Productivity Spillovers Across Firms through Worker Mobility
Andrey Stoyanov and Nikolay Zubanov
February 3, 2011
Abstract
We study productivity spillovers through worker mobility between Danish firms, by linking the
receiving firm’s productivity one year after it hired new workers to the gap between the sending
firms’ and own productivity one year before. Consistent with the spillover hypothesis, we find a
positive effect of the gap on the receiving firm’s productivity when the gap is positive, and zero
effect when the gap is negative. Surviving a variety of statistical controls, this effect increases with
education and skill level of hired workers, persists for several years after the hiring was done, and
remains broadly similar for different industries and measures of productivity. Explanations for this
effect other than spillovers are discussed and ruled out.
Key Words: Productivity spillovers, worker mobility, matched employer-employee data
1
1
Introduction
Although knowledge spillovers, whereby firms improve their performance through learning from each
other, have attracted considerable attention, the mechanisms behind them are little known. Earlier
empirical studies proposed that patent citations facilitated spillovers (Jaffe, Trajtenberg, and Henderson, 1993; Hall, Jaffe, and Trajtenberg, 2001). This mechanism, however, cannot be the only one at
work, or even the most important one, since patenting is practiced by relatively few innovating firms
and excludes a wealth of uncodified knowledge, for example management practices. More recent studies focussed on employee turnover as an alternative mechanism (Song, Almeida, and Wu, 2003; Kim
and Marschke, 2005). Besides being far more widely observed than patent citations, employee turnover
is more likely to explain spillovers from large to small (more to less productive) firms, understanding
which is important for the development and calibration of modern endogenous growth models with
heterogeneous firms (Eeckhout and Jovanovic, 2002; Luttmer, 2007; Atkeson and Burstein, 2010).
That new workers have been relied upon as a source of knowledge is evident as firms try to
prevent their former employees from being hired elsewhere. For instance, many firms add non-compete
covenants (NCCs) in their contracts with workers, resulting in a number of court cases dealing with
their violations.1 Where NCCs cannot be enforced in court, as in California or North Dakota, firms
sue their former employees for disclosing trade secrets, even though trade secret law violations are
harder than NCCs to detect and prosecute. One prominent case is that of Hewlett-Packard (HP)
versus its former CEO Mark Hurd, in which the plaintiff has sought injunction to prevent Hurd taking
up employment with Oracle, HP’s competitor (The Economist, September 8th, 2010), on the grounds
that he cannot do his work without necessarily revealing HP’s trade secrets. At the same time, one
often observes firms poaching employees from competitors, to try to benefit from their knowledge.
Thus, poaching among Silicon Valley firms became so intense that Adobe Systems, Apple, Google,
Intel Corporation, Intuit, and Pixar agreed in 2009 not to approach each other’s employees, even at
the risk of violating the U.S. competition law.
The above examples suggest significant gains to be made from applying other firms’ knowledge
brought in by their former employees. In this study, we attempt to estimate the value of this knowledge
in terms of productivity gains by the receiving firms. (We therefore use the terms knowledge spillovers
1
Siegel, Brill, Greupner, Duffy & Foster (http://www.siegelbrill.com), a law firm based in Minnesota, lists fifty-six
non-compete cases heard in Minnesota courts alone during 2000-2008.
2
and productivity spillovers interchangeably.) The first indication of productivity spillovers through
employee turnover from our data is a positive correlation between the productivities of the sending
and receiving firms. Denoting t the year in which a job changer left his old firm and joined a new firm,
the correlation between the total factor productivity (TFP) in the new firm in t + 1 (one year after the
move) and that in the old firm in t − 1 (one year before the move) is 0.15. Workers moving between
similarly productive firms can hardly explain this correlation, since in year t − 1, when the leaver still
worked in the old firm, the contemporaneous correlation between the old and new firms’ TFP was just
0.05. That this correlation is high when workers move from more to less productive firms (0.214), and
low otherwise (0.097), further points to spillovers and suggests that less productive firms benefit from
more productive ones, while the performance of the more productive firms is unaffected.
Additionally, if job changers spread knowledge from more to less productive firms, one would expect
a more concentrated productivity distribution in industries with higher rates of worker movement
from more to less productive firms. In Figure 1 we plot the relationship between the TFP variance
in twenty-one two-digit NACE industries and the 1995-2007 average turnover rate from top 40% to
bottom 40% of firms (red dots) and from top quartile to bottom quartile (black dots). There is a
strong negative correlation between worker turnover and TFP dispersion, −0.45 for the top to bottom
40% and −0.58 for the top to bottom quartile, which confirms our expectations. Moreover, that this
correlation becomes stronger as we increase the productivity gap between sending and receiving firms
suggests that productivity spillovers are a function of this gap – an insight we use for developing our
empirical model in section 3.
The remainder of this paper elaborates on the correlation between the receiving firm’s productivity
in year t + 1 and the productivity gap between the sending and receiving firms in year t − 1. We add
various controls to rule out explanations for this correlation other than productivity spillovers, and
explore conditions under which it is expected to increase or decrease. One of such conditions has to do
with heterogeneous effect of productivity gap. If there is learning by less productive firms from more
productive, one would expect the correlation between the gap and productivity of the receiving firm to
be positive when the gap is positive. At the same time, we would expect this correlation to be zero or
insignificant when the gap is negative, since the knowledge brought in by workers from less productive
firms cannot adversely affect the receiving firm. Both of these expectations are confirmed. Other
conditions affecting the strength of productivity spillovers that we consider are common technology
and education and skills of job movers. We propose that the knowledge transferred by job movers is
3
to a large extent specific to a particular technology operating in a given industry, and find spillover
effect within the same industry to be larger than when workers move between industries. We also find
as expected that spillover effects are enhanced by education and skills of new hires, though even the
least skilled workers are capable of bringing useful knowledge.
In our analysis, we strengthen the case for productivity spillovers through employee turnover by
ruling out alternative explanations to our statistical results. For instance, one might question the
spillover interpretation of our findings, proposing instead that new workers’ human capital explains
the correlation between the gap and the receiving firm’s productivity. It is true that workers recruited
from more productive firms tend to have more human capital than the incumbent workers. However,
human capital transfer falls short of explaining the asymmetry in the effect of the gap on the receiving
firm’s productivity. Even then, we do allow for this alternative explanation to be borne out by the data,
by controlling for observed and unobserved parts of the workers’ human capital through a measure
developed in Abowd, Kramarz, and Margolis (1999), which is essentially the wage net of firm-specific
effects estimated from the wage equation.
Another alternative explanation to our findings relates to the difficulty of identifying spillover
effects, since receiving firms may hire workers from more productive sending firms, whom they can
now better afford, after experiencing a positive productivity shock in year t or t − 1. We present three
approaches to eliminating this alternative. First, as part of our baseline empirical model, we control
for the receiving firm’s productivity in t and t − 1; hence, we estimate average productivity effect of
the gap for equally productive receiving firms. Second, as an extension to the baseline specification,
we apply the estimator developed in Olley and Pakes (1996) which proxies productivity shocks by
capital investments. Finally, as another extension, we repeat our analysis on the subsample of “green
field” firms which did not exist in t − 1, and thus no productivity shock could have affected their hiring
choices. All approaches bring similar results to our baseline specification, suggesting that firms’ hiring
practices are little affected by past productivity shocks.
Our three most important findings are as follows. First, we find that, at the hiring rate of 10% of its
workforce (about sample average), the receiving firm gains 3.5% of the positive productivity gap and
about zero of the negative gap. For an average firm, this implies a productivity gain from spillovers of
0.84% a year. The asymmetry of the gap’s effect implies that productivity gains from spillovers will
accrue only when new workers come from firms having more knowledge factored in their productivity.
Second, the gap’s effect lasts at least five years, implying the long-run spillover effect from hiring even
4
larger than 0.84%. The persistence of the productivity gap’s effect suggests long-term consequences
of spillovers for receiving firms, and is also a novel finding. Finally, spillovers occur through hiring
even the least skilled workers, which implies that a substantial part of the knowledge transferred by
job movers is not particularly sophisticated and thus unlikely to be patented or otherwise codified.
Taking account of this knowledge, as we do in this this study, is therefore an important addition to
the R&D spillovers literature typically dealing with codified knowledge embodied in patents.
Our work’s contribution to the literature on spillovers goes beyond factual findings. Thus, our
unique data enable us to present what we believe is most detailed and robust empirical evidence to
date on the source of spillovers through employee turnover, and their size. We find a direct spillover
effect on the receiving firm’s productivity rather than on some indirect indicator of firm performance
such as the number of patents or R&D expenditure. Therefore, our results can be directly applied in
calibrating theoretical models of spillovers to analyze the effect of labor mobility on the distribution of
firm size, productivity, growth, and welfare. We identify a measure of the receiving firm’s exposure to
spillovers – the productivity gap – thus extending the relevant literature which has so far operated with
a 0 − 1 variable denoting experience at a foreign firm, or an aggregate thereof. The gap performs well
in our regressions, giving consistent results for various measures of it: value added, TFP, and profit.
Furthermore, our research widens the scope of the literature on spillovers through labor mobility, by
studying the spillovers of uncodified as well as codified knowledge happening between nearly all firms
in the Danish manufacturing sector. Our results are thus more widely applicable, while agreeing with
those reported in earlier studies.
The rest of the paper is organized as follows. In section 2, we take stock of the existing literature on
spillovers and identify directions in which we can contribute to it. The empirical model underlying our
study is outlined in section 3; therein we also discuss how we deal with the estimation issues involved in
identifying spillovers through employee turnover. Section 4 describes our data. The regression results
along with various extensions and robustness checks are presented in sections 5, 6 and 7. Section 8
concludes.
2
Literature review
It is commonly agreed that not all knowledge which benefits firm economic performance is generated
within a firm, but a large portion of it is acquired, or ‘spilled over’, from other firms. In the theoretical
5
literature, knowledge spillovers are often described as a major channel for economic growth (Romer,
1990, Grossman and Helpman, 1991). In particular, spillovers from old (large, more productive) to
new (small, less productive) firms is a central element of many recent models of endogenous growth
with heterogeneous firms (Eeckhout and Jovanovic, 2002; Atkeson and Burstein, 2010; Luttmer, 2007).
For instance, Luttmer (2007) relies on spillovers to “ensure that the technologies available to potential
entrants are never so far behind those of incumbent firms that entry of new firms is not feasible”
(p.1106).
The empirical literature on spillovers has developed in two directions. Studies within the first
direction found productivity spillovers within particular industries or geographical areas. Early work
on technological innovations (see Griliches, 1992, for a survey) showed that firms’ productivity depends positively on both its own R&D spending and on that of other firms in the same industry or
geographic area. More recent studies revealed that spillovers are not confined to R&D-intensive firms
and industries. Thus, the findings of Battu, Belfield, and Sloane (2003) and Martins and Jin (2010)
that worker wages grow with the average workforce education level in a firm, and of Moretti (2004)
that firms’ productivity increases with their region’s workforce average education level, indicate that
spillovers are in fact ubiquitous.
Another direction in the spillovers literature, to which our study also belongs, has looked into
mechanisms behind spillovers. Although historically the first spillovers mechanism proposed was
patent citations (Jaffe, Trajtenberg, and Henderson, 1993; Hall, Jaffe, and Trajtenberg, 2001), it is
employee turnover that fits the ubiquity of spillovers better. Maintaining a historic focus on innovation
activities, a number of studies have looked at R&D spillovers through turnover, and generally found
that hiring workers from firms actively engaged in R&D increases the same activity in their new firms.
Thus, Rao and Drazin (2002) establish that new firms with low rates of product innovation tend
to recruit workers from more established rival firms, which stimulates their own innovation activity.
Song, Almeida, and Wu (2003), looking at the patenting activities of firms in the U.S. semiconductor
industry, find that higher mobility of engineers within the sector is associated with increased citations
by their new employers of the patents of their previous employers. Kim and Marschke (2005) show with
a theoretical model and empirically that the risk of R&D workers moving to other firms reduces R&D
expenditure by their current employer and stimulates it to patent more in order to protect itself against
the possibility of knowledge duplication by the departing worker. Kaiser, Kongsted, and Thomas
(2008) show that R&D workers (defined as those with a university degree in science) coming from
6
firms with active patenting tend to increase patenting activity in their new firms. Maliranta, Mohnen,
and Rouvinen (2009) using Finnish matched employer-employee data, show that labor productivity,
profitability and average wages are all positively affected by hiring workers involved in R&D activities
at their previous firms. Theirs is one of the very few studies in this domain looking not at inputs,
such as R&D, but at performance outcomes as we do.
One common limitation of these studies is that only relatively few well-established firms are actively
engaged in R&D; hence, it is difficult to study productivity spillovers from large (more productive)
to small (less productive) firms by looking at the exchange of workers between such firms. Another
limitation is that, relying on R&D activities such as patenting as a measure of knowledge being
transferred, one will miss spillovers of uncodified knowledge which can also affect firm performance.
In fact, uncodified knowledge is likely to be more important economy-wide than its codified variety.2 A
more inclusive performance measure and a wider data sample are required to address these limitations.
The literature on spillovers from foreign to domestic firms has made good progress addressing
the above limitations. It is motivated by foreign-owned firms being more productive than domestic
firms and possessing superior technologies and business practices, a significant portion of which is
embedded in individuals and is thus transferable. Our approach echoes this literature in that we
too focus on spillovers from more to less productive firms. Notable studies in this field are Gorg
and Strobl (2005) who find that domestic businesses in Ghana managed by ex-employees of foreignowned companies tend to be more productive and less likely to exit the market, and Malchow-Moller,
Markusen, and Schjerning (2007) who develop a Melitz-type model of trade with heterogeneous firms
where ex-employees of (more productive) foreign firms transfer their knowledge to their new domestic
employers. Applying their model to Danish data, they show that workers with an experience in foreignowned firms enjoy a wage premium at domestic firms in return for this knowledge. Relatedly, Poole
(2009) finds a positive effect on wages paid in domestic firms in Brazil of the share of new workers
with an experience at foreign-owned firms. She identifies this effect as evidence of knowledge transfer
from foreign firms, since hiring workers with similar human capital but not previously employed at
foreign firms had no effect on wages. As Poole (2009), we also use a measure of human capital in the
spirit of Abowd, Kramarz, and Margolis (1999) to isolate spillover effects from those due to the new
workers’ human capital. (More detail on our implementation of this measure, and on our identification
2
For example, according to Duguet and MacGarvie (2005), 36% of French firms said they had obtained new technolo-
gies by hiring new employees, whereas only 17% learned from patents and licenses.
7
strategy in general, in the following section 3.)
Though closest to our research, the literature on foreign–domestic spillovers has important limitations as well. First, it uses a 0 − 1 variable denoting a new worker’s experience at a foreign firm (or an
aggregate thereof at the firm level), thus losing potentially useful variation of the amount of knowledge to be learned through hiring ex-foreign firm employees. Second, and relatedly, it concentrates on
foreign-owned companies as the source of spillovers, whereas domestic firms can produce spillovers as
well. We address both these limitations by looking at all firms in the economy, and by introducing a
measure of spillover as we explain in the next sections.
3
Empirical model
We estimate spillover effects from the relationship between the productivity level of the receiving firm
and the gap between the productivity of the sending and the receiving firms, including lags of receiving
firm’s productivity and additional controls (vector Y) which we will specify later. Thus, the initial
model looks as follows:
Ari,t+1 = α1 Ari,t + α2 Ari,t−1 + β · gapi,t−1 · Ii,t + Yi,t γ + εi,t+1 ,
(1)
where indices i, and t denote worker and year, respectively, Ar refers to a measure of the receiving
firm’s productivity, Ii,t is an indicator variable equal to 1 if worker i changes firm in year t and 0
otherwise, gapi,t−1 = Asi,t−1 − Ari,t−1 is the productivity gap between worker i’s previous and current
employers in year t − 13 , and εi,t+1 is the error term. Thus, if worker i did not change firms in year t,
equation (1) is just an AR(2) model; the extra term, gapi,t−1 , is added if she did.
The task is to estimate coefficient β in equation (1), which measures the average effect of productivity gap on the receiving firm’s productivity. However, the problem with estimating (1) is that its
dependent variable, Ari,t+1 is the same for all workers working in a given firm in a given year, while
part of the gap variable, Asi,t−1 , varies by worker. Ari,t+1 staying fixed within the same firm induces a
negative correlation between Asi,t−1 and the error term, because, all other regressors being fixed in a
3
Since we only have records of the worker’s employer at the end of the calendar year, the exact time of job transfer is
unknown, so we analyze the relationship between productivity of sending firm in year (t − 1) and that of the receiving
firm in year (t + 1) .
8
given firm and year, the error term and Asi,t−1 will be moving in opposite directions. Consequently,
the least squares estimate of β from (1) will be downward-biased.4
Still, β can be consistently estimated from a direct analogue of equation (1) specified at the firm
level (j indexes firms):
1
2
g j,t−1 + Xj,t γ1 + Ȳj,t
γ2 + Ȳj,t
γ3 + ε̄j,t+1 ,
Arj,t+1 = α1 Arj,t + α2 Arj,t−1 + β · gap
(2)
PNj,t
Ii,t (Asi,t−1 − Arj,t−1 )/Nj,t , Nj,t is the total number of workers in firm j in
PNj,t
1 =
year t, Xj,t is the set of firm characteristics, Ȳj,t
i=1 (1 − Ii,t ) Yi,t /Nj,t is a set of firm-average
PNj,t
2 =
characteristics of incumbent workers at period t, Ȳj,t
i=1 (Ii,t Yi,t ) /Nj,t is a set of firm-average
g j,t−1 =
where gap
i=1
characteristics of workers hired at year t, and Xj,t are firm-level characteristics. Note that the expresP j,t s
Hj,t
r
g j,t−1 = H
g j,t−1 in equation (2) can be rewritten as gap
sion for gap
i=1 (Ai,t−1 − Aj,t−1 )/Hj,t · Nj,t , where
g j,t−1 is the average productivity
Hj,t is the number of new workers hired by firm j in year t. That is, gap
gap weighed by the share of new workers. Intuitively, weighing by the share of new workers is needed
to account for the exposure of the receiving firm to new knowledge as measured by the sending firms’
productivity: the larger the share, the higher the exposure.
5
g j,t−1 is free
To take β as evidence for spillover effects from hiring, we must ensure that: (i) gap
from the effect of new workers’ human capital, and (ii) it does not pick up unobserved shocks to the
receiving firm’s productivity coinciding with hiring new workers. The first requirement is important
because a sending firm’s productivity and its workers’ human capital are likely to be correlated. Not
isolating this correlation could therefore confuse spillovers with human capital transfer, the two effects
having different nature and implications. To control for this correlation, we introduce a comprehensive
measure of workers’ human capital, including a variety of observed characteristics (age, gender, salary,
experience, education, professional status), as well as unobserved human capital. Our measure of
unobserved human capital, based on the work of Abowd, Kramarz, and Margolis (1999), uses workers
4
Consider a regression where the dependent variable is the same for all observations i from group j but the independent
variables vary by i and j: yj = xi,j β + ε (i). If the researcher is interested in the effect of the group average x̄j =
PNj
i=1 xi,j /Nj on y, estimating equation (i) will produce the wrong estimate, since the OLS estimate for β from this
equation is β̃ = (x0 x)−1 x0 y = (x0 x)−1 x̄0 y, whereas the correct estimate is β̂ = (x̄0 x̄)−1 x̄0 y.
5
Estimating equation (2) with the average gap not weighed by the share of new workers gives a lot less precisely
estimated regression coefficients (though still statistically significant), presumably because, unless controlled, the variation
in the degree of exposure to new knowledge among the receiving firms becomes part of the measurement error in the gap
variable.
9
movement across firms to identify the person-specific component θi from the wage equation:
wi,j,t = λ + xi,j,t β + θi + ψj + εi,j,t
(3)
Specifically, our measure of workers’ human capital in the receiving firm includes both observed and unobserved components and is calculated as the average of individual measures, hj,t = xi,j,t β + θi + εi,j,t =
1 PNj,t
i=1 (wi,j,t − λ − ψl ). Note that hj,t is free from firm-specific effects on wage (such as compenNj,t
sation policies or aggregate productivity), ψ, and hence is a good proxy for portable, rather than
firm-specific, human capital.
The second requirement concerning the validity of our procedure of estimating spillovers concerns
endogeneity of the productivity gap in equation (2). Namely, if a receiving firm j experiences a
positive productivity shock in year (t − 1) it may respond by hiring workers from more productive
firms who are likely to be of better quality and whom it can now better afford. Then, in addition to
g j,t−1 will carry firm j’s own productivity shock
the effect of sending firms’ average productivity, gap
in t − 1. We present three approaches to isolating this productivity shock. First, as part of our
baseline empirical model, we control for the receiving firm’s productivity in t and t − 1; hence, we
estimate average productivity effect of the gap for equally productive receiving firms. Second, as an
extension to the baseline specification, we apply the estimator developed in Olley and Pakes (1996)
which proxies productivity shocks by capital investments (results presented in section 7.2). Lastly,
as another extension, we repeat our analysis on the subsample of “green field” firms which did not
exist in t − 1, and thus no productivity shock could have affected their hiring choices. The results
for new firms are reported in section 6.4. All three approaches produce similar results, implying that
the productivity gap’s effect on which we base our main story cannot be explained by unobserved
productivity shocks.
4
Data
The key features of our data, provided by Statistics Denmark, are nearly total coverage of employees
and firms, and the match between the employee and firm records. Both these features makes these
data particularly suitable for our purposes. We use manufacturing firm-level data from 1995 to 2007
which include sales, employment, value added, materials and energy input, profit, fixed assets stock
and investments, and the two-digit NACE industry identifier. A large part of firm-level data comes
10
from annual surveys in which all firms employing fifty or more workers must participate. For smaller
firms, the data are interpolated and therefore are less reliable. The individual-level data are available
from 1983 onwards and cover all individuals aged fifteen to sixty-five and include salary (if applicable),
age, gender, experience in thousands of hours, highest completed education, and occupation. In the
analysis that follows, we only include manufacturing employees with a positive annual salary. All
individuals with multiple jobs are treated as different. Educational attainment is measured in three
levels: high school, college, and university. The occupation variable consists of three categories: lowskilled and skilled workers, and managers. The employment record is as of the end of the calendar
year, so if a worker changed job we only observe the year in which it happened.
The dependent variable in most of our analysis is firm’s productivity measured as value added per
worker weighted by firm’s average wage relative to the industry average. This weighing is applied
to control for differences in productivities which originate from differences in labor quality across
firms and are reflected in workers average compensation. In addition to applying weights to our
main productivity measure, we also include various measures of workers’ human capital in regression
specifications as extra controls for human capital effects. Furthermore, in Section 7.5 we try several
alternative measures of productivity (to which weighing is not applied), and obtain similar results.
Table 1 lists descriptive statistics measured at the worker level. Between 1995 and 2007 there are
about 5.8 million worker-year observations, of which 668,034 are job changers, implying an average
hiring rate of 11.5%. The average job stayer is 39.6 years of age and has 14.7 years of experience.
The majority of stayers have a (technical) college degree (49.8%), 12.2% have a university degree, and
38% a high school diploma. Most are classified as skilled (65.4%) followed by less skilled (25.5%) and
managers (9.2%). In comparison, the average job changer is 2.7 years younger and has half a year less
experience. He is more likely than a job stayer to be a skilled worker (71.8% vs. 65.4%) and to have
completed an education beyond high school (64.3% vs. 62%). There is no difference in the average
productivity of the job changer’s previous and new firm: both produced about 580,000 Krones worth
(= e6.36 ) of value added per worker per year. These averages, however, disguise a significant variation
in the productivity levels of the sending firms from which new workers are hired. Thus, for an average
receiving firm, 45% of new hires come from more productive firms (10% above market average) and
55% from less productive firms (9% below market average).
During the time period covered by our sample the wage of an average job stayer was 205,000
Danish Krones (= e12.23 ), or 27,000 Euro, per annum. The salary of an average job changer was 2%
11
below that, but those moving from more to less productive firms, as measured by value added per
worker, earned, on average, 3% extra. This wage premium is consistent with the idea that firms try to
attract workers from more productive firms by offering them higher salaries. Having said this, other
reasons such as higher quality of workers coming from more productive firms, as well as new employers’
characteristics, most notably larger firm size and per-workers value added, cannot be ruled out at this
point.
Table 2 shows summary statistics aggregated at the firm level. Productivity and wages averaged at
the firm level are lower than their respective averages at the worker level, as a result of smaller firms,
which weight in total observations is now greater, being less productive and paying less than larger
firms. Of the 173,929 firm-year observations in the sample, hiring took place in about half (85,123).
Size is the biggest difference between hiring and non-hiring firms: the hiring firms tend to be larger.
Another important difference is that hiring firms are more productive. As we wrote in section 3, the
productivity shock that might have caused the expansion of the hiring firms needs to be isolated for
the proper identification of spillovers. Table 2 gives a simple illustration of this shock.
5
Results
5.1
Baseline results
Table 3 reports the benchmark regression results for equation (2) estimated for all manufacturing firms
during 1995-2007. The dependent variable is firm productivity measured as value added per worker
weighted by firm’s average wage relative to the industry average (see section 4). Each specification
includes as controls the AR(2) lags of the receiving firm’s productivity, the average size of sending
firms, and year dummies. The estimates are consistent with our hypothesis of productivity spillovers
through worker turnover. For instance, the coefficient 0.199 in column (1) (the specification with no
additional controls) implies that, at the hiring rate of 10% of the total yearly headcount (close to the
sample average hiring rate of 10.6% per firm), the productivity gain of the receiving firm is 1.91% of
the average gap.
In the next three specifications, we include firm characteristics (column 2) followed by averages of
incumbent (column 3) and newly hired workers’ (column 4) characteristics.6 As a result, the estimate
6
The coefficient estimates for the control variables are skipped for brevity but are available on request.
12
for the effect of the gap goes down a little, to just under 0.18. One of the most important controls
here is the newly hired workers’ human capital measured as their wage net of firm-specific effects (see
section 3) and averaged at the firm level. One could argue that, because workers at more productive
firms tend to be more productive themselves, part of the positive effect of productivity gap is due to
the new workers’ human capital rather than knowledge transfer. We do indeed find that more human
capital of the new hires, as well as incumbent workers, is associated with higher productivity in the
receiving firms. Yet, since the inclusion of human capital is largely inconsequential for the estimate
of our interest, our conclusion is that this estimate measures the effect of knowledge transfer rather
than that of human capital. Telling between these two effects is important: while human capital, in
its portable part that we measure, is adequately priced on a competitive labor market, the transfer of
knowledge from one company to another is an externality which may require a policy response.
5.2
Spillovers from more and less productive firms
Our baseline specification (2) implies that the productivity effects are equal whether a worker is hired
from a more or a less productive firm. In other words, if a worker is hired from a 10% less productive
firm, the effect of the receiving firm’s productivity will be negative, and if another worker is hired
from a 10% more productive firm, the total effect will be zero. While it is possible, in principle, that
positive effects of new knowledge obtained from more productive firms will be offset by the costs of
training up workers from less productive firms, our human capital measures should account for the
latter effect. Hence, since there can be no negative learning, the effect of the gap should be positive
when the gap itself is positive, and zero when the gap is negative.
Consequently, in Table 4 we present the results for specification (4) where the averages are calculated separately for positive and negative productivity gaps:
g Pj,t−1 + βN · gap
gN
Arj,t+1 = α1 Arj,t + α2 Arj,t−1 + βP · gap
j,t−1
1 γ + Ȳ 2P γ
2N
+Xj,t γ1 + Ȳj,t
2
j,t 3P + Ȳj,t γ3N + ε̄j,t+1 ,
P
g j,t−1 =
where gap
PNj,t
i=1
N
g j,t−1 =
Ii,t Di,t (Asi,t−1 −Ari,t−1 )/Nj,t , gap
PNj,t
i=1
(4)
Ii,t (1 − Di,t ) (Asi,t−1 −Ari,t−1 )/Nj,t ,
and Di,t is an indicator variable equal to one if (Asi,t−1 −Ari,t−1 ) > 0.7 Note that in this specification we
control for new worker characteristics separately for those hired from more and less productive firms.
7
2P
2N
Variables Ȳj,t
and Ȳj,t
are defined similarly.
13
The results in column (1) confirm our expectations. The estimate for the negative productivity gap is
insignificant, implying that there are no gains from hiring workers from less productive firms, but no
losses either. The effect of hiring workers from more productive firms is 0.351, almost twice as high
as that estimated for the total gap (0.179). These two estimates are consistent with each other: since
45% (55%) of all job changers move from more (less) productive firms, the positive productivity effect
of hiring a worker from a more productive firm is mixed with the neutral effect of hiring a worker from
a less productive firm. As an extra extension to the results for the positive and negative productivity
gaps separately, we include their squares (column 2), to see whether the knowledge spillover effect
is getting stronger or weaker as the gap between sending and receiving firms widens. We find that
there is a second-order effect of the positive productivity gap, implying that gains from new knowledge
increase somewhat faster than the productivity gap. However, because this effect is only weakly significant and of small magnitude, we will not include it in further extensions presented in the following
section.
The main message from the results in Table 4 is that the effect we capture is not due to the sending
firm workers’ human capital, since it would have been symmetric otherwise. Another important
message is that hiring is beneficial as long as at least some new workers come from more productive
firms, even if the average productivity gap across all new hires is negative. To illustrate, with the
P
mean value of gg
ap equal to 2.4%, the estimate of βP = 0.35 implies that the effect of knowledge
transfer through labor turnover on productivity of an average receiving firm is 0.35 × 2.4% = 0.84
percentage points a year. In other words, a median firm would move to 51st centile if it were the only
one to hire workers from more productive firms.
6
6.1
Extensions
Spillovers within and between industry sectors
Knowledge can be general or specific to a particular firm or industry. Firm-specific knowledge does
not get transferred, and so cannot be part of the effect of the productivity gap. General knowledge,
while perfectly transferable, can be learned through many channels and does not require hiring workers
from more productive firms. Previous results suggest that knowledge coming with new hires is general
enough to be applied in different firms. In this section, we want to see whether, and to what extent,
14
this knowledge travels through technologies employed in different industries. Accordingly, we estimate
the effect of the productivity gap separately for workers hired from firms within the same two-digit
industry (NACE classification) and for those hired from outside, with the following equation:
f
g same
g dif
Arj,t+1 = α1 Arj,t + α2 Arj,t−1 + βdif f · gap
j,t−1 + βsame · gapj,t−1 +
1 γ + Ȳ 2 γ + ε̄
Xj,t γ1 + Ȳj,t
2
j,t+1
j,t 3
g same
where gap
j,t−1 =
PNj,t
i=1
same (As
r
g dif f
Ii,t
i,t−1 − Ai,t−1 )/Nj,t , gapj,t−1 =
PNj,t
i=1 (1
(5)
same )(As
r
− Ii,t
i,t−1 − Ai,t−1 )/Nj,t ,
same is an indicator variable which takes the value of one if worker i moved from one firm
and Ii,t
g same
to another in period t within the same two-digit industry, and zero otherwise. That is, gap
j,t−1 and
f
g dif
gap
j,t−1 are productivity gaps between the same and different industry sending firms and the receiving
firms weighed by their respective shares in the receiving firm’s workforce. Variables in Ȳ2 are also
redefined separately for the workers coming from within and outside the industry where the receiving
firm belongs. There are nine two-digit industries in the manufacturing sector, and 55% of all job
changes took place between firms operating in the same industry.
If knowledge transferred by new hires knows no technology borders, the coefficients β same and β dif f
should be equal. In fact, as Table 5 shows, the gap’s effect is much stronger when workers come from
the same industry. Breaking down both productivity gaps onto their positive and negative parts, in the
same way as in equation (4) (column 2), we find that only positive productivity gaps are significant,
implying, as before, that receiving firms learn useful knowledge from more productive sending firms,
while hiring workers from less productive firms brings no extra benefit or cost apart from their human
capital. That the effect of hiring workers from more productive firms within the same sector (0.33) is
about 60% larger than for workers from other sectors (0.21) implies that knowledge brought in by new
workers is in large part industry-specific. Hiring within the same industry thus brings more relevant
new knowledge than what can be learned from workers previously employed outside.
6.2
Spillovers by worker education and occupation
Previous research found differences in the ability of workers to transfer and apply new knowledge
depending on their occupation (Song, Almeida and Wu, 2003) and education (Kaiser, Kongsted and
Ronde, 2008). In this section, we apply insights from these studies to ascertain whether new hires’
education and occupation within their sending firms influence the strength of spillovers. Starting with
15
education, we classify the new workers’ educational attainment into three categories: high school,
college (or a comparable vocational degree), and university degree. We upgrade equation (2) by
including interactions between gap and education level dummies as follows:
g coll
g high
Arj,t+1 = α1 Arj,t + α2 Arj,t−1 + βhigh · gap
j,t−1 + βcoll · gapj,t−1 +
univ
1 γ + Ȳ 2 γ + ε̄
βuniv · gg
apj,t−1 + Xj,t γ1 + Ȳj,t
2
j,t+1
j,t 3
g kj,t−1 =
where gap
PNj,t
i=1
(6)
k (As
r
k
Ii,t
i,t−1 − Ai,t−1 )/Nj,t , k = {high school; college; university}, Ii,t is an
indicator variables which takes the value of one if worker i with education level k was hired by firm j
k
apj,t−1 is the average productivity of firms from where workers with education
in period t. Therefore, gg
level k were hired, weighed by their respective shares in total workforce. We also include in vector Ȳ2
firm average characteristics of new hires by level of education weighed by their shares in the receiving
firm’s workforce. If more educated workers can convey knowledge better, then we would expect βhigh <
βcoll < βuniv , meaning that higher educated workers will transfer more knowledge and hence will cover
a higher share of the productivity gap between their old and new employers.
Table 6 presents estimation results for equation (6). The effect of the productivity gap is stronger
for new workers with college or university degrees. For instance, for college graduates this effect is
75% greater than for high school graduates, and the effect for university graduates is more than 2.5
times as large. Even though the latter effect is estimated with high variance and is not significant
individually, there is a clear tendency for the spillover effects to increase with the level of education
of new workers. Breaking the productivity gaps by education level down to positive and negative
parts (column 2) shows the same tendency for the gap’s effect to grow with education and produces
larger estimates for the positive part of the gap. Thus, hiring 10% of the workforce from a 10% more
productive firm will raise productivity of the receiving firm by 0.54% if the new hires have university
degrees, and by about 0.28% if they have a college degree or a high school diploma. Workers coming
from less productive firms bring no new knowledge regardless of their education level.
Turning to differences in the efficiency of knowledge transfer by worker occupation in the sending
firm, we divide all workers into three categories: unskilled, skilled, and managers, and estimate the
following version of equation (2):
unskilled
g j,t−1
Arj,t+1 = α1 Arj,t + α2 Arj,t−1 + βunskilled · gap
manager
g j,t−1
βmanager · gap
k
apj,t−1 =
where gg
PNj,t
i=1
skilled
g j,t−1 +
+ βskilled · gap
1 γ + Ȳ 2 γ + ε̄
+ Xj,t γ1 + Ȳj,t
2
j,t+1
j,t 3
(7)
k (As
r
Ii,t
i,t−1 − Ai,t−1 )/Nj,t , k = {unskilled; skilled; manager} indicates worker’s
16
k is an indicator variables which takes the value of one if worker i’s occupation at the
occupation, Ii,t
new firm is k. Table 7 reports estimation results.
At the first glance (column 1), unskilled workers appear to be able to transfer knowledge just
as well as skilled workers, and only managers are more efficient at it than the rest. However, when
we look at the effects of occupation in knowledge transfer separately for more and less productive
sending firms (column 2), the estimates follow the same pattern as for education. If coming from
more productive firms, skilled workers can transfer knowledge 50% more efficiently than unskilled
workers, and managers are twice more efficient.8 As before, the effect of new workers coming from less
productive firms is statistically insignificant for all occupations.
In sum, the findings in this section demonstrate that productivity spillovers through labor mobility
are larger when new hires are more educated and more skilled as defined by their occupation, since
they had more opportunity to accumulate knowledge in their previous firms and apply it with their
new employers. These workers should therefore be more attractive to potential employers. However,
that even unskilled workers can transfer some valuable knowledge suggests that knowledge transferred
through hiring does not have to be of a particularly sophisticated nature and can consist, in part, of
relatively simple techniques and tricks. Since this knowledge is unlikely to be patented or otherwise
codified, labor turnover seems the most plausible and reliable mechanism of its transfer.
6.3
Spillover dynamics
As another extension to our baseline results, we study the persistence and duration of the productivity
gap’s effect on the receiving firm’s productivity. Estimates of specification (4) imply that hiring workers
from more productive firms today will raise productivity in the next year. Since firm’s productivity
is an autoregressive process, the effect of a one-off hiring will carry over a number of years through
the AR(2) terms and can be estimated from the impulse response function. For instance, given the
estimates for the AR(2) terms in equation (4), the implied impulse response estimates for the effect of
the positive productivity gap in year t − 1 on the productivity in years t + 2 to t + 5 are 0.168, 0.176,
0.130 and 0.110, respectively. However, this effect does not have to propagate exclusively through
autoregression and can have its own dynamics. In particular, if the gap’s effect is more persistent
8
As with the effect of university degree on spillovers, the coefficient βmanager has high variance and the effect is
therefore insignificant. The likely reason here is the relatively small number of managers among the job changers. Thus,
g manager was zero for 98% of observations.
the variable gap
17
than the AR(2) process for productivity in (4), the impulse response function will underestimate the
dynamics of productivity spillovers through hiring.
To gauge the persistency of the effect of productivity gap in period t − 1 on the receiving firm’s
productivity in periods t + 2 onwards, we estimate the following forecast equation
Arj,t+k
=
α1k Arj,t
+ α2k Arj,t−1
+
k−2
X
1 k
2 k
g j,t−1 + Xj,t γ1k + Ȳj,t
γ2 + Ȳj,t
γ3 + ε̄j,t+k , k > 1 (8)
δi Asj,t+i + β k gap
i=0
This method, also known as local projections (Jordà, 2005), is easy to implement and more robust
to possible dynamic misspecifications in the original regression equation that estimating from impulse
responses. Because the AR(2) terms in equation (8), Arj,t+k−1 and Arj,t+k− , are substituted recursively
for Arj,t and Arj,t−1 , the coefficient β k measures the total effect of the productivity gaps in t − 1 on the
productivity in t + k, both through autoregression and own dynamics. Specification (8) also includes
P
k−2
s
all leads of sending firms’ productivities
i=0 δi Aj,t+i to control for the regular spillover effects on
the receiving firm’s productivity in year t + k of sending firms’ productivity two year earlier.
The results are presented in Table 8. Moving the dependent variable forward in time in specification
(8) reduces the sample size due to firms’ exit. Therefore, for consistency, we estimate the dynamics
of productivity spillovers using only the subsample of firms with observations available for at least five
consecutive years. In the first two columns of Table 8, the estimated spillover effect is higher than
on the entire sample (Table 4), for instance, the positive gap’s effect is 0.536 compared to 0.351 in
Table 4. However, the subsample in Table 8 is also different from the entire sample in that it consists
of relatively long-lived firms which are bigger and more productive than average. As a result, the
average positive gap on this subsample is smaller, and the mean spillover effect is of about the same
magnitude as on the entire sample.
The results in Table 8 also show that much of the gap’s effect preserves for as long as six years
after a hiring is done. Consistent with our previous findings, this lasting effect rests on hiring workers
from more productive firms. For instance, the effect of hiring workers from more productive firms in
year t on productivity in years t + 2 to t + 5 is two to three times stronger than that implied by the
impulse response function alone. Hence, the knowledge brought in by new workers brings their new
firms sustained competitive advantage rather than a short-term productivity boost. Another, more
technical, implication of the persistence of the gap’s effect is that a large part of the spillover effect
applies to the receiving firm’s average productivity. Estimating this effect in isolation from other
18
firm-specific characteristics contributing to its average productivity is, therefore, difficult. Indeed, as
we find in section 7.3, the fixed effects estimator, using only the within-firm variation of gap in time,
gives a much lower estimate.
6.4
Spillover effects for new firms
In this section we look at the productivity spillover effect for startups, which will extend our results
in two ways. First, as was discussed in the introduction, knowledge spillovers through labor mobility
can present a valuable opportunity for small and less productive firms to learn from more successful
competitors. Focusing on the startups is thus an ideal setting to study this effect, since new entrants
are typically small and less productive and have a lot to learn from more experienced firms. Second,
as discussed in the empirical model section 3, past productivity shocks can affect firm’s hiring strategy
and thus stimulate firms to seek new workers with characteristics more likely to be observed among
the personnel of more productive firms. For startup firms there is no performance history, and hence
no feedback from past events to current hiring practices.
To estimate knowledge transfer effect for startups, we use the following reduced form of model (2):
fs
2
Arj,t+1 = α1 Arj,t + β · A
j,t−1 + Xj,t γ1 + Ȳj,t γ3 + ε̄j,t+1 ,
(9)
1 variables are removed due to their absence for startups. Similarly, the
where the Arj,t−1 and Ȳj,t
productivity gap cannot be constructed for startup firms and the relationship we explore is the one
PNj,t
es
s
between average productivity of sending firms, A
j,t−1 =
i=1 Ii,t Ai,t−1 /Nj,t weighed by the share of
new workers, and future productivity of the receiving firm, Arj,t+1 . The coefficient β in equation (9) is
nevertheless comparable to the β in (2), since (9) is its reduced form.
Estimation results for equation (9) are presented in column (1) of Table 9. Positive and significant
coefficient β corroborates our earlier findings on productivity spillovers for the entire sample of firms.
At the hiring rate of 100% for startups, a 10% increase in the average productivity of the sending
firms leads to a 2.06% increase in the productivity of the receiving firm - an estimate close to that for
the whole sample of receiving firms with all controls included (Table 3). Breaking the sending firms
down to above- and below the manufacturing sector’s average productivity (column 2), we observe
the same tendency as before: the productivity effects of hiring from more-than-average productive
19
firms are stronger than from less productive.9 Although the gap’s effect is also present for less-thanaverage productive sending firms, this effect is much smaller than the effect brought in by workers
from above-average productive sending firms.
Finally, in columns (3-4) we report estimates of the effect of sending firms’ average productivity on
the probability of the receiving firm’s survival in the first year after its start. Consistently with its effect
on productivity, higher average productivity of sending firms increases the chances of the receiving
firm’s survival (column 3), but this effect seems to work only for hires from firms with above average
productivity (column 4). To gauge the importance of productivity spillovers for a startup’s survival,
we calculate the marginal effect of the sending firms’ productivity for an average receiving firm (shown
in square brackets in Table 9). The estimated marginal effect of hiring from firms with above average
productivity (column 4 in Table 9) implies that a 10% increase in sending firms’ productivity results
in 0.26% increase in the receiving firm’s probability of survival, a very small increase relative to the
first year exit probability of 16.7%.
7
Robustness tests
7.1
Contemporaneous correlation between sending and receiving firms’ productivities
In every regression specification so far we have maintained that productivity of the sending firm in
year t − 1 (when the worker in question was still employed there) will have an effect on productivity
of the receiving firm starting from year t + 1, the year after the worker changed firms. Indeed, it takes
time for the new employee to transfer his knowledge to new coworkers, to convince the management to
change their practices, and to observe the effect of these changes on the receiving firm’s performance.
Suppose, however, that there is a productivity effect instantaneous to hiring decision in year t. Such an
effect is unlikely to be due to spillovers, and its existence would question our interpretation of the gap’s
effect as evidence of spillovers and suggest instead that there may be other factors co-determining the
sending and receiving firms’ productivity in each year. Adding a contemporaneous measure of sending
firms’ productivity would control for these factors and reveal the independent effect of productivity
gap, bringing us closer to a causal interpretation of our earlier results.
9
fs , reveals the same pattern.
An alternative specification, one with the square and cubic terms for A
20
In columns (1)-(2) of Table 10 we report estimation results from the specification (2) augmented
with the average productivity of sending firms from which workers were recruited in year t + 1 (Asi,t+1 ).
The estimates show that recruiting 10% of total workforce from a 10% more productive firms is associated with an 0.076% instantaneous increase in productivity of the receiving firm, which result
presumably reflects the positive correlation between productivity levels of sending and receiving firms
reported in the introduction. The contemporaneous link between sending and receiving firms’ productivity is weak relative to the effects of productivity gap in years t − 1 to t − 5, and becomes insignificant
1 , and Ȳ 2 )
when (t + 1)-year controls for sending firm and new workers characteristics (Xt+1 , Ȳt+1
t+1
are included (columns 3 and 4). Anyway, adding Asi,t+1 does not materially affect the estimates for
the productivity gap.
Summing up, the results in columns (1)-(4) have two implications. First, that the estimate for
1 , and Ȳ 2
Asi,t+1 becomes insignificant once Xt+1 , Ȳt+1
t+1 are included implies that the contemporaneous
link between sending and receiving firms’ productivities can be explained away by controlling for
similarities in observed firm and worker characteristics, most importantly by the size of the sending
firm. Second, that the inclusion of Asi,t+1 does not change the estimates for the gap’s effect implies that
common factors affecting sending and receiving firms’ productivities cannot explain the productivity
gap’s effect we have found earlier. The spillover interpretation that we offer in this study is a far more
likely explanation.
7.2
Firm-level productivity shocks
The identifying assumption in equation (2) and its extensions is that the error term ε̄j,t+1 is uncorrelated with the productivity gap measure. If however, a firm has experienced a positive productivity
shock in year (t − 1), it may affect the firm’s hiring behaviour in year t when the new hires come. For
instance, a positive productivity shock can affect the firm’s willingness and ability to hire new workers
from more productive firms by offering them more attractive wages. The positive correlation between
past productivity shock and the sending–receiving firm productivity gap will induce an upward bias
to the estimate of the gap’s effect.
Although in our model past productivity shocks are controlled by means of the lags of the dependent variable, as an additional robustness test we apply the estimation procedure developed in
Olley and Pakes (1996) which offers extra controls for past productivity shocks. This procedure uses
21
the theoretical fact that a profit-maximising firm will increase capital investment after experiencing a
positive productivity shock. Assuming firm i’s current capital stock Kit is equal to the sum of capital
from the previous period and capital investments, the profit-maximizing choice of investment, Iit , is
described as a function f (·) of the current capital stock and the unobserved productivity shock ωit :
Iit = f (Kit , ωit )
Assuming f (·) is monotonic in both capital and productivity, it can be inverted to express ωit as a
function of observable investments and capital (all in logs)
ωit = g (kit , iit )
As in Olley and Pakes (1996), we approximate the unknown function g with a third-degree polynomial series of capital and investments and include this approximation in equation (2) to control for
ωit−1 . The estimation results presented in columns (5) and (6) of Table 10 do not suggest that past
productivity shocks affect the choice of firms from which the new hires come, since the estimates for
the gap are similar to those obtained earlier from specifications without extra controls for unobserved
productivity shocks. That said, these extra controls do help explain the variation in productivity
among firms, since most of the terms in the polynomial approximation for function g(·) (skipped) are
statistically significant.
7.3
Firm-level fixed effects
Continuing on the issue of identifiability of productivity spillovers separately from other unobserved
influences, suppose now that firms do not hire workers randomly but target sending firms based on
their characteristics. The possible presence of (long-term) preferences in hiring implies a correlation
between the sending and receiving firms’ productivities over time, which the productivity gap may
pick up. For instance, a positive correlation, 0.09, between the productivity levels of sending and
receiving firms averaged over the length of the sample suggests that firms tend to hire workers from
similarly productive firms. Although, by construction, productivity gap cancels common influences to
the receiving and sending firms’ productivity, we now include the receiving firm’s fixed effects in the
regression as an extra control for their time-invariant productivity determinants.
Including the receiving firm fixed effects in equation (1) leads to a reduction of the estimate of the
effect of productivity gap by more than a half, from 0.18 to 0.074 (column 7, Table 10). The estimates
22
in Table 10’s column 7 imply that the productivity spillover effect for an average receiving firm hiring
10% of workers from 10% more productive firm falls to 0.07 percentage points per year, suggesting that
most of the previously found effect is due to a regression misspecification through failure to account
for unobserved productivity components. The reduction in the coefficient on the positive productivity
gap is even more pronounced. With these estimates, the mean productivity gain falls to 0.2% per year
for an average firm.
However, we caution against relying too much on the fixed effects results. The correlation between
average productivity levels of the sending and receiving firms is unlikely to account for more than
three quarters of the previously reported gap’s effect, since this correlation’s coefficient of 0.09 is
much lower than that between the lagged productivity of the sending firm and lead of the receiving
firm’s productivity, 0.15 (see Introduction). Moreover, 0.09 is probably an overestimate of the true
correlation between the sending and receiving firms’ fixed effects, since, as we have seen earlier, the
effect of the gap lasts several periods after a hiring was done and thus affects average productivity over
the duration of the sample. In fact, since the fixed effects estimator uses only the within-firm variation
in the regression variables for identification, it will ignore any long-term effect of productivity gap.
Therefore, the fixed-effects estimate of β is, at best, the lower bound of the true effect, which is still
positive and statistically significant.
7.4
Sorting of workers by firm type
One argument against the productivity spillover hypothesis is the sorting of more productive workers
into better firms. Workers employed by above-average productive firms can be ex ante more productive
than workers from relatively less productive firms, and then the estimated effect of productivity gap
may be due to unobservable skills of switching workers. If high-productivity firms provide better
compensation for these skills, our human capital measure will control for this alternative interpretation.
If, however, the skill is not fully reflected in the salary – for instance, more productive firms can screen
high-quality workers better – then the coefficient on productivity gap will be contaminated by the
effect of workers unobserved skills.
We propose in this section that looking at the effects of the gap averaged for workers with short
and long tenure at the sending firms can reveal the importance of unrewarded human capital for the
estimate of the productivity gap. Suppose that the worker’s ability to carry knowledge from one
23
firm to another depends on her tenure at the sending firm – the longer, the more knowledge she can
absorb and transfer. Screening, on the other hand, takes little time to perform. Then, if the effect of
short-tenure workers on the receiving firm’s productivity is as strong as that of longer-tenure workers,
it is (mostly) sorting on unobservables that explains the effect of the productivity gap. If, however,
the effect of the gap increases with the tenure of switching workers, screening cannot explain it, and
we are back to productivity spillovers as the main explanation.
Since we do not have information on worker’s employment outside our sample period, the constructed measure of tenure will be censored for early years. For this reason, we focus on the time
period between 2001 and 2007, which will enable us to derive a reasonably uncensored tenure variable
for the first six years. With this measure, we construct average positive productivity gaps for six
groups of new workers who have tenure in the sending firm varying from 1 to 6-plus years, the last
group including all observations with censored tenure.
Results presented in Table 11 are supportive of the spillovers hypothesis. The effect of the positive
productivity gap is insignificant for workers with less than three years of tenure at the sending firm.
Admittedly, the insignificant result for the workers with one year’s tenure could be down to a bad
worker match which resulted in a quick termination of employment. However, this explanation hardly
applies to the workers with two years of tenure for whom the gap’s effect is also insignificant. That
the effect becomes significant and increases in magnitude starting at three years of tenure does not
support the view that the gap’s effect simply reflects higher quality of workers from relatively more
productive firms, pointing instead to the importance of tenure for workers’ ability to absorb knowledge
accumulated in their firms.
7.5
Alternative measures of productivity
Until now we have analyzed the effect of knowledge transfers using (wage-adjusted) value added per
worker as a measure of firm productivity. Although it is the most widely used measure of labor
productivity, it disregards differences in the intensity of capital use which may also affect productivity.
In this section we use several alternative measures of productivity, defined relative to a multifactor
production technology, which take into account the intensity of factors of production other than labor.
With firm level output Q, production technology F, and the vector of input factors X, we can define
24
the total factor productivity (TFP) of firm i at time t as its output net of input factor contributions
ait = qit − f (xit )
(10)
where z = ln Z. Using different parametrizations of the production function and estimates of its
coefficients, we construct several measures of firm productivity. To remove common influences on
productivity of various firms, we normalize the productivity levels calculated with equation (10) by
subtracting their averages across firms taken over each industry-year pair.
As a first parametrization of F (·) we take the Cobb-Douglas production function with capital,
labor, and materials and energy inputs as the factors of production, calculating
ait = qit − αk kit − αl lit − αm mit
(11)
We apply a selection of empirical methodologies to estimate the parameters of Cobb-Douglas production technology, αk , αl , αm . Our starting point is the ordinary least squares (OLS) estimator of the
production function, which we apply separately for each three-digit industry group in our sample, to
allow for differences in input elasticities within the sample. The regression results with TFP estimated
through OLS are reported in columns (1) and (2) of Table 12. The results with this alternative measure of productivity are broadly consistent with our benchmark results for value added per worker.
The coefficient on the productivity gap and its positive part are positive and statistically significant,
while the effect of new workers coming from less productive firms is insignificant.
In addition to the OLS estimates of TFP, we employ a two-step semiparametric estimator by Olley
and Pakes (1996), the one we used in section 7.2, to control for input factor endogeneity to unobserved
past productivity shocks. The TFP measure based on Olley and Pakes-estimated production function
is highly correlated with that based on OLS. Consequently, the changes in the estimates of our interest
(columns 3-4) are fairly small.10 Next, we use a more general parameterization of production technology F (·) with a full set of input interactions and order terms, known as the translog production
function. The translog specification offers a number of advantages over Cobb-Douglas function, most
notable of which is the ability to control for the effect of firm size on output by allowing for non-linear
effects of factor inputs on output. Estimation results for equations (2) and (4) with productivity
measure derived from the translog production function are presented in columns (5) and (6) of Table
10
Alternative estimates of Cobb-Douglas production function, such as Levinsohn and Petrin (2003) and Wooldridge
(2009), yield productivity measures which are very similar to OLS and Olley-Pakes estimates.
25
12. Although the coefficient on the productivity gap becomes insignificant, the effect of hiring from
more productive firms is stronger than in columns (2) and (4).
Comparing the magnitude of the spillover effects estimated on different measures of productivity,
we see that TFP-based estimates are only about half of those in the benchmark specification. For
instance, taking the Olley and Pakes (1996) measure of TFP, the estimated productivity gain of a
receiving firm from hiring 10% of new workers from 10% more productive firms falls from 0.351%
(Table 4) to 0.178%. In fact, however, the two measures productivity produce similar results when
we relate the regression estimates to their respective sample moments. Taking the sample average
and standard deviation of the gap in value added, 0.024 and 0.1, respectively, the average firm gains
0.024 × 0.351/0.1 = 0.084 standard deviations of the productivity gap by hiring workers from more
productive firms. Doing the same calculations with the Olley and Pakes’ measure of productivity gap
(average 0.013, standard deviation 0.025) produces a gain of 0.093 standard deviations of the gap.
Hence the results for different measures of productivity are closer to each other than simple regression
estimates seem to suggest.
Finally, in the last six columns of Table 12 we look at the effect of knowledge transfers on the
receiving firm’s profitability. Columns (7) and (8) show the results for the gap measured as the
difference between the average profitability of sending firms and the profitability of the receiving firm
one year before a hiring is done. Consistent with our earlier results, this relationship is positive for all
new workers and is stronger for workers coming from more profitable firms. This positive relationship
remains broadly the same for other measures of the gap, such as weighted value added per worker
(columns 9 and 10) or TFP estimated from the translog production function (columns 11 and 12).
Hence, our results are robust to a variety of ways in which the sending and receiving firms’ economic
performance are measured.
8
Conclusion
Let us now take stock of our results. Our basic finding is that hiring workers from firms more productive
that the receiving firm reduces the productivity gap between the sending and receiving firms. This
effect is equivalent to a rise in the productivity of an average firm by 0.8% a year and persists for at
least five years after the hiring. We argue that this effect is the evidence for productivity spillovers
from more to less productive firms, and we support this argument by ruling out plausible alternative
26
explanations. One such explanation rests on the transfer of human capital, not knowledge, from
the receiving firms. However, we do control for the workers’ human capital, both its observed and
unobserved parts, and this measure, though important for the receiving firm’s productivity, makes
little difference to our spillover estimates. Moreover, the appeal of the human capital explanation is
weakened by the lack of the effect of hiring from less productive firms: if it were due to human capital,
the effect would have been symmetric. Finally, if the gap’s effect were really due to new workers’
human capital, it would not depend on the workers’ tenure at their previous firms, whereas in fact it
does.
Another alternative explanation for the link between the productivity gap and the receiving firm’s
productivity level could be a correlation between the productivities of sending and receiving firms.
This correlation could be long-term, due to hiring practices, or short-term, due to positive productivity
shocks allowing firms to attract workers from better performing firms. However, a positive effect of
hiring from above-average productive firms exists for startup firms, and of a similar magnitude to that
found on the whole sample. We also find that controlling for unobserved shocks to receiving firms’
productivity makes little difference to the gap’s estimated effect, and hence these shocks could not
have accounted for any significant part of our results. Although the long-term correlation between
the sending and receiving firms’ productivities is much harder to control for, our calculations suggest
that it is too weak to explain the gap’s effect. This effect remains significant even when we include
the firm fixed effects, despite a downward bias in its estimate that adding fixed effects incurs.
In addition to the above results, our other findings offer some intuitively appealing yet useful characterizations of the productivity spillover effect. For instance, we find that the knowledge transferred
by workers is to a large extent industry-specific, and that more educated and skilled workers are can
transfer more knowledge. Yet, even unskilled workers previously employed at more productive firms
can improve the receiving firms’ productivity, implying that the knowledge transferred through hiring
is not necessarily sophisticated and/or codified. Labor turnover is the most plausible mechanism for
the transfer of such knowledge.
It is also a universal mechanism, applicable for the whole economy, which is important for modern
endogenous growth models relying on productivity spillovers between more and less productive (large
and small) firms (Eeckhout and Jovanovic, 2002; Luttmer, 2007; Atkeson and Burstein, 2010). A
continued inquiry into its effects is important for further development of these models, and for deriving
economic policy implications from them.
27
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Figure 1. The relationship between labor turnover and industry-­‐level TFP variance by 3-­‐digit NACE industry. Table 1. Summary statistics for workers Wage (log) Age (years) Experience (years) Male (share) High school (share) College (share) University degree (share) Unskilled workers (share Skilled workers (share) Managers (share) log value added per worker Share in the labor force Firm size (# of workers) Number of observations stayers new hires new hires from more productive firms 12.23 39.6 14.7 67.7 38.0 49.8 12.2 25.5 65.4 9.2 6.36 0.885 1,105 5,127,165 12.21 36.9 14.2 72.1 35.7 51.8 12.6 19.4 71.8 8.8 6.36 0.115 1,118 668,034 12.31 37.9 14.8 72.4 34.9 55.2 9.8 18.6 72.1 9.3 6.40 0.023 1,413 135,006 Notes: Summary statistics is calculated for all workers in manufacturing industry for the time period 1995-­‐2004. The share of new hires from less productive firms is 0.027. For the rest 6.5% of new hires the productivity of sending firm is unknown Table 2. Summary statistics for firms Wage (log) Age (years) Experience (years) Male (share) High school (share) College (share) University degree (share) Unskilled workers (share Skilled workers (share) Managers (share) log VA per worker log VA per worker, previous firm Share of new workers Firm size (# of workers) Number of observations All firms No hiring Hiring firms stayers hires from more productive firms 11.9 40.5 9.2 71.9 34.1 55.4 10.4 54.0 41.0 5.0 6.03 11.8 42.6 9.1 72.4 32.7 57.2 10.0 67.5 28.6 4.0 5.93 12.0 37.9 9.2 71.2 36.2 52.8 11.0 34.4 59.1 6.5 6.19 12.1 34.8 9.1 77.5 33.1 55.8 11.1 17.1 75.8 6.9 12.1 35.7 9.0 74.3 35.1 53.6 11.3 29.5 64.8 5.7 10.6 27 173,929 0 7 88,806 56 85,123 6.76 5.65 3.5 3.0 hires from less productive firms Notes: Summary statistics is calculated for all workers in manufacturing industry for the time period 1995-­‐2004. Statistics show average values for different firms and subgroups of workers. Table 3. Knowledge spillovers, benchmark results Productivity gap ( β ) X (firm characteristics) (1) (2) (3) 0.199** 0.182** 0.175** (0.023) (0.023) (0.023) NO YES YES (4) 0.179** (0.024) YES Y1 (average characteristics of stayers) NO NO YES YES Y2 (average characteristics of new workers) R2 N NO NO NO YES 0.570 0.575 0.560 100,195 100,195 100,195 0.560 100,195 Notes: All specifications include year fixed effects and average size of sending firm as additional controls. Robust standard errors in parentheses are clustered at the firm level. ** significant at 1%, * significant at 5%. Time period covered is 1995-­‐2007. Table 4. Knowledge spillovers from more and less productive firms Positive productivity gap ( βP ) Negative productivity gap ( βN ) Positive productivity gap squared Negative productivity gap squared R2 N (1) 0.351** (0.054) (2) 0.330** (0.063) 0.069 (0.042) 0.012 (0.051) 0.560 100,185 0.034* (0.015) 0.013 (0.046) 0.560 100,185 Notes: All specifications include year fixed effects, average size of sending firm, characteristics of receiving firm (X), firm-­‐average characteristics of new and incumbent workers (Y1 and Y2) as additional controls. Robust standard errors in parentheses are clustered at the firm level. ** significant at 1%, * significant at 5%. Time period covered is 1995-­‐2007. Table 5. Knowledge spillovers from same and different industries Productivity gap, same industry ( βsame ) Productivity gap, different industry ( βdiff ) Positive productivity gap, same industry ( βP,same ) Positive productivity gap, different industry ( βP,diff) Negative productivity gap, same industry ( βN,same ) Negative productivity gap, different industry ( βN,diff ) Test βsame = βdiff , p-­‐value Test βP,same = βP,diff , p-­‐value Test βN,same = βN,diff , p-­‐value R2 N (1) (2) 0.231** (0.032) 0.145** (0.036) 0.334** (0.051) 0.210** (0.070) -­‐0.002 (0.045) -­‐0.043 (0.063) 0.017 0.003 0.554 0.558 0.558 99,715 99,715 Notes: All specifications include year fixed effects, average size of sending firm, characteristics of receiving firm (X), firm-­‐average characteristics of new and incumbent workers (Y1 and Y2) as additional controls. Robust standard errors in parentheses are clustered at the firm level. ** significant at 1%, * significant at 5%. Time period covered is 1995-­‐2007. Firms are considered to be in the same industry if they have the same 2-­‐digit NACE industry code. Table 6. Knowledge spillovers by education of moving workers Productivity gap, high school ( βhigh ) Productivity gap, college ( βcoll ) Productivity gap, university ( βuniv ) Positive productivity gap, high school ( βP,high ) Positive productivity gap, college ( βP,coll ) Positive productivity gap, university ( βP,univ ) Negative productivity gap, high school ( βN,high ) Negative productivity gap, college ( βN,coll ) Negative productivity gap, university ( βN,univ ) Test βhigh = βcoll , p-­‐value Test βhigh = βuniv , p-­‐value Test βP,high = βP,coll , p-­‐value Test βP,high = βP,univ , p-­‐value R2 N (1) 0.111** (0.029) 0.196** (0.041) 0.284 (0.159) 0.096 0.283 0.560 100,195 (2) 0.277** (0.046) 0.299** (0.064) 0.540** (0.157) 0.015 (0.039) 0.103 (0.057) -­‐0.043 (0.332) 0.773 0.107 0.560 100,195 Notes: All specifications include year fixed effects, average size of sending firm, characteristics of receiving firm (X), firm-­‐average characteristics of new and incumbent workers (Y1 and Y2) as additional controls. Robust standard errors in parentheses are clustered at the firm level. ** significant at 1%, * significant at 5%. Time period covered is 1995-­‐2007. Table 7. Knowledge spillovers by skill type of moving workers Productivity gap, unskilled ( βunskilled ) Productivity gap, skilled ( βskilled ) Productivity gap, managers ( βmanager ) Positive productivity gap, unskilled ( βP,unskilled ) Positive productivity gap, skilled ( βP,skilled ) Positive productivity gap, managers ( βP,manager ) Negative productivity gap, unskilled ( βN,unskilled ) Negative productivity gap, skilled ( βN,skilled ) Negative productivity gap, managers ( βN,umanager ) Test βunskilled = βskilled , p-­‐value Test βunskilled = βmanager , p-­‐value Test βP,unskilled = βP,skilled , p-­‐value Test βP,unskilled = βP,manager , p-­‐value R2 N (1) 0.179** (0.045) 0.180** (0.030) 0.315* (0.181) 0.997 0.329 0.560 100,195 (2) 0.221** (0.080) 0.326** (0.052) 0.460 (0.451) 0.118 (0.079) -­‐0.012 (0.048) 0.223 (0.190) 0.267 0.809 0.560 100,195 Notes: All specifications include year fixed effects, average size of sending firm, characteristics of receiving firm (X), firm-­‐average characteristics of new and incumbent workers (Y1 and Y2) as additional controls. Robust standard errors in parentheses are clustered at the firm level. ** significant at 1%, * significant at 5%. Time period covered is 1995-­‐2007. Table 8. Time persistency of knowledge spillover effect Dependent variable: Productivity gap ( β ) Positive productivity gap ( βP ) Negative productivity gap ( βN ) R2 N TFP in 1 year (1) (2) 0.209** (0.041) 0.536** (0.113) 0.100 (0.060) 0.591 0.593 45,723 45,723 TFP in 2 years (3) (4) 0.175** (0.045) 0.513** (0.109) 0.009 (0.078) 0.526 0.528 45,723 45,723 TFP in 3 years TFP in 4 years TFP in 5 years (5) (6) (7) (8) (9) (10) 0.173** 0.147** 0.138** (0.044) (0.041) (0.044) 0.538** 0.546** 0.449** (0.109) (0.095) (0.119) 0.065 -­‐0.036 0.002 (0.074) (0.071) (0.069) 0.475 0.477 0.434 0.436 0.401 0.402 45,723 45,723 45,723 45,723 45,723 45,723 Notes: All specifications include year fixed effects, average size of sending firm, characteristics of receiving firm (X), firm-­‐average characteristics of new and incumbent workers (Y1 and Y2) as additional controls. Robust standard errors in parentheses are clustered at the firm level. ** significant at 1%, * significant at 5%. Time period covered is 1995-­‐
2007. In all specifications the sample is restricted to the one used in the estimation in columns (9) and (10). Table 9. Knowledge spillover effect for new firms Dep. Variable: (1) 0.206** (0.017) Productivity of sending firm Productivity of sending firm above industry average Productivity of sending firm below industry average R2 N Probability of survival for at least 3 years after start Future productivity 0.330 5,421 (2) 0.316** (0.029) 0.094** (0.026) 0.334 5,421 (3) 0.086** (0.042) [0.015] 0.022 5,206 (4) 0.147* (0.081) [0.026] 0.030 (0.069) [0.005] 0.022 5,206 Notes: All specifications include year fixed effects, average size of sending firm, characteristics of receiving firm (X), firm-­‐average characteristics of new and incumbent workers (Y1 and Y2) as additional controls. Robust standard errors in parentheses are clustered at the firm level. Marginal effects are in square brackets. ** significant at 1%, * significant at 5%. Time period covered is 1995-­‐2007. Columns (1-­‐2) are estimated with OLS; columns (3-­‐4) are estimated with Probit. Table 10. Robustness tests: Alternative specifications of regression equation (2) (1) 0.182** Productivity gap ( β ) (0.024) Positive productivity gap ( βP ) Negative productivity gap ( βN ) Mean future productivity of sending 0.057* firms (0.027) Mean future productivity of more productive sending firms Mean future productivity of less productive sending firms X, Y1, and Y2 for period (t+1) NO Control for TFP shocks with investments NO Firm-­‐level fixed effects NO R2 0.570 N 99,875 (2) 0.325** (0.054) 0.070 (0.042) 0.076* (0.037) 0.017 (0.049) NO NO NO 0.575 99,875 (3) 0.182** (0.024) 0.032 (0.034) YES NO NO 0.576 98,388 (4) 0.393** (0.053) 0.064 (0.042) 0.052 (0.056) 0.014 (0.050) YES NO NO 0.578 98,388 (5) (6) (7) (8) 0.182** 0.074** (0.024) (0.015) 0.354** 0.080** (0.053) (0.028) 0.077 0.043 (0.042) (0.032) NO NO NO NO YES YES NO NO NO NO YES YES 0.570 0.575 0.560 0.560 100,195 100,195 100,195 100,195 Notes: All specifications include year fixed effects, average size of sending firm, characteristics of receiving firm (X), firm-­‐average characteristics of new and incumbent workers (Y1 and Y2) as additional controls. Robust standard errors in parentheses are clustered at the firm level. ** significant at 1%, * significant at 5%. Time period covered is 1995-­‐2007. In columns (5-­‐6) a third order polynomial of investments and capital is included to control for firm-­‐
level TFP shocks in period t. Columns (7-­‐8) include firm-­‐level fixed effects. Table 11. Robustness tests: The effect of tenure at sending firm on knowledge transfers Positive productivity gap for workers with 1 year of experience at sending firm Positive productivity gap for workers with 2 years of experience at sending firm Positive productivity gap for workers with 3 years of experience at sending firm Positive productivity gap for workers with 4 years of experience at sending firm Positive productivity gap for workers with 5 years of experience at sending firm Positive productivity gap for workers with 6+ years of experience at sending firm X (firm characteristics) Y1 (average characteristics of stayers) Y2 (average characteristics of new workers) R2 N 0.144 (0.095) 0.177 (0.151) 0.331* (0.145) 0.275* (0.140) 0.348* (0.166) 0.233** (0.057) YES YES YES 0.570 55,335 Notes: All specifications include year fixed effects and average size of sending firm as additional controls. Robust standard errors in parentheses are clustered at the firm level. ** significant at 1%, * significant at 5%. Time period covered is 2001-­‐2007. Table 12. Robustness tests: Productivity spillovers using alternative measures of firm-­‐level productivity Productivity gap ( β ) Positive productivity gap ( βP ) Negative productivity gap ( βN ) R2 N OLS (2) (1) Productivity measure Translog Profit (5) (6) (7) (8) OP (3) (4) Profit (9) Profit (11) (12) (10) 0.083** 0.093** 0.050 0.059** 0.064** 0.107 (0.028) (0.035) (0.026) (0.018) (0.022) (0.072) 0.151** 0.178** 0.207** 0.454** 0.199** 0.373* (0.049) (0.068) (0.071) (0.053) (0.041) (0.184) 0.049 0.056 -­‐0.022 -­‐0.109** -­‐0.110 -­‐0.108 (0.048) (0.038) (0.055) (0.026) (0.060) (0.118) 0.313 0.313 0.297 0.297 0.332 0.332 0.519 0.502 0.442 0.442 0.444 0.444 103,505 103,505 103,505 103,505 103,505 103,505 83,477 83,477 33,944 33,944 34,051 34,051 Notes: All specifications include year fixed effects, average size of sending firm, characteristics of receiving firm (X), firm-­‐average characteristics of new and incumbent workers (Y1 and Y2) as additional controls. Robust standard errors in parentheses are clustered at the firm level. ** significant at 1%, * significant at 5%. Time period covered is 1995-­‐2007. In columns (1-­‐2) productivity is constructed from Cobb-­‐Douglas production function estimated by OLS. In columns (3-­‐4) productivity is constructed from Cobb-­‐Douglas production function estimated by Olley-­‐Pakes methodology. In columns (5-­‐6) productivity is constructed from translog production function estimated by OLS. In columns (9-­‐10) productivity gap is constructed using wage-­‐
adjusted value added per worker (benchmark measure), and in columns (11-­‐12) it is constructed using Solow residuals from translog production function.