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Electronic copy available at: http://ssrn.com/abstract=1850434
DOCUMENT DE TREBALL
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DECOMPOSING DIFFERENCES IN TOTAL FACTOR
PRODUCTIVITY ACROSS FIRM SIZE
Laia Castany; Enrique LópezBazo
and Rosina Moreno
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Electronic copy available at: http://ssrn.com/abstract=1850434
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DECOMPOSING DIFFERENCES IN TOTAL FACTOR
PRODUCTIVITY ACROSS FIRM SIZE*
Laia Castany†, Enrique LópezBazo‡
and Rosina Moreno§
Abstract:
This paper investigates the extent to which the gap in total factor productivity between small
and large firms is due to differences in the endowment of factors determining productivity and
to the returns associated with these factors. We place particular emphasis on the contribution of
differences in the propensity to innovate and in the use of skilled labor across firms of different
size. Empirical evidence from a representative sample of Spanish manufacturing firms
corroborates that both differences in endowments and returns to innovation and skilled labor
significantly contribute to the productivity gap between small and large firms. In addition, it is
observed that the contribution of innovation to this gap is caused only by differences in quantity,
while differences in returns have no effect; in the case of human capital, however, most of the
effect can be attributed to increasing differences in returns between small and large firms.
Keywords: Total Factor Productivity; skilled labor; innovation; firm size; Oaxaca
decomposition
JEL Codes: D24, J24, L25
* Acknowledgments: The authors acknowledge financial support from Ministerio de Ciencia y
Tecnología, Programa Nacional de I+D+I, SEJ200507814/ECON. Thanks are also due to the Fundación
Empresa Pública for supplying the data.
† Research Group AQRIREA, University of Barcelona, Av. Diagonal, 690, 08034 Barcelona, Phone:
+34.934021010; +34.934037041; +34.934027042 Fax: +34934021821, Email: lcastany@ub.edu
‡Research Group AQRIREA, University of Barcelona, Av. Diagonal, 690, 08034 Barcelona, Phone:
+34.934021010; +34.934037041; +34.934027042 Fax: +34934021821, Email: elopez@ub.edu
§ Research Group AQRIREA, University of Barcelona, Av. Diagonal, 690, 08034 Barcelona, Phone:
+34.934021010; +34.934037041; +34.934027042 Fax: +34934021821, Email: rmoreno@ub.edu
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1.
Introduction
The relationship between size and productivity has been studied for some time now both at a
theoretical and empirical level. Jovanovich (1982) proposed a model in which, as firms gain
experience, they learn about their levels of costs and efficiency. If they are efficient, they will decide
to expand, or otherwise, they will decide to contract or even exit the market. Thus, the most efficient
firms are expected to survive and grow, while the most inefficient will fail. In addition, Ericson and
Pakes (1995) propose a model in which firms invest in R&D to improve their productivity levels. This
way, their productivity is a function of their own R&D investment, of the productivity of their
competitors and of the pressure of firms entering the market. If a firm succeeds and is sufficiently
productive, it will grow. In the model by Olley and Pakes (1996), firms will decide to continue in the
market and demand a certain amount of inputs, or otherwise, exit the market. This decision depends on
whether firms expect to achieve a certain (unobservable) efficiency level or not. As long as firms
continue in the market, firm size and productivity are also related in this model.
On the basis of these ideas, it is sensible to think that controlling for firm size in regressions to analyse
firm productivity can even be considered a routine procedure (Geroski, 1998). Thus, when we add a
firm size variable to a regression we are accounting for different technologies associated with a certain
firm size, which, according to Geroski, is referred to as the direct effect of size on productivity: that is,
as a variable that ceteris paribus improves efficiency. This author claims that size may also have an
indirect effect on productivity, conditioning the effect of other variables on productivity as they will
show different patterns of behaviour for small and large firms.
Technological and human capital are among the main factors that have traditionally been considered to
foster productivity. Griliches (1979) is a pioneer study in assessing the contribution of research and
development to productivity growth. Most literature on innovative activity estimates the elasticity or
the rates of return to a stock of knowledge (calculated on the basis of the R&D effort) on productivity.
Studies that use firm level data show a wide range of estimates and some have found weaker
correlations than at sectoral or national level, particularly when industry dummies are included (see
Mairesse and Sassenou, 1991, for a survey). However, the relationship between productivity and R&D
expenditure embodies two different processes: the production of innovations starting from R&D
activities, and the incorporation of these innovations into production (Griffith et al., 2004). Firms
invest in R&D in order to develop process and product innovations, which in turn may contribute to
their productivity and economic performance. Crépon et al. (1998) emphasize that it is not innovative
input (R&D) but rather innovative output that increases firm productivity. Measures of innovative
output allow us to measure the changes that firms consider relevant to their production processes and
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avoid the need to distinguish between formal and informal R&D activities (Huergo and Jaumandreu,
2004a).
Other studies have gone a step further by relating the innovative capacity to firm characteristics such
as size and have found positive relation between them. Schumpeter (1942) hypothesized that large
firms have an advantage over small companies as their financial situation allows them to be the most
capable innovators. Acs et al. (1994) found that large firms invest more in R&D and innovate more,
although small firms appear to have higher innovative productivity. Huergo and Jaumandreu (2004b)
in Spanish case study reach the conclusion that “innovation is strikingly related to size”. In these
studies the underlying hypothesis is that firms show different patterns of innovative activity according
to size. However, small and large firms can differ not only in their innovative intensity but also in the
returns to such innovative activity. Klepper (1996) proposed a theoretical model in which firm size
plays a crucial role in the appropiation of returns to innovation and in the engagement in R&D
activities. The larger the firm, the greater the output over which fixed costs of process R&D can be
averaged, which means that returns to process innovations are higher and encourages additional
innovative effort. Cohen and Klepper (1996) corroborate the hypothesis of easier appropiability of
returns to innovation in the case of large firms for the US case. These papers suggest the existence of
differences in returns to innovation between small and large firms. Parisi et al. (2002) analyze the
impact of innovations on productivity for different firm sizes for the Italian case and conclude that
innovation in large firms has a greater impact on productivity.
On the other hand, Becker (1964) is a pioneering study in highlighting the importance of human
capital. The literature on the effects of human capital on productivity argues that those workers with
better problem solving and communication skills will perform any task requiring more than simple
labor in a more efficient way. The microeconomic literature, which concerns the impact of investment
in human capital on productivity levels, has typically estimated Mincerian equations (see Harmon et
al. 2003, for a survey). Nevertheless, only a few microeconomic studies have analyzed the effect of
human capital on productivity at the firm level. One exception is Griliches and Regev (1995), which
estimates a production function that includes R&D capital services and a measure of labor quality as a
proxy for human capital in Israeli industry. The authors find a coefficient of skilled labor of
approximately 0.4 for the total sample and 0.5 for large firms in the pooled regressions using
differences to control for individual heterogeneity, which they acknowledge to be quite high.
Haltiwanger et al. (1999) used a matched employeremployee dataset and found that labor
productivity is associated with certain characteristics of the workforce, such as the proportion of
educated workers. The results are consistent with a human capital model in which more highlyskilled
workers make the firm more productive. In addition to the fact that large firms employ a more skilled
labor force, it is also possible that returns to human capital are higher in large firms. In fact, in the
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literature that aims to explain the positive relationship between firm size and wages, Oosterbeek and
Van Praag (1995) found that larger firms pay higher returns to human capital (which can explain part
of the sizewage relation).
The empirical evidence and the arguments given above suggest that technological and human capital
(which can be combined under the term knowledge capital) affect productivity. There are also
arguments which suggest that larger firms have better endowments of these factors. We argue that
technological and human capital play different roles in determining productivity for small and large
firms: firstly, because large firms are usually more innovative and employ more skilled workers;
secondly, because the returns of these endowments on productivity may be higher in the case of large
firms. In other words, an additional innovation implemented in a large firm or a skilled employee hired
by the firm would result in a higher return than if the same situation arose in a small firm.
Consequently, size would be exerting an indirect influence on firm productivity, as it conditions the
impact of other factors on productivity. According to this hypothesis, the observed gap in productivity
between small and large firms would be caused by both differences in the endowment of technological
and human capital between firms of different size, and by differences in the returns to the use of these
types of capital.
Therefore, the main objective of this paper is to investigate the differences in total factor productivity
(TFP) between small and large firms and to establish the extent to which this gap is caused by
differences in the endowment of the main factors that determine firm productivity or to the returns
obtained from these factors. Building on this idea, one of the main contributions of the present analysis
is the use of the traditional OaxacaBlinder decomposition to assess the relative importance of
differences in firm endowments and in their returns to explain the productivity differential between
small and large firms. To the best of our knowledge, Smith et al. (2004) is the only study that uses this
decomposition to analyze differences between firms. More specifically, the authors compare firms that
carry out R&D activities and firms that do not.
We provide empirical evidence for a representative sample of Spanish manufacturing firms in the
period from 1990 to 2002. The results corroborate that both differences in endowments and returns to
knowledge capital significantly contribute to the TFP gap between small and large firms. In addition,
it is observed that the contribution of innovation to this gap is caused only by differences in quantity
and that differences in returns have no effect, while in the case of human capital the contribution is
largely attributable to increasing differences in returns between small and large firms.
The paper is structured as follows. After the introduction, Section 2 presents the empirical
specification and some methodological issues. In Section 3 we present the data and make a descriptive
analysis. Section 4 shows the results and Section 5 concludes the study.
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2.
Empirical specification and methodological issues
Our empirical framework relates a TFP index to innovation and skilled labor, the variables of interest
and to several control variables. Our approach is fairly close to that of Griliches and Regev (1995),
who estimate production function at firm level including measures of human and technological capital.
Instead of the production function, we use an estimate of the TFP as the dependent variable and
innovation and skilled labor as the explanatory variables whose effects on productivity we wish to
assess.5 The empirical model can therefore be expressed as follows:
it ititit it
uZH INN TFP
++++=γ
'
βββ
210
(1)
where TFP is the logarithm of the total factor productivity index in firm i in year t, INN and H are
variables proxying for the innovation activity and the level of human capital in the firm, Z is a set of
standard control variables (size, age, industry and year effects) and u is an error term.
In order to analyze the causes of differences in TFP by firm size we use the methodology given by the
OaxacaBlinder decomposition. This decomposition has been widely used to study wage gaps
associated with differences in worker characteristics and with discrimination by gender or race.6 We
apply the decomposition to analyze differences in TFP between small and large firms. This
methodology allows us to analyze the extent to which the TFP differential between small and large
firms can be explained by differences in endowments of human and technological capital and
differences in the returns to these endowments.
The standard methodology decomposes the TFP differential between small and large firms based on
two auxiliary regressions specified as in (1) for each type of firm. From these regressions, the average
TFP in the sample of small and large firms is obtained as:
5 We overcome the endogeneity problem in labor, capital and materials when estimating production functions by
calculating a TFP index and using input prices instead of estimating their returns to calculate the participation of
each input in the production function. Endogeneity problems associated with the demand of labor, capital and
intermediate inputs when estimating production functions are well known: the demands of inputs not only
determine productivity, but they also depend on the productivity they obtain. Then, the residual is correlated with
the part of the inputs that is endogenously determined, which produces biased coefficients for the inputs and
therefore an inconsistent estimation of the production function parameters. In addition, if a given variable is
omitted in the estimation of the production function and this variable is also relevant, the error term in the
production function and the demand of inputs will be correlated, which produces biased coefficients.
6 Following Oaxaca (1973) and Blinder (1973), the difference between the mean wages between two groups, for
example men and women, in period t can be decomposed into an explained or predicted difference due to
disparities in observed or measured characteristics between the two groups, and an unexplained or residual
difference attributable to both wage discrimination and unmeasured disparities in characteristics.
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LL
L
SS
S
X TFP
X TFP
β
ˆ
β
ˆ
'
'
=
=
(2)
where TFP denotes the mean of TFP, X is the vector of the mean values of the regressors in
specification (1), βˆ is the conforming vector of estimated coefficients and subscripts S and L refer to
small and large firms respectively. Then, differences in TFP between small and large firms can be
decomposed as:
()
()
SLSLSL
SL
XXX TFP TFP
β
ˆ
β
ˆ
β
ˆ
'''
−+−=−
(3)
where the first term on the righthand side is the part of the TFP gap caused by differences in
characteristics between the representative small and large firms, and the second term on the righthand
side is the contribution of differences in returns between the two types of firm.
The first term on the right hand side of expression (3) assumes that all the firms have the returns of
large firms,
L
βˆ . In the second term, we assume that all firms have the endowments of small firms,
S
X .
However, we could write a symmetric equation in which these values are replaced by
S
βˆ and
L
X
respectively. The standard version of the decomposition is based on the assumption that one of the two
equations is the “natural” one. For example, in the case of wage differentials by gender, it may appear
fairly natural to assume that women are the “discriminated” group: we would assume that women have
the same returns as men for the first term, and the second term could therefore be interpreted as wage
discrimination by gender. In our case there is no compelling reason to calculate the differences in firm
endowments with the assumption that all firms had the returns of either large or small firms. One
strand of the literature considers that it is not always easy to establish which is the natural model and
that results may often differ considerably. This literature suggests a variation of the standard
decomposition in which it is not necessary to make an assumption about which is the natural model.
According to this perspective, there is a “nondiscriminatory structure of returns” in relation to which
one group is “discriminated” while the other is “favored”. The TFP differential without the assumption
that one of the two equations is the natural model is expressed as:
()
()()
SSLLSL
SL
XXXX TFP TFP
β
ˆ
β
ˆ
β
ˆ
β
ˆ
β
ˆ
''''
***
−+−+−=−
(4)
where
*ˆ β is the estimated nondiscriminatory returns structure. The first term on the righthand side
of (4) is an estimate of the productivity differential in the absence of differences in returns between
small and large firms, which reflects productivity differences caused by differences in firm
endowments. The second and third terms are estimates of the advantage of large firms and the
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disadvantage of small firms in relation to the nondiscriminatory returns structure. The two terms
together are considered differences in TFP according to firm size, associated with differences in
returns without imposing a discriminated group. Since we are not interested in distinguishing the
advantage and disadvantage effects but in evaluating the differences in returns as a whole, without
imposing a discriminated returns structure, here we will report these two terms together.7 To
implement this decomposition, it is necessary to make an assumption regarding what the non
discriminatory returns structure would be. Oaxaca and Ransom (1994) deal with a proper selection of
the nondiscriminatory structure and propose estimating it as a weighted average of the two returns
structures,
SL
I
β
ˆ
)
β
ˆ
β
ˆ*
(
Ω−+Ω=
, in which the weights Ω are calculated as
)''()'(
1
LLXXXX
−
and where X is the matrix of regressors for the entire sample of firms.
3.
Data and Descriptive Analysis
3.1. Description of the dataset
We use a sample of Spanish manufacturing firms from the official survey Encuesta de Estrategias
Empresariales (ESEE). This survey is an unbalanced panel that covers the period 19902002 and
collects information on strategic decisions and the behavior of firms. Firms answered a comprehensive
questionnaire every four years (covering those issues that would supposedly change annually) and a
reduced questionnaire in the intervening years, so that complete information is available for 1990,
1994, 1998 and 2002. The reference population of the ESEE was a sample of firms with 10 or more
employees, working in one of the activities corresponding to divisions 15 to 37 of NACE93,
excluding division 23 (activities related to oil refinement and fuel treatment). During the initial
period, all firms with more than 200 employees were required to participate (70% did). Firms with 10
to 200 employees were sampled randomly according to industry and four size strata, retaining about
5%, in order to guarantee representativity for every industry and firm size. The ESEE is designed to
change as the composition of industry evolves. Newly created firms are selected using the original
selection criteria. Due to death and attrition, some firms were replaced by others in their industry and
size group so as to maintain representativity.8
The measure of TFP we use is based on the index developed by Good et al. (1996), which is derived
from a translog production function. Its analytical expression for a firm f in period t is as follows:
7 Detailed results are available from the authors upon request.
8 See Fariñas and Jaumandreu (1999) for further details.
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∑∑
=
s
2
∑
=
s
∑
=
i
=
−−−
−+−−+
−+−−=
tn
i
si issi is
t
ss
n
it iftitiftt ft ft
XXSSYY
XXSSYY TFP
1
1,1,
2
1
1
) lnln )((
2
1
) lnln(
) ln )(ln(
2
1
) ln (ln ln
where Y and Xi are quantities of output and the ith input respectively, Si is the costbased share of the
ith input and the bar over variables refers to their average. The upper part of the expression is the
deviation of the firm output and inputs from those of a hypothetical firm, which is the reference point
in year t. The lower part of the expression is the cumulative change in the output and input reference
point between year t and the initial year. This second part introduces a productivity differential every
year (as output, inputs and shares may change) and therefore accounts for possible technological
changes. The productivity index for a given firm and year is expressed in relation to the hypothetical
firm in the base period, 1990. Following Hall’s (1990) suggestion, weights are calculated as the share
of every input in the total cost of inputs.
Firm size (SIZE) is defined as the log of the total number of employees. In our database, small firms
are those with 200 or fewer employees. Many databases and studies consider that small and medium
enterprises are those firms with fewer than 250 employees. However, our database makes the
distinction at 200 employees and uses different sampling schemes for the two groups. We consider it
is more appropriate to use the same criterion to guarantee representativity by size strata.9
The literature suggests a wide variety of variables for measuring innovative activity at the firm level.
On the one hand, R&D expenditure is a measure of innovative inputs or the R&D effort of firms. On
the other hand, the innovative capacity can also be measured by process and product innovations.
These variables are a measure of the innovative output or the innovative effort that effectively
becomes an innovation. Similarly to previous studies of Spanish manufacturing firms (Huergo and
Jaumandreu 2004a), we use process innovation as the measure of a firm’s innovative activity, as it is
assumed that process and not product innovations are the ones that improve the mechanisms through
which inputs are transformed into output (Ornaghi, 2006). Specifically, it is a dichotomous variable
(INN) that takes value 1 if the firm has implemented a process innovation in the same year. Process
innovations improve the mechanisms through which an input is transformed into output. Process
innovations are assumed to take place when the firm gives a positive response to the following
request: “Indicate if your firm introduced some significant modification in the production process
(process innovation). If the answer is yes, please indicate the way: (a) introduction of new machines;
(b) introduction of new methods of organization; (c) both”.
9 Delgado et al.(2002), Fariñas and Ruano (2004), and Máñez et al. (2004) use the same criterion when using
data from the ESEE.
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Human capital (HK) is measured in terms of formal education of the labor force. This variable is
defined as the ratio of skilled workers according to educational level. Specifically, it includes
engineers, graduates, middle level engineers, experts and qualified assistants.
Of the control variables, the age (AGE) is defined as the number of years since the firm was set up,
whereas the sectoral heterogeneity is proxied by a set of 20 dummy variables (DSEC) according to the
NACE93 classification, where the omitted category is “Other manufacturing industries”. Finally, a set
of year dummies is included to control for exogenous technical progress and effects of the business
cycle that are common to all firms (DYEAR).
3.2. Descriptive Analysis
Table 1 shows some basic statistics for TFP for the years on which our analysis is focussed (1994,
1998 and 2002) for the total sample, and for the subsamples of small and large firms.10 The evolution
of TFP over the period under analysis in our sample is similar to that reported at the firm and
aggregate levels in some other studies of the Spanish economy (Estrada and LópezSalido, 2001;
Huergo and Moreno, 2006). If we focus on TFP differences by firm size, we find that large firms have
higher TFP than small ones and that the difference is statistically significant for all three years. In fact,
the ttest for equality of means rejects the null hypothesis that the average TFP is equal in the two
subsamples.
[Insert Table 1 around here]
Tables 2 and 3 contain basic descriptive statistics for the two other variables of interest: innovation
and human capital. The percentage of skilled workers increases over time but, surprisingly, the firms
do not report an increase in innovative output between 1994 and 2002. If we focus on differences by
firm size, these tables confirm our a priori reasoning that large firms are associated with greater
innovation activity and a more skilled labor force. The figures show that the proportion of innovative
large firms almost doubles that of innovative small firms. In terms of human capital, large firms also
report much larger proportions of skilled workers than small firms. The test for equality of means
rejects the null that, on average, the two types of firm have the same ratio of whitecollar workers, and
the test for equality of proportions rejects the null that small and large firms report similar proportions
of innovation activity. Differences in innovation and skilled labour endowments between small and
large firms remain quite stable over time, which is reflected later in the decomposition of the TFP gap.
10 As explained later in the paper, we use the lag of innovative activity and the percentage of skilled workers to
mitigate the effects of simultaneity. Therefore, we give the description of these measures for only 1994, 1998
and 2002, since the description for 1990 cannot be considered in the estimation.
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[Insert Tables 2 and 3 around here]
This descriptive analysis so far basically shows that large firms are more productive, more innovative
and invest more in human capital than their smaller counterparts. In addition, Table 4 shows that
innovation and employing skilled workers are associated with higher TFP levels in both small and
large firms. The table shows the average TFP for innovative and noninnovative firms with different
proportions of skilled workers and considering small and large firms separately. In general, TFP
increases as the proportion of whitecollar workers increases, which indicates a positive relationship
between these variables. In general, small innovative firms in a given quartile of human capital
distribution have higher TFP than small noninnovative firms. The same result is found for large
innovative and noninnovative firms. When we compare small innovative and large innovative firms,
we also find that the large firms are more productive than their smaller counterparts. Finally, the large
noninnovative firms are more productive than small noninnovative firms with the same percentage
of skilled workers. These results form the basis of the following analysis. Firms that innovate and have
a higher proportion of skilled workers are more productive, and among these firms, large firms are
also more productive.
[Insert Table 4 around here]
4.
Results
4.1. Estimation of the TFP specifications
The first step in our analysis is to estimate by OLS the empirical specification in (1) for the total
sample of firms and for the small and large subsamples. It should be noted that, to mitigate the effects
of simultaneity, we use the lag of innovative activity and the percentage of skilled workers. For the
total sample, column (i) of Table 5 shows that the estimated coefficients for the two variables of
interest (innovative activity and worker qualifications) are positive and significant at 1%. Therefore,
our results support the hypothesis that the knowledge capital used by a firm improves the mechanism
through which inputs are transformed into output. Specifically, process innovations reduce the unitary
cost of production and contribute to increased productivity. However, the effect seems to be modest:
changing from a noninnovative to an innovative firm increases TFP by only 3.4%.
The contribution of human capital to productivity is also positive and clearly significant. The
estimated coefficient for this factor confirms that more intensive use of skilled labor produces a higher
level of productivity. Specifically, increasing the ratio of skilled workers by 10% raises the TFP of the
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average Spanish manufacturing firm by 2.1%. For the control variables, both firm size and age have a
significant coefficient with the expected sign, while the sets of industry and time dummies are jointly
significant.
[Insert Table 5 around here]
Since we are interested in studying whether innovation and human capital make different contributions
to productivity enhancement in firms of different size, we estimate their effect on the subsamples of
small and large firms separately. As shown in columns (ii) and (iii) of Table 5, coefficients for
innovation are positive and significant at 1% in both cases. More concretely, small and large
innovative firms are more productive than their respective noninnovative counterparts. However, the
difference in the effect of innovation on firms of different size is moderate (3.5% for small firms
versus 3.7% for large firms), which suggests that once the innovation is implemented it exerts the
same effect on productivity regardless of firm size.
The effect of human capital is also positive and significant at 1% in both types of firm. However, the
most interesting feature of this variable is that its effect on TFP seems to be much greater for large
firms. Specifically, increasing the ratio of skilled workers by 10% raises TFP by 3% in large firms and
by only 1.8% in the case of small firms. Coefficients of the control variables remain significant for
both small and large firms, except for the coefficient of size in the sample of large firms.
The general conclusion we can draw is that innovation and employing more skilled workers enhance
productivity in both small and large firms. Furthermore, the impact of these variables on TFP seems to
be greater in large firms than in small firms. The fact that the impact of human capital is different
between the two subsamples indicates that small and large firms do not only have different human
capital endowments but also different returns to this factor. Therefore, the incentive to hire skilled
workers as a way of increasing productivity seems to be stronger in large firms. In contrast, the
differences in returns to innovative activity are not as large. This suggests that the impact of
innovation on differences in TFP across firms of different size seems essentially to be related to
differences in the propensity to innovate, which is much higher in large firms.
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4.2. Robustness Analysis
Additional control variables
The results presented so far are based on our baseline specification in Equation (1), which controls for
firm size and age, sector and time period. An initial robustness analysis of the estimated effects of
knowledge capital (i.e. innovation and human capital) and differences between small and large firms is
performed by including additional control variables related to particular characteristics of the firm.
Specifically, the variables added to the initial specification are defined as follows:

The proportion of the productive capacity used by the firm (PRODCAP).

The proportion of foreignowned capital (FOREIGNK), the proportion of publiclyowned capital
(PUBLICK) and a dummy to represent whether the firm belongs to a group of firms (GROUP).
They are intended to proxy for the ownership structure of the firm.

The degree of competition faced by the firm, proxied by the geographical scope of its principal
market (MARKET). We use a set of dummy variables to consider whether the market is local and
provincial, regional, national and international, or all three. The latter is considered as the omitted
category.

The (log of the) value of exports expressed in constant pesetas, base year 1990 (EXPORT).

A set of 17 dummy variables for the Spanish regions as defined in the NUTS II database (DREG).
The omitted category is “La Rioja”.
It should be noted that the effect of knowledge capital may well be related to these additional control
variables. Some characteristics may cause firms to obtain a higher return to the use of knowledge
capital, so that when controls are included that proxy for these characteristics we obtain a lower
estimate of the return.11
The results are summarized in columns (iv) to (vi) of Table 5. In general terms, the effect of the
control variables is as expected, although whether the firm is supported by public capital and whether
it belongs to a group do not seem to exert a significant effect on TFP over the whole sample. The
effect of foreign capital and the volume of exports varies between small and large firms. However,
more importantly for our analysis, the estimates of the effects of innovation and human capital are
fairly robust to the inclusion of these additional control variables. The greatest change is observed in
the estimates of the return to human capital which, as expected, decrease in magnitude (from over 20%
11 This argument is similar to the one usually formulated when analyzing the return to human capital from the
estimation of Mincerian wage equations (Pereira and Martins, 2004).
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to 14% over the whole sample, and a decrease of the same order of magnitude for the sample of small
and large firms).
Unobserved heterogeneity
As well as introducing additional control variables, we estimate a random effects model to account for
the existence of unobserved firm heterogeneity that is likely to affect our estimates of the returns to
knowledge capital.12 Columns (vii) to (ix) of Table 5 show the results of the estimation of the random
effects model for the whole sample and for small and large firms. In all three samples, a standard
Lagrange multiplier test clearly rejects the null of the absence of unobserved random effects.
When performing estimates with the whole sample, the coefficients of our variables of interest remain
positive and significant at 5% after controlling for firmspecific heterogeneity and the set of additional
control variables. However, in this case the estimate of the two coefficients is lower than the estimate
obtained when not controlling for unobserved heterogeneity. However, when firms are separated by
size, the estimated effect of innovation and human capital only seems to be significant (at the usual
probability levels) for large firms. In fact, the main conclusions are maintained in the case of large
firms, with an estimated return to innovation of approximately 3.5% and a return to human capital of
approximately 16.2%. However, neither of these coefficients is significant in the case of small firms.
In summary, both innovation and human capital seem to have an effect on productivity enhancement,
although the evidence suggests that the magnitude of this effect is very strongly related to firm size.
After controlling for an extensive set of conditioning variables and for unobserved firm heterogeneity,
the effect of the knowledge capital variables is only marginal and is not statistically significant for the
group of small firms.13 This suggests the existence of a threshold in the effect of innovation and
human capital that is related to the size of the firm.
Consequently, small and large firms show different patterns of behavior in relation to these variables:
they not only have different endowments, but the returns to these endowments differ substantially
between firms. In this framework we argue that differences in TFP between small and large firms are
12 This model assumes that firm heterogeneity is part of a compound error term that is uncorrelated with the
regressors. It has been common practice to estimate a random effects model when, as in our dataset, firms in the
sample are selected randomly from a larger population. Barrios et al. (2003), Máñez et al. (2004), and Licandro
et al. (2004) use this type of specification in analyses using ESEE.
13 It should be kept in mind that by controlling for the observable and unobservable heterogeneity in the last set
of estimates, we are considering the channels through which knowledge capital may be exerting its influence on
TFP. In such a case, the estimate of the returns from the specification that include firm heterogeneity should be
considered as a lower bound. This can be particularly important in the group of small firms if only those firms
with favorable characteristics are able to obtain profit from innovations and human capital.
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associated with differences in endowments and with differences in the returns to these endowments. In
the next section we analyze the relative contribution of these effects to productivity differences
according to firm size.
4.3
Decomposition of the TFP gap between small and large firms
As described in Section 2, the detailed decomposition of the productivity differential between small
and large firms allows us to assess the relative contribution of firm characteristics and the returns to
these characteristics, as well as decompose the individual effect of each variable. The individual
decomposition is particularly useful in this study, since we are interested in determining the
contribution of both human and technological capital. We calculate the decomposition based on the
specification with additional control variables with both the OLS and the RE estimates. Although in
our opinion the RE estimation would be preferable given that it considers unobserved firm
heterogeneity, we also obtain the decomposition based on the OLS estimation since it provides an
exact decomposition whereas the one based on RE does not.14, 15
Table 6 shows the results for each of the years under analysis, based on the OLS estimation (Panel A)
and the RE estimation (Panel B), for the specification that includes the whole set of control variables.
The TFP differential between small and large firms was approximately 0.08 in 1994 and decreased to
0.06 in 2002. The decomposition based on OLS estimates shows that differences in endowments
almost completely account for the TFP gap. Specifically, in 1994, differences in endowments
accounted for approximately 95% of the differential, while differences in returns accounted for the
remaining 5%. Between 1994 and 2002, the contribution of endowments increased and reached 104%
in 2002. A contribution of differences in endowments with a value higher than 100% implies that
differences in aggregate returns favored small firms in the last two years of the analysis (negative
contribution of differences in returns).
However, this general result is an aggregation of the effects of all variables in the specification, thus
positive and negative effects may be compensated. As stated above, the detailed decomposition allows
us to assess the individual contributions of innovation and human capital. The results suggest that
these two variables together, including differences in endowments and differences in returns, account
14 In the RE model the transformed residuals have zero mean, but the residuals from the original specification do
not. This prevents us from obtaining an exact decomposition of the TFP gap based on the RE estimates of the
coefficients.
15 The decomposition described below is robust to the choice of omitted category in the dummy variables in the
TFP specification, as the estimates used to compute it have been obtained by imposing the parametric
identification constraints suggested in Gardeazabal and Ugidos (2004). This is particularly important in the case
of innovation, which is one of the variables that interests us in this study.
14