocation of labor across sectors,
and the wedge between market and optimal wages by sector. I find that,
for the whole period, optimal employment in manufacturing and trade &
transportation is, respectively, 20% and 27% above market. As a result
optimal output in these sectors is 12% and 16% higher than the market’s,
and optimal wages in manufacturing are 54% above market wages.
Keywords: Knowledge spillovers; productivity; human capital; learning; wages.
JEL Classification: D24, J24, O30, O40.
Knowledge Spillovers and TFP Growth Rates 3
1 Introduction
Although spillovers have always had an important role in economic theory and pol-
icy design, the difficulties involved in their measurement have made their empirical
computation far less popular.
In this paper I compute a matrix of unobserved labor-generated knowledge spillovers
within and between six large macroeconomic sectors covering the whole U.S. civilian
economy: manufacturing, mining, construction, services, trade & transportation, and
agriculture.1I show that, from 1948 to 1991, manufacturing and trade & transporta-
tion are undisputedly the leading knowledge generators for the whole U.S. economy.
Moreover, I also compute the gap between the market and the optimal sectoral al-
location of labor and its return rates. I find that efficiency requires the market to
increase employment in manufacturing by 20% and in trade & transportation by 27%,
so that output in these sectors increases by 12% and 16% respectively; and wages in
all sectors, except for mining and trade & trasnportation, increase by at least 54%.
I also show that the productivity slowdown of the early seventies coincides with
trade & transportation taking over manufacturing as the main generator of knowledge
spillovers to the whole economy and with increasing sectoral integration, that is, with
spillovers within sectors declining in favor of spillovers between sectors.
Two bodies of literature have particularly concerned themselves with the mag-
nitude of externalities: economic growth has focused on the role of externalities in
generating long run growth; real business cycles research has used externalities to ex-
plain why total factor productivity (TFP) is procyclical once imperfect competition
and increasing returns to scale proved insufficient to account for it. A third strand
of work has concentrated on the imperfect measurement of output and inputs as a
source of the erroneous measurement of productivity growth rates. This paper sits at
the cross-roads of these three bodies of work.
1Because of data availability and/or quality, previous measurements of external economies refer
to manufacturing.
Knowledge Spillovers and TFP Growth Rates 4
I start from a production theoretic framework and propose a static model, ex-
tendable to a dynamic setting. The model presents a multisector economy where
the production function incorporates knowledge externalities in labor employed at
all stages and levels of the production process. Knowledge spillovers in a particular
industry are generated by the capacity of all employees to learn from their own and
from others’ productive experience. In other words, employees learn by observing as
well as by doing.2Arrow (1962) was among the first to consider the economic impact
of learning from experience and to formally model spillovers of any kind. Further-
more, Lucas (1988, 1993) emphasized the centrality of learning on the job and its
external effectsasanengineofgrowthbeyondspecific production processes, that is,
the importance of spillovers from learning by doing for entire economic sectors and
economies and the supporting role of physical capital accumulation.3More recently,
Jovanovic and Rousseau (2002) have extended these arguments to the “new econ-
omy.” Among others, Lieberman (1984), Cohen and Levinthal (1990), Young (1993),
Jovanovic and Nyarko (1995), and Klenow (1998) have also worked along the same
lines.4
In order to calibrate the parameters characterizing the model I use the database
developed by Dale W. Jorgenson for the U.S. civilian economy from 1948 through
1991 containing quality-adjusted factor and product sectoral panel data. The use of
this database allows me to distinguish between substitution among different types
of inputs (with different combinations of marginal productivity in their components)
2Early on, Rapping (1965) applied data on the production of the Liberty Ship to a Cobb-Douglas
production function within a neoclassical framework to illustrate the learning principle present in
many other industries, namely that workers’ performance of a task improves with increases in the
repetition of that task, albeit decreasingly.
3Benhabib and Jovanovic (1991) examine a variety of bodies of data within an augmented
Solow model and show that aggregate data are not consistent with physical capital as the source of
spillovers, leaving open the possibility that social increasing returns are caused by human capital
instead; ideas come first, capital investment follows. Klump, McAdam and Willman (2007) use a
CES production function to show that technical progress is purely labor augmenting in the long run
while capital-augmenting progress fades away.
4Given the sectoral approach of this paper and its time scope, I fully abstract from consideration
of geographic or agglomeration effects on knowledge spillovers. See Thompson (2006) for evidence
that intranational localization effects become weaker with the passage of time.
Knowledge Spillovers and TFP Growth Rates 5
and growth in productivity. Often, what previous studies have called spillovers were
really input quality improvements. Once input heterogeneity and quality changes are
taken into account, the TFP term will only pick up the costless spillover effects.
The remainder of the paper is organized as follows. Next section describes a
model with inter- and intra-industry labor generated knowledge spillovers and states
the difference between the market and the optimal solution in terms of resource
allocation and return to labor; Section 3 goes through the calibration choices necessary
to measure these spillovers, including the dataset used and the literature of reference,
and discusses the resulting matrix of knowledge flows. Section 4 reexamines the gap
between the market and the optimal solution in light of the data. Section 5 explores
the possibility of a shift in spillovers being associated with the productivity slowdown
of the early seventies. Finally, Section 6 summarizes the paper’s main conclusions.
2Model
This section presents a multiple sector model where the production function incorpo-
rates knowledge externalities in labor. Consequently, while private returns to scale
are constant, social returns are increasing. Knowledge spillovers in a particular sector
stem from its own workers’ skill level and productive experience (learning by doing),
and from the quality of labor employed in all other sectors in the economy and what
can be learnt from their experience (learning by observing).
Consider an economy consisting of nsectors, each producing a differentiated final
good Yiwith capital Ki,laborLi, and intermediate goods Mi. The production
function at any given period is characterized by sectoral knowledge spillovers in labor,
that is,
Yi=AiKβiK
iLβiL
iMβiM
i
n
Y
j=1
Lγij
j,i=1,2,...,n.
The exogenous time-invariant scale factor Aiis here unrelated to the input variables
Knowledge Spillovers and TFP Growth Rates 6
and, hence, there is no endogenous growth derived from it.5The Lγij
jare sectoral
spillovers that improve the marginal productivity of all inputs in the sector equally
and costlessly. They are characterized by the learning parameters γij ≥0that mea-
sure the extent to which sector ilearns from sector j.Ifi=j, they are called
sector-specific or intra-sectoral knowledge spillovers; if i6=j, they are inter-sectoral
knowledge spillovers. All learning parameters are non-negative because un-learning
from one’s own or others’ productive experience has no economic meaning.6
Every sector iexhibits private constant returns to scale βiK +βiL +βiM =1.
Endowments are fully used: K=Pn
i=1 Ki,L=Pn
i=1 Li,andM=Pn
i=1 Mi.Sectoral
production sumps up to the economy’s output: Pn
i=1 Yi=Y,andtheconsumer’s
utility function is U(C1,C
2,...,C
n)=Qn
i=1 Cαi
i,wherePn
i=1 αi=1and αi>0∀i.
Each sector ireceives total spillover qi=Pn
j=1 γij and emits total spillover
Γi=Pn
j=1 αjγji. The economy-wide coefficient for each factor X=K, L, M is
βX=Pn
j=1 αjβjX and the economy-wide emission (and reception) of spillovers is
Q=Pn
j=1 αjqj=Pn
i=1 Γi.7
Social returns to any sector are 1+qiwhich, unless qi=0, means there are really
sectoral and, hence, economy-wide increasing returns to scale.8Thus, TFP estimates
will reflect the labor generated knowledge externality and, therefore, there will be a
gap between the market’s sectoral allocation of labor and its rate of return and what
5A dynamic extension of this model would have Aias a Hicksian neutral shift parameter: the
scale factor Aiwould vary over time as the productivity of inputs and/or the knowledge spillovers
change. In this model Aiis the ratio of output to total factor input plus spillovers.
6Learning as a source of knowledge spillovers rules negative externalities out. Consider a simple
sectoral production function with labor as the only factor of production and learning by doing
Yi=f(Ni)Yθ
i. The learning elasticity or slope of the learning curve is, for the sake of simplicity, a
constant 0≤θ<1and the learning effect Yθ
iis bounded. With constant returns on the production
function, f(Ni)=Ni, the previous expression can be rewritten as Yi=N
1
1−θ
i,where 1
1−θ≥1and,
therefore, Yi≥f(Ni). Compare this form with a production function similar to the one in this
model but with labor as the only input and no inter-sectoral externalities: f(Ni)=N1+γii
i,∀i. Then
1+γii =1
1−θor θ=γii
1+γii .Thus, 0≤γii
1+γii <1,and0≤γii.
7Ultimately, the set of sectoral spillovers qiand the economy-wide spillover Qwill depend on the
sectoral structure of the economy and its employment schedule.
8Note that sectoral private returns to spillover-generating Liare really βiL +γii and social returns
are βiL +Γi.
Knowledge Spillovers and TFP Growth Rates 7
is optimal.
The market sets a unique competitive return rate for each input
wc
X=βiX
PiYi
Xi
,X=K, L, M,
whereas the optimal wage rate is sector-specific: ws
i6=ws
j,∀i6=jand
ws
i
wc=³1+ γii
βiL ´Ys
1/Y c
1
Ls
i/Lc
i,whereYs
1/Y c
1
Ls
i/Lc
iis the optimal-to-market average product of
labor ratio measured in units of the numeraire.
The market sectoral allocation of inputs is
Xc
i
X=αiβiX
βX
,X=K, L, M.
Because of Cobb-Douglas preferences and technology, planner and market allocate
capital and intermediate goods the same way, but the planner will optimize the allo-
cation of labor:
Ls
i
L=αiβiL +Γi
βL+Q.
In principle, both the market and the planner respond to an increase in consumers’
preferences for one good increasing labor allocated to its production. However, the
planner also takes into consideration how much productive knowledge workers em-
ployed in each sector generate for the benefit of the overall economy. If employing
more workers in a particular sector will generate more knowledge for the whole econ-
omy and, thus, make it more productive, the planner will allocate more workers
to this sector than strictly determined by consumers’ preferences and technological
needs. That is,
Proposition 1 The planner allocates more labor than the market to sector i,Ls
i>L
c
i,
iffΓi
Q>Lc
i
L. Similarly, Ls
i<L
c
i,iffΓi
Q<Lc
i
Land Ls
i=Lc
i,iffΓi
Q=Lc
i
L.Proof: Ls
iQLc
i
if αiβiL+Γi
βL+QQαiβiL
βLwhich is equivalent to Γi
QQLc
i
L¥
Knowledge Spillovers and TFP Growth Rates 8
This Proposition determines the sign of the efficiency gap for each sector, as will
be seen in Section 4.
3Calibration
In order to compute the magnitude and directionality of knowledge spillovers I must
first determine the numerical value of the model’s parameters. These values are set
according to the data used and to estimates in previous literature, both discussed
below.
Data
The panel dataset used in the calibration is an update on the original sectoral input-
output database developed by Dale W. Jorgenson for the 1948-1979 period, also
described in Jorgenson and Stiroh (2000), Jorgenson (1990), and Jorgenson, Gollop
and Fraumeni (1987). It covers 35 sectors at roughly the 2-digit Standard Industrial
Classification (SIC) 1987 level, that is, the whole of the U.S. civilian economy from
1948 to 1991. For each sector, it contains annual observations on the value and the
price of output and four inputs (capital, labor, energy and material), quality-adjusted.
Because input growth reflects increases in input quantity as well as changes in
input quality or marginal productivity, estimated TFP only captures the effect of
costless spillovers.9As a result computed TFP growth becomes smaller (Jorgenson
and Griliches 1967).
Using the index number approach, I then compute sectoral input quantities and
value added. Industrial value added is more advantageous than gross output measures
because it always sums up to total value added (GDP), independently of the degree
of vertical and horizontal integration and of the proportion of intermediate goods
9According to Jorgenson, Ho and Fraumeni (1994) about ten percent of the growth of the US
economy in between 1947 and 1989 is due to increases in labor quality, which is the source of the
spillover, but not the spillover itself.
Knowledge Spillovers and TFP Growth Rates 9
used.10
Grouping of Industries into Sectors
To make results tractable, government enterprises are eliminated, and energy and
material are consolidated into a single intermediate inputs category. The remaining
34 industries are then aggregated into six larger sectors following the division drawn
by Long and Plosser (1983) when analyzing real business cycles: manufacturing (M),
mining (N), construction (C), services (S), trade & transportation (T), and agricul-
ture (A). The interested reader can see the industrial composition of each sector in
Appendix A1.
For ea ch p er io d tI generate a five-year central moving average from original annual
data. This, together with the fact that inputs in Jorgenson’s dataset are measured
in flows of services, rather than in stocks, reduces the unwanted short-term effects
of business cycles (i.e. of changes in the rate of utilization of inputs) on the model’s
productivity estimates.
Aggregation of industries into a smaller number of sectors generates, on the one
hand, an increase in the heterogeneity of the labor input, which the index number
approach handles without difficulty and, on the other, an increase in the magnitude
of sectoral spillovers qi, as more sources of spillovers “pile up” in a given sector.11
Consumers’ Preferences
The values of consumers’ preferences for each sector, αi, are computed directly from
the data:
αi=Yi
Y,
10Aggregate value-added is immune to the kind of aggregation bias that occurs when sectoral
share-weights change with the reallocation of GDP among sectors with different TFP levels and
growth rates, creating a path dependence problem for the aggregate productivity index. Moreover,
value added is impervious to outsourcing.
11A sector’s spillovers reflect the combined effect of spillovers within the individual industries and
the induced effects on those industries of intermediate inputs produced themselves with markups or
externalities and under increasing returns that pile up in aggregation.
Knowledge Spillovers and TFP Growth Rates 10
where Yiis the market demand for sector iwhich, in this model, is equal to sector i’s
production, given Pn
i=1 αi=1and αi>0∀i.
Table 1 shows the numerical values of consumers’ preferences and of all the model’s
calibrated parameters discussed below.
[Insert Table 1 here]
Technology
Output elasticities of inputs by sector, βiX , are calibrated from the data’s average
between-period cost-shares of each input, SiX ,X=K, L, M. I start by using index
prices and index quantities to compute SiX =wxiXi/PiYi,where wxiistherateof
return of input Xin sector i,andPiis the price of sector i’s product. Given that
under perfect competition and constant returns to scale output elasticities are equal
to factor shares, I can safely assume βiX =SiX , as seen in Appendix A2.
Table 1 shows the numerical values of output elasticities for each input by sector.
For the overal economy, the elasticities of capital, labor, and intermediate goods are,
respectively, 0.15,0.34,and0.50.
Magnitude and Ranking of Sectoral Spillovers
The empirical estimation of external economies operating at the national and industry
level can be traced back to Lucas (1988) and Hall (1988, 1990), respectively. Lucas
estimated the external effects of human capital for the whole U.S. economy from
1909 to 1957 to be around 0.4. Hall measured the industry level externality for
manufacturingfrom1958to1981around0.3.
Domowitz, Hubbard and Petersen (1988), Caballero and Lyons (1992), Baxter
and King (1991), and Bartelsman, Caballero and Lyons (1991, 1994) all started from
a Cobb-Douglas production function with perfect competition and constant returns
to scale to explain the gap between manufacturing output growth and the growth of
Knowledge Spillovers and TFP Growth Rates 11
its inputs, labor in particular. And all came up with a manufacturing externality in
between 0.3and 0.4.
These estimations set the range for the value of sectoral knowledge spillovers qi
in this model.Within this range, sectors are then ranked ordinally according to their
relative learning potential.12 Sectors that are more intensive in skilled labor will
exhibit higher overall marginal productivity, higher learning capability, and higher qi.
Undoubtedly, R&D is one of the most skill-intensive productive activities.13 Thus,
in order to proxy a sector’s learning potential I use the dataset by Hadlock, Hecker
andGannon(1991)onthesectoralproportionofR&Demploymentrelativetothe
average and rank the paper’s six sectors according to their qi.AlltenR&D-moderate
industries and twenty-four of the thirty R&D-intensive industries in Hadlock et al.
are in manufacturing, five are in services, and one in mining (crude petroleum and
natural gas operations). Therefore manufacturing’s spillover is set at a conservative
maximum of 0.3; services and mining follow as the most knowledge absorptive sectors
in the economy. The distance between sectoral spillovers is normalized at 0.05.
According to McKinsey Global Institute (2001), the US productivity jump that
began in 1995 is structural in nature (i.e. due to earlier fundamental changes) and
can be explained by the performance of retail, wholesale, securities, telecom services,
semiconductors, and computer manufacturing. Retail and wholesale constitute a large
percentage of the value added in trade & transportation; securities and telecom are
part of services; and the last two, of manufacturing. Thus, trade & transportation
ranks fourth.
Agriculture is last in the ranking because most of the research that has played
a vital role in its growth has been in biotechnology and the food industry (Fuglie,
MacDonald and Ball 2007), both within manufacturing. Similarly, fragmentation
of the construction industry has led to low investment in R&D (Federal Facilities
12See Lucas (1988) for a multi-sector model with different sectoral learning rates.
13See Young (1993) for a model in which the interdependence betweeninnovationattheR&D
lab and learning by doing at the production floor determine cumulative experience and the costs of
production.
Knowledge Spillovers and TFP Growth Rates 12
Council 1995).
In summary, estimates in previous literature set the value range for qi,andeach
sector’s relative learning potential determines its place in the general ranking of
spillovers, which can be seen in Table 1. Using these sectoral values, the model’s
economywide knowledge spillover Qcomes up to be 0.23, well within the range set
by previous estimates.
Learning Parameters: the Matrix of Knowledge Flows
The last section of Table 1 records the numerical values of learning parameters γij ,
expressed as percentages of the total sectoral spillover received qi,intheformofa
6×6matrix of intra- and inter-sectoral spillovers flowing from sectors of origin jto
sectors of destination i. Appendix A2 describes how these values were computed.
Table 1 shows that manufacturing and trade & transportation are generating most
of the knowledge that spills over to the other sectors in the economy. Services and
agriculture, on the other hand, benefit from knowledge generated elsewhere but make
no contribution to the economy’s knowledge externality. Furthermore, all sectors
receive spillovers from, at least, one other sector in the economy, but manufacturing
and trade & transportation are the only two sectors to learn exclusively from each
other: 100% of the knowledge trade & transportation benefits from is originated in
manufacturing, as is construction’s. In fact, all other sectors, except for services, are
completely dependent on one unique source for the totality of their spillover.
Most flows occur between industry (manufacturing, mining, construction) and
the tertiary sector (trade & transportation, services). Clearly, industry is the most
dynamic sector, both internally and externally, that is, industry as a whole generates
and receives most flows in the matrix. As for intra-sectoral flows, manufacturing is
the one and only sector to learn from its own productive experience (55%), more so
than from the rest of the economy as a whole, absorbing the remaining knowledge
(45%) from trade & transportation.
Knowledge Spillovers and TFP Growth Rates 13
To fully gauge the relative importance of each sectors’ knowledge emissions at the
national level, consumers’ preferences have to be taken into account. Each sector’s
share of consumer demand determines the weight it has in the economy and, hence,
the overall impact of the knowledge flows it generates and receives.14 The first part of
Table 2 compares relative emission of knowledge by sector: Γi/Q is the weight of the
total knowledge generated by sector ibenefitting the whole economy, including sector
iitself; the second row presents the weight of sector i’s emissions to sectors other
than itself, ˜
Γi=Γi−αiγii
1−αi, in the economy’s total inter-sectoral spillover, ˜
Q=Pn
i=1 ˜
Γi.
[Insert Table 2 here]
Clearly, for the period 1948-1991 manufacturing and trade & transportation gen-
erate most knowledge, but whereas the weight of both sectors is similar for total
knowledge generated in the overall economy (45% and 46%, respectively), trade &
transportation’s outgoing flows to other sectors represent 63% of the economy’s total
inter-sectoral flows, compared to 27% for manufacturing. The reason is that manu-
facturing’s outflows to the rest of the economy, although large, benefitsectorswhose
aggregate demand amounts to slightly over one fourth of the total (construction and
trade & transportation); whereas trade & transportation’s smaller outflows benefit
the two sectors with the largest demand (manufacturing and services) which, by them-
selves, account for two thirds of the total demand. Therefore, knowledge generated
by trade & transportation has a larger impact in the economy, slightly so for the
overall economy, noticeably so for the rest of the economy.
Mining and construction also generate spillovers for other sectors. While con-
struction’s knowledge outflows only benefit agriculture, the second smallest sector,
and hence have scarce impact (1% of the total), mining’s outflows benefit services
and constitute around 9% of the total spillover.
14If a sector sends large knowledge flows to sectors experiencing little demand, the final weighted
spillover will be of little importance to the overall economy. In contrast, the overall importance of
a small knowledge flow received by a high-demand sector will be large.
Knowledge Spillovers and TFP Growth Rates 14
These results show that knowledge outflows are concentrated in manufacturing and
trade & transportation. Other sectors are basically receivers of knowledge, generating
little or no learning for the economy.
Comparison
It is instructive to compare these results with previous estimates. Bernstein (1988)
estimated spillovers generated by R&D capital (physical and human) and their private
and social rates of return for seven Canadian two-digit SIC industries from 1978
through 1981. He found that intra- and inter-sectoral spillovers do affect production
costs and the structure of production; he also computed the wedge between private
and social rates of return to the spillover-generating input. The first three columns
of Table 3 show that his results and my estimations coincide broadly. Bernstein uses
industries at a more disaggregate level, which partly explains why the value of his
total sectoral spillovers is below 0.2. See Section 4 for comment on column four.
[Insert Table 3 here]
Van Stel and Nieuwenhuijsen (2004) use data for six macroeconomic sectors for the
Netherlands from 1987 to 1995 and, assuming geographical proximity as a necessary
condition, find that inter-sectoral knowledge spillovers are particularly important in
their service sector (trade, transport & communication, financial services), whereas
local competition is particularly important in the industry sector (manufacturing and
construction). High extents of diversity seem to encourage spillovers from industry
sectors towards service sectors. The fact that the service sector is the leader in
generating knowledge spillovers could arguably be due to the fact that their time
period does not include the productivity slowdown of the early seventies.
Thus, comparable estimates corroborate the existence of both intra- and inter-
sectoral spillovers and their effect on resource allocation and production costs.
Knowledge Spillovers and TFP Growth Rates 15
4HowInefficient Is the Market?
Given these knowledge spillovers, the market does not allocate quality-adjusted labor
among sectors optimally. The wedge between social and private rates of return to
labor is reflected in the sectoral residuals via the knowledge spillovers. The market
inefficiency, formalized in Proposition 1, is reflected in Table 2. This table presents
also the relative sectoral allocation of the inputs that do not generate spillovers,
capital and intermediates, for which the market solution is already optimal.
The second part of Table 2 shows it would be optimal to increase the market’s
allocation of labor to manufacturing, trade & transportation, and mining. As per
Proposition 1 it is optimal to increase labor input in sectors for which relative knowl-
edge emission is above labor market share, Γi
Q>Lc
i
L. This happens in manufacturing
(0.45 >0.30), trade & transportation (0.46 >0.27), and mining (0.08 >0.02). Thus,
it is optimal to increase labor input in manufacturing by 20% so this sector goes from
employing 30% of total labor in the competitive solution to 36% in the optimal solu-
tion, maintaining its position as the largest employer in the economy and increasing
its output by 12%. Likewise, it is optimal to increase employment in trade & trans-
portation by 27%, so this sector increases its share of total labor employment from
27% to 34%, becoming the second employer in an efficient economy and increasing
its output by 16%.
Mining is such a small sector that its optimal 144% increase in employment and
29% in output have minimal impact on the overall efficiency gap. Optimal labor and
output in all other sectors including construction, a spillover generating sector, and
services, the second largest sector in the economy, are below market levels.
As a result, optimal wages are above (below) market rates in all sectors where op-
timal employment is below (above) market, except for manufacturing, where optimal
employment and wage rates are both above market, the reason being that manu-
facturing is the only sector learning from itself, hence an optimal increase in labor
Knowledge Spillovers and TFP Growth Rates 16
also leads to an optimal increase in wages.15 Thus it is optimal to increase wages in
manufacturing by 54% and decrease them in trade & transportation by 12%.
These results can be compared to those obtained by Bernstein (1988) and shown
in the last column of Table 3. Not only does he find that spillovers create a wedge
between the private and the social rates of return to the spillover-generating input,
but his social-to-private ratio for all seven Canadian industries is substantially higher
than mine for the whole of manufacturing.16
Summarizing, it would be optimal to redistribute quality-adjusted labor into man-
ufacturing, trade & transportation, and mining and away from all other sectors. As
a consequence output in these sectors would increase, and wages in manufacturing,
the only sector learning from its own productive experience; construction; services;
andagriculturewouldalsoincrease.
5 The Seventies Slowdown: a Shift in Spillovers?
The productivity slowdown of the early seventies has been attributed to a large num-
ber of competing reasons. Explanations range from the reduction in real company
financed R&D (Scherer 1984) to the incorrect measurement of output, particularly in
services (Corrado and Slifman 1999), to an increase in the underlying rate of techno-
logical change (Greenwood and Yorukoglu 1997). Jorgenson, Gollop, and Fraumeni
(1987), and Jorgenson, Ho, and Fraumeni (1994) attribute the slowdown to the stag-
nation of the growth in the quality of human capital derived from formal education,
which would, in this model, reduce the magnitude of knowledge spillovers.
15Remember that relative optimal-to-market wages are ws
i
wc=³1+ γii
βiL ´Ys
1/Y c
1
Ls
i/Lc
i, therefore as long
as sector iexhibits some degree of learning-by-doing (i.e. γii >0), productivity in real terms for
sector iwill be larger in the optimal allocation of labor.
16A larger propensity to invest in R&D capital unambiguously leads to high intra-industry
spillovers, which account for most of the wedge between social and private rates of return. Whereas
investing in high-quality human capital (i.e. shifting the composition of the labor input toward higher
marginal productivity workers) does lead to larger intra-sectoral spillovers, γii, but the upward im-
pact on the social rate is dampened by the simultaneous downward pressure of higher elasticities,
βiL.
Knowledge Spillovers and TFP Growth Rates 17
Alternatively, we can inquire whether the slowdown is associated with changes in
the creation and/or the absorption of knowledge. That is, whether sectoral spillovers
shifted after 1973. To that purpose, I split data into a pre-73 and a post-73 period
and calibrate learning parameters independently for each period. The results are
presented in Table 4.
[Insert Table 4 here]
After 1973, manufacturing’s demand is offby 6 percentage points (from 44% of
total demand to 38%), whereas services’ grows by 9 points (from 21% to 30% of
total demand); the remaining sectors’ relative demand variations are, overall, negligi-
ble. Moreover, manufacturing’s importance as a source and destination of knowledge
diminishes. The number of manufacturing’s knowledge outflows into the economy de-
crease: from mining and construction prior to the slowdown to only services after it.
On the contrary, post-73 trade & transportation emerges as the source of knowledge
outflows: all sectors except services and agriculture derive the totality of spillovers
from trade & transportation. In particular, mining and construction have entirely
switched the source of their inflows from manufacturing to trade & transportation.
In addition, not only is post-slowdown trade & transportation the only sector to learn
from itself: it learns only from itself.
Post-73 services and construction lose their capacity to generate knowledge, but
services experiences a relative gain in learning capabilities; it diversifies its inflow
sources. Prior to 1973 services only learned from trade & transportation; post-73 it
absorbs knowledge from manufacturing and mining, although not from itself.
In summary, after the slowdown the number and relative weight of sector-specific
spillovers in the total diminish in favor of inter-sectoral knowledge flows. The indus-
trial sector, in particular manufacturing, lose importance in favor of trade & trans-
portation as the source of knowledge for the overall economy, to the point where
industry becomes completely dependent on trade & transportation for its knowledge
Knowledge Spillovers and TFP Growth Rates 18
inflows.17 Specifically, after 1973, manufacturing’s sector-specific spillovers disappear,
whereas trade & transportation only learns from itself.
Table 5 compares the relative weight of a sector’s total spillover in the overall
economy, as well as the importance of each sector’s knowledge outflows to the rest of
the economy before and after 1973.
[Insert Table 5 here]
Prior to the slowdown construction is the main generator of knowledge (34% of
the total), followed by manufacturing and trade & transportation (26% and 23%)
and, at a distance, by services (17%). After 1973 trade & transportation alone emits
over two thirds of all spillovers, whereas manufacturing’s share falls to 23%, and the
importance of construction and services fades altogether. Mining emerges as a new
source of spillovers.
Post-1973, the weight of construction and services as a source of spillovers for
other sectors also disappears. On the contrary, manufacturing appears to integrate
with the rest of the economy and its 31% contribution takes second place to trade &
transportation’s 59%. Mining is the third sector to benefit other sectors with 10% of
the total inter-sectoral spillover.
The second part of Table 5 shows the change in the efficiency gap before and after
1973. To begin with, employment decreases in manufacturing and increases in services
in both the competitive and the optimal solution. But, whereas after 1973 the market
assigns less labor to manufacturing than to services, it is still optimal to keep more
employment in manufacturing than in services because 67% of services knowledge
inflows originate in manufacturing (while no knowledge originates in services), and
post-73 services is the only sector in the economy that has grown substantially.
As for trade & transportation, after 1973 the market and the planner pull in
opposite directions: while the market reduces the amount of labor input it allocates
17These results predate what McKinsey Global Institute (2001) found with regards to the U.S.
productivity jump that began in 1995.
Knowledge Spillovers and TFP Growth Rates 19
to this sector, it is optimal to increase it by 16 percentage points, making it the largest
employer in the economy (42% of all labor input) and reversing the optimal-to-market
labor ratio from a reduction of 8% prior to 1973 to an increase of 70% after (which
results in a 39% increase in this sector’s output). This is because the relative amount
of knowledge trade & transportation generates for the overall economy trebles up to
68% after 1973.
The market does not alter its labor allocation in mining, construction, and agri-
culture significantly after 1973, but the planner increases labor in mining and reduces
it in agriculture and, especially, construction. This is because post-73 mining is gen-
erating knowledge for services, while spillovers generated by construction no longer
benefit manufacturing and construction itself, but only agriculture.
Regarding wages, the optimal-to-market gap in manufacturing decreases by 37
percentage points to 1.25 after 1973 as a consequence of the loss of sector-specific
learning. Construction also ceases learning from itself after the slowdown, but the
reversal in the optimal-to-market employment gap more than compensates for this
loss, setting optimal wages 81% above market. The exact opposite happens in trade
& transportation that, after 1973, only learns from itself but where the reversal in
the optimal-to-market employment gap results in optimal wages 11% below market.
As for mining, the optimal increase in employment is so large (184%) that it pushes
optimal wages to 60% below market.
In summary, after the slowdown inter-sectoral knowledge flows gain relative im-
portance. Simultaneously, the industrial sector in general, and manufacturing in par-
ticular, lose importance in favor of trade & transportation as the source of knowledge
for the overall economy. Moreover, manufacturing’s learning capability diminishes
and this sector stops cumulating knowledge derived from its own innovation and
productive processes. On the contrary, trade & transportation begins applying fun-
damentally new processes and technologies in the delivery of products and services,
which requires more skills from its workers, who move on to steeper learning curves
Knowledge Spillovers and TFP Growth Rates 20
and become the new source of knowledge for the overall economy. As a result, it is
optimal to have trade & transportation be the main employer in the post-73 economy.
6Conclusions
While there is no agreement on the exact source and form of externalities, its impor-
tance for economic growth and business cycles has been accepted; constant returns do
a poor job replicating reality. Moreover, previous empirical work has found evidence
on the existence of external economies operating at the national level.
In this paper I use quality-adjusted data on inputs and output at the industry
level to estimate labor generated knowledge spillovers within and across industries.
The purpose is to shed some light on whether knowledge diffuses across sectors when
one firm’s productive experience may enhance other firms’ efficiency as well as its
own. The source of TFP growth or productivity gains at the aggregate level is, thus,
the existence of learning by observing as well as learning by doing, along the lines of
Arrow (1962) and Lucas (1988).
To this purpose I establish a method to compute the learning parameters that
characterize a Cobb-Douglas production function in which the employment schedule
or sectoral structure of the economy determines productivity in each industry.
Ifind that from 1948 to 1991 the manufacturing and trade & transportation
sectors were the undisputed engines of growth for the U.S., generating knowledge for
the overall economy. I also find that there is indeed a wedge between how the market
allocates and rewards labor and the optimal, which disagrees with some recent stream
of literature concerning geographically localized spillovers. That is, economywide
market wages do not absorb the totality of the costless productivity gains generated
by the spillovers. Thus, the market allocates resources inefficiently: more labor should
go to sectors generating knowledge for the whole economy, so that quality-adjusted
employment in manufacturing would increase by 20% and in trade & transportation
Knowledge Spillovers and TFP Growth Rates 21
by 27%. As a consequence, output in manufacturing would go up by 12% and in
trade & transportation by 16%. Wages in all sectors, except for mining and trade &
transportation, ought to increase by, at least, 54%, with workers in agriculture and
services perceiving wages 86% above market.
Furthermore, the productivity slowdown of the early seventies coincides with a
change in the pattern of generation and diffusion of knowledge. After 1973, manufac-
turing ceases learning from itself and integrates with the rest of the economy, whereas
trade & transportation goes on to learn only from itself. Morevoer, the capability
of manufacturing to generate knowledge wanes, while trade & transportation comes
to generate over two thirds of the knowledge flows benefitting the overall economy.
Simultaneously, the slowdown is associated with a decrease in the relative importance
of spillovers within sectors in favor of spillovers between sectors.
The proposed framework can be extended to a dynamic setup that takes into
account forward-looking decisions on investment in physical or human capital. The
results presented here are encouraging about the feasibility of these extensions in
future research.
Knowledge Spillovers and TFP Growth Rates 22
Appendix
A1. Industry Classification
The following Table presents the equivalence between the original 35-sector classification
used by D. Jorgenson, the SIC (1987), and the six-sector classification used in this model.
Note sector 35, Government Enterprises, has been eliminated from the final selection.
D. Jorgenson SIC (1987) Model
1Agriculture,fisheries and forestry 01, 02, 07, 08, 09 A
2 Metal mining 10 N
3Coalmining 12 N
4 Oil and gas extraction 13 N
5 Non-metallic mining 14 N
6 Construction 15, 16, 17 C
7 Food and kindred products 20 M
8 Tobacco 21 M
9 Textile mill products 22 less 225 M
10 Apparel 23, 225 M
11 Lumber and wood 24 less 2451 M
12 Furniture and fixtures 25 M
13 Paper and allied 26 M
14 Printing, publishing and allied 27 M
15 Chemicals 28 less 282 M
16 Petroleum and coal products 29 M
17 Rubber and misc plastics 30,282 M
18 Leather 31 M
19 Stone, clay, glass 32 M
20 Primary metal 33 M
21 Fabricated metal 34 less 348 M
22 Machinery, non-electical 35 M
23 Electrical machinery 36 M
24 Motor vehicles 371 M
25 Transportation equipment & ordnance 348, 2451, 37 less 371 M
26 Instruments 38 M
27 Miscellaneous manufacturing 39 M
28 Transportation 40 to 47 less 43 T
29 Communications 48 S
30 Electric utilities 491 S
31 Gas utilities 492 S
32 Trade (retail and wholesale) 50 to 59 T
33 Finance, insurance, and real estate (FIRE) 60 to 67 S
34 Services 70 to 89 S
35 Government enterprises 91 to 99, plus 43 -
Knowledge Spillovers and TFP Growth Rates 23
A2. Computation Procedure
In order to recover the learning parameters I follow a strategy that assumes constant returns
to scale and perfect competition, and that stems directly from the relationship between rates
of growth implied by the production function:
˙
Yi=βiK ˙
Ki+βiL ˙
Li+βiM ˙
Mi+
n
X
j=1
γij ˙
Lj
where ˙
Y,˙
K,˙
L,and ˙
Mare, respectively, the growth rates of the index quantities of output,
physical capital, labor inputs, and intermediate inputs.
To compute sectoral productivity growth rates I use the Tornqvist index, a discrete-time
approximation to the Divisia index:
˙
θi=˙
Yi−SiK ˙
Ki−SiL ˙
Li−SiM ˙
Mi,
where ˙
θiis the growth rate of TFP for sector iin terms of the differences of natural
logarithms, and SiK,SiL,andSiM are the average between-period cost-shares and output
elasticities of each input. Thus, we can rewrite this equation as:
˙
θi=
n
X
j=1
γij ˙
Lj,
that is, actual (observed) productivity growth equals productivity growth predicted by the
model’s production function. The variation of the residual associated to sector iis the
sumofeachsector’svariationinemploymentweightedbysectori’s learning parameters or
absorptive capacity. It measures the cos tless gains to sector ifrom the overall employment
scheme. Hence, the residual is not a non-parametric estimation of a fixed parameter of the
production function, but the reflection of a process.
To recover the learning parameters I minimize the distance between predicted and ob-
served TFP growth, subject to the calibrated values of qiand to a non-negativity constraint.
The problem is then to choose parameters γi1,γi2,...,γin,∀i=1,2,...,n,to
min
t
X
t=1
⎡
⎣˙
θit −
n
X
j=1
γij ˙
Ljt⎤
⎦
2
,
subject to
qi=
n
X
j=1
γij and γij ≥0,∀i, j.
Each coefficient will measure how much productive knowledge flows within or between
sectors, given the sectoral allocation of labor.18
18Because Aiis time-invariant it is absent in the right hand side of the equation relating actual
and predicted productivity growth. In consequence, these are non-intercept estimations and the R-
square statistic does not produce valuable information about goodness of fit: the sum of the squared
errors may exceed the total sum of squares (Casella 1983, Kvalseth 1985).
Knowledge Spillovers and TFP Growth Rates 24
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Knowledge Spillovers and TFP Growth Rates 27
Table 1: Calibrated Parameters, 1948-1991
Parameter Value Target
i=MNC S T A
Consumers’ Preferences
αi0.41 0.03 0.08 0.24 0.18 0.05 Yi/Y
Technology
βiK 0.09 0.36 0.08 0.26 0.15 0.15
βiL 0.25 0.23 0.37 0.39 0.51 0.27 wxiXi/PiYi,
βiM 0.65 0.41 0.55 0.34 0.34 0.58 X=K, L, M
Spillovers
qi0.30 0.20 0.10 0.25 0.15 0.05 Literature
Learning Parametersa
j=
γij/qi
⎧
⎪
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎪
⎩
M
N
C
S
T
A
0.55
0
0
0
0.45
0
0
0
0
0
1.00
0
1.00
0
0
0
0
0
0
0.30
0
0
0.70
0
1.00
0
0
0
0
0
0
0
1.00
0
0
0
⎫
⎪
⎪
⎪
⎪
⎪
⎬
⎪
⎪
⎪
⎪
⎪
⎭
˙
θi
a. Rows are sectors of origin j, columns are sectors of destination i.
i, j =M, N,C,S,T, A, where M=manufacturing; N=mining; C=construction; S=services;
T=trade & transportation; and A=agriculture.
Knowledge Spillovers and TFP Growth Rates 28
Table 2: Market Inefficiency, 1948-1991
MN C S T A
Relative Spillover Emission: Total and Inter-Sectoral
Γi/Q0.45 0.08 0.01 0 0.46 0
˜
Γi/˜
Q0.27 0.09 0.01 0 0.63 0
Market and Optimal Solutionsa
Lc
i/L0.30 0.02 0.09 0.28 0.27 0.04
Ls
i/L0.36 0.04 0.06 0.17 0.34 0.02
Ls
i/Lc
i1.20 2.44 0.65 0.60 1.27 0.60
Ys
i/Yc
i1.12 1.29 0.87 0.91 1.16 0.85
ws
i/wc1.54 0.46 1.72 1.86 0.88 1.86
Common to Market and Optimal Solutions
Ki/K0.25 0.06 0.04 0.42 0.18 0.05
Mi/M0.53 0.02 0.09 0.17 0.12 0.06
a. Manufacturing is the numeraire.
Table 3: Bernstein’s Knowledge Spillovers for Canada, 1978-1981
Knowledge Spillovers Social to Private
Sector of Intra-sec. Inter-sec. Total Rates of Returna
Destination (i)γii/qiPγij /qiqiωs
i/ωc=1+qi/ωc
Chemical Products 0.84 0.16 0.148 2.27
Electrical Products 0.84 0.16 0.141 2.22
Aircraft & Parts 0.81 0.19 0.114 1.98
Pulp & Paper 0.81 0.19 0.088 1.76
Metal Fabricating 0.75 0.25 0.086 1.74
Food & Beverage 0.77 0.23 0.084 1.72
Non-electrical Machinery 0.71 0.29 0.077 1.66
a. ωc=0.1162 for all industries.
Knowledge Spillovers and TFP Growth Rates 29
Table 4: Calibrated Parameters, Pre- and Post-1973
Param. Value
i=MN C S T A
Pre Post Pre Post Pre Post Pre Post Pre Post Pre Post
Consumers’ Preferences
αi0.44 0.38 0.02 0.03 0.09 0.08 0.21 0.30 0.19 0.18 0.06 0.04
Technology
βiK 0.10 0.09 0.36 0.36 0.07 0.08 0.29 0.23 0.16 0.13 0.14 0.17
βiL 0.26 0.24 0.24 0.22 0.36 0.39 0.39 0.39 0.54 0.47 0.29 0.24
βiM 0.64 0.67 0.40 0.42 0.57 0.53 0.32 0.38 0.30 0.39 0.57 0.59
Spillovers
qi0.30 0.30 0.20 0.20 0.10 0.10 0.25 0.25 0.15 0.15 0.05 0.05
Learning Parametersa
j=
M0.39 0100.49 000.67 0000
N00000000.33 0000
γij/qiC0.33 0000.51 0001001
S0.27 00000000010
T010101100100
A000000000000
a. Rows are sectors of origin j, columns are sectors of destination i.
i, j =M, N,C,S,T, A, where M=manufacturing; N=mining; C=construction;
S=services; T=trade & transportation; and A=agriculture.
Knowledge Spillovers and TFP Growth Rates 30
Table 5: Sectoral Spillovers and Input Allocation, Pre- and Post-1973
MN C S T A
Pre Post Pre Post Pre Post Pre Post Pre Post Pre Post
Relative Emission of Spillovers: Total and Inter-Sectoral
Γi/Q0.26 0.23 00.09 0.34 00.17 00.23 0.68 00
˜
Γi/˜
Q0.06 0.31 00.10 0.40 0.01 0.24 00.30 0.59 00
Market and Optimal Solutionsa
Lc
i/L0.33 0.27 0.02 0.02 0.09 0.09 0.23 0.35 0.29 0.25 0.05 0.03
Ls
i/L0.30 0.25 0.01 0.05 0.19 0.06 0.20 0.21 0.26 0.42 0.03 0.02
Ls
i/Lc
i0.91 0.92 0.61 2.84 2.04 0.63 0.89 0.60 0.92 1.70 0.64 0.60
Ys
i/Yc
i1.03 1.15 0.87 1.40 1.33 0.88 0.94 0.88 1.06 1.39 0.88 0.86
ws
i/wc1.62 1.25 1.71 0.40 0.58 1.81 1.16 1.93 1.13 0.89 1.61 1.93
Common to Market and Optimal Solutions
Ki/K0.28 0.23 0.06 0.07 0.04 0.04 0.38 0.46 0.19 0.16 0.05 0.04
Mi/M0.56 0.49 0.02 0.02 0.10 0.08 0.13 0.22 0.11 0.14 0.07 0.05
a. Manufacturing is the numeraire.
