Technology and Investment, 2013, 4, 1-9
doi:10.4236/ti.2013. 43B001 Published Online August 2013 (
Assessing Some Determinants of the Regional Patenting:
An Essay from the Mexican States
Vicente German-Soto1, Luis Gutiérrez Flores2
1Facultad de Economía, Universidad Autónoma de Coahuila, Unidad Camporredondo,
Edificio “E”, Planta Baja, C.P. 25280, Saltillo, México
2Centro de Investigaciones Socio-Económicas (CISE), Universidad Autónoma de Coahuila, Unidad Camporredondo,
Edificio “S”, Planta Baja C.P. 25280, Saltillo, México
Received April, 2013
The aim of this work is to study the environment that affects and influences in the creation of regional patents. With this
purpose the patenting process is modeled as dynamic one where, beside other factors, its past values contribute to create
synergies to continue patenting in a feedback process. Using a dynamic panel data estimator we find that past patenting
level trends to encourage the actual one. Also, a positive and significant effect from education, university expenditure,
population density and industrial concentration on patents is reported in the Mexican states set. Conclusions highlight
that agglomeration forces are the main factors for patenting, followed by university expenditure and industrial concen-
Keywords: Patents; Innovation; Agglomeration; Dynamic Panel Data; Education
1. Introduction
Patents itself are expressions of new knowledge and in-
novative activities on how to produce and how to in-
crease the productivity and despite of the existence of
clear disadvantages in its use as an output of the innova-
tion activity –about it, see [2,18]– it has widely been ac-
cepted everywhere. One explanation could be that the
innovation is a wide concept very difficult to measure
and one of its preferred measures has been the count of
patents. Another explanation is, maybe, that count of
patents is a statistical number easy to obtain for a great
set of countries and economies.
There is an extensive literature considering patents for
several purposes, but mainly as measure to analyze the
technical change. For example, it has been considered as
a catalyst for technical change and the technical change
as key element to reach majors levels of economic
growth and international trade, primarily from a theo-
retical perspective. At this respect, [29] examines a
search model of growth in which ideas are productivity
levels that are drawn from a distribution. He shows that
only way to get exponential growth in such model is if
ideas are drawn from a Pareto distribution. [26] maps a
production function where the elasticity of substitution
depends on the extent to which new techniques that are
appropriate at higher capital-labor ratios have seen dis-
covered. In his model the global production function is
Cobb-Douglas and technical change in the long run is
labor-augmenting. Others, such as [10], and Slottje (2007)
present a model where patent activity serves as catalyst
for technical change and they examine if it has occurred
over time. [34] reports a decreasing relationship between
how strong the optimal patent protection should be and
the ability of the economy to successfully follow risky
innovation strategies. This finding suggests that devel-
oping economies should adopt a more strict intellectual
property policy, compared to the ones followed by more
advanced economies.
Other studies have used patents statistics to examine
different aspects about the realization of technological
change. The relationship between patents and Research
& Development (R&D) expenditures, patents and
knowledge spillovers, patents and inventiveness rate of
growth, patents and economic growth, and some others
have been examined in some detail in literature –see, for
instance, [3,9,23]. There appears to be a consensus that
patent statistics reflect somehow the technological state
of the art of a country, or its ability to embed technical
change into the functioning of the economic system.
However, count of patents is a general measurement of
the innovation level and its only consideration is not suf-
ficient to estimate the true level of innovation of the
economies. One patent has the property of being useful
Copyright © 2013 SciRes. TI
for many years and so impacting the incomes of its
trademark owner a long time. This particularity suggests
that other ways must be considered if the purpose is to
take into advantage of the number of patents generated in
one economy, although there has been little progress on
the creation of more robust measurements mainly due to
the scarcity of information. In this work, we consider that
a most complete measure of the innovation level would
be the accumulation of patents.
There are at least two empirical reasons to consider the
patents accumulation. First, a patent is useful for many
years and so it impacts in the economy a long time. Sec-
ond, a majority of variables are accumulated amounts
that not only represent the performance of that year or
time period. As examples we have some indexes of edu-
cation such as the average schooling years, the general
domestic product of the economy is influenced by the
added value created in that year but also by the corre-
sponding figures of the past years, agglomeration indexes
also constitute aggregations along the time of a set of
variables, the employment level, etc. In this way, the
only consideration of the number of patents created in a
specific year would give an incomplete picture of the
relationship among the economic variables and innova-
On the other hand, the economic theory predicts a pos-
itive effect of knowledge on productivity and innovation
on knowledge, but size and importance of factors that
promote the patents as via to increase the knowledge and
innovation kept yet under research. The purpose of this
paper is to explore how patent activity can be determined
by some factors arising from the “macro” sphere. We
estimate a dynamic panel data (DPD) model to observe
the relationship between accumulated patents (as per-
centage of population) against some of its primary fac-
tors. This technique has the advantage that takes into
account the past patenting as other factor that affects and
stimulates the actual activity of patenting. As it is known,
DPD model presents a difficulty because lagged de-
pendent variable included in the right side of the regres-
sion equation is correlated with the error term and so it
presents problems of endogeneity. Regarding this aspect,
we follow the econometric suggestions and a Generalized
Method of Moments (GMM), as in [7], is implemented.
The contribution of this work is in several directions.
First, the implemented model tests if determined primary
economic factors are performing as is expected from the
theory –magnitude and direction of the effect. Second, at
empirical level this essay has not been undergone, while
commented papers above are concentrated in theoretical
issues on technical change, they not specifically consider
how patenting can be stimulated with the end to reach a
technical change. Third, the empirical essay allows quan-
tifying how economic environment is impacting in the
patenting activity. And, finally, DPD and GMM methods
are yet a novelty in the patenting theme.
The application to the regional Mexican case gives
light to understand two phenomena occurring in the last
few years. First, rates of economic growth in Mexico are
erratic and mainly low –below of 3% in the last ten
years– and, second, Mexican regions are increasingly
more uneven. Both problems have practical cones-
quences in a variety of ways, such as the creation of new
employment, reduction of poverty, improving the pro-
ductivity, and stabilizing the rate of exchange, among
other. Specifically, the exercise allows responding to
how much patenting activity is linked to the industrial
structure, urbanization degree, education level and re
search activities in the Mexican states?
Our results suggest that, effectively, agglomeration
(population density), education, industrial concentration
and government subsidy to public universities have sig-
nificant and positive impacts on patenting process of the
Mexican states. Agglomeration forces and industrial
concentration are identified as the main factors for pat-
enting. It means that innovation in Mexico follows a
geographical pattern in areas densely settled and techno-
logically advanced in line with previous findings by [19].
We hope that these results become helpful to understand
the patenting process in Mexico and its relevance to
achieve major stadiums of economic development.
The layout of this document is as follows. The first
section below presents a theoretical point of view re-
garding knowledge, innovation and patents and their
links with economic growth that can be used to generate
specific hypotheses. Then, section 2 presents the econo-
metric model, the variables and availability of informa-
tion to conduct the empirical essay. The section 3 com-
ments the main results and details about direction of the
estimates. Finally, section 4 highlights some conclusions
reached in this work.
2. Theoretical Standpoint
As the economy has evolved over time, the key factor
behind growth also has been displaced from labor to
knowledge accumulation. Nevertheless, accumulated
knowledge finds its raison dêtre through innovation.
The interaction between knowledge and innovation
shapes the necessary strength to allow the economy to
remain competitive. The essence of any modern econ-
omy relies on its ability to increase the application of
knowledge ([17]), which makes us think about innova-
tion in terms of knowledge used to create new knowl-
In this sense, firms and industries produce technologi-
cal knowledge which is internal to its activities, but later
might spill over to the rest of the industry or the economy
Copyright © 2013 SciRes. TI
when such knowledge gets imitated or copied at a very
low cost by other firms ([36]). This spillover effect al-
lows for the production function to operate with increas-
ing returns, thereby creating a process of sustained eco-
nomic growth as long as the economy continues to gen-
erate knowledge aiming to innovate. Under this analyti-
cal view, the application of new technologies becomes
fundamental in achieving the goals of innovation and
economic productivity growth.
The mechanisms implemented to foster knowledge
based innovation can be observed in two levels of analy-
sis. In the first one, which can be labeled as the “micro”
level, there are the firms. Internally, firms make efforts to
enhance their technological capacity aiming to increase
productivity that finally traduces in a better market posi-
tioning. Since academic researchers began to recognize
the importance of knowledge accumulation for develop-
ing innovative procedures or in the design of new prod-
ucts, there has been increasing interest in inquiring about
the determinants that cause firms to enhance their inno-
vation performance. The most explicit determinant is the
amount of resources devoted by firms to R&D. It is usu-
ally thought that R&D helps in accelerating scientific
innovations that lead to productive growth of firms, in-
dustries and the economy.1 For instance, the works of
[2,11,18,24,25,30], develop the analytic perspective of
R&D impact on firm innovation performance in several
The second level of analysis involves an aggregated
perspective. We label this as the “macro” level. In the
“macro” level case an important element in the discus-
sion of innovation, knowledge accumulation, and growth
is added. That element is space. As economic integration
has been moving forward across the world, then regions,
rather than countries, have been considered as units of
analysis ([37]). This of course arises from the fact that
regions are more homogeneous and better connected
within themselves, and that the flow of information fa-
cilitates the exchange of new ideas.
In the “macro” level, innovation is the result of the
combination of several factors such as education, Indus-
trialization degree, concentration and agglomeration
forces, which tend to accelerate the economic growth of
a country and determine international trade patterns. In
this context, the works of [14,28,31,33] relate innovation
to the geographical concentration in order to establish
production patterns. The “macro” level is precisely the
analytical perspective adopted in this work.
The aforementioned used ways to characterize the
mechanisms implemented to foster knowledge based
innovation (micro and macro levels) are not opposed to
each other. Instead, they should be regarded as comple-
mentary results of the process in which innovation is
incorporated into the economic system of production.
However, some market economy disadvantages cause
public entities, mainly governments and universities, to
assume the responsibility in financing innovative active-
ties. As a matter of fact, public entities are instrumental
in providing resources, incentives and opportunities for
the private sector to innovate ([15]). Additionally, in
many cases there are policy instruments designed to fos-
ter scientific research and higher education implemented
by governments as responses to market failures.2 Not
only the public sector provides incentives and financial
resources, but also protects property rights and helps
mitigating risks ([15,16]). Particularly, governments tend
to fund basic research, in contrast to private firms which
tend to develop market rewarded activities (applied re-
search). In turn, universities produce and disseminate
knowledge while educating its students becoming in a
fundamental source of human capital. Universities also
serve as a potential source of technological advances for
the industry.
In Mexico, some studies have marked the start of a re-
search area of interest given the relevance of the tech-
nology innovation diffusion on productivity and growth.
Particularly, the works of [1,13,19-21,35] have all at-
tempted to characterize the recent phases of the devel-
opment and growth process in Mexico through the use of
The theoretical path that we follow is summarized in
Figure 1. In there, is showed that technical change is
driven by knowledge and innovation, while technical
change is a determinant factor to push economic growth
and international trade. Also it is assumed that knowl-
edge and innovation have some characteristics (previ-
ously commented) that make necessary the design of
government policies favoring the technical change.
Figure 1 also shows that accumulation of knowledge
begins the mechanism that results in innovation, but in-
novation itself reinforce the knowledge generating more
knowledge and it in turn reinforces the innovative activity,
and so on. However, knowledge–and innovation– is con-
sidered to have the characteristics of a public good,
which can then cause the market to fail in assigning the
right amount of knowledge required to innovate. The
government appears in the scene to facilitate the flow
from knowledge and innovation towards technical
change through implementing policies related to science
and technology, industrial policies, higher education and
very importantly, property rights protection via the patent
sytem. In the final stage of the process, innovation and s
2Two examples of this type of policies are the direct financing of basic
research and the enhancement of the intellectual property protection
mechanism available in a lot of countries.
1[32] discusses some of the disadvantages in the use of R&D expendi-
tures as an indicator of innovation performance.
Copyright © 2013 SciRes. TI
Copyright © 2013 SciRes. TI
Figure 1. An innovation and technical change scheme from a macro perspective.
knowledge foster economic growth and enhances inter-
national trade.
3. Data Availability and Econometric
3.1. Description of Variables
For the Mexican case, taking advance of the year-to-year
patents disposition and for each federal entity we built an
inventive coefficient through the accumulated average
patents per 100,000 inhabitants (PAT). This way we as-
sess how this index is evolving along the period by
means of a regression equation. Data on patents and
population of states were obtained from IMPI (Mexican
Institute of Property Rights) and INEGI (National Insti-
tute of Statistics). As explanatory variables we consider
the population density (POPDEN) as a proxy of agglom-
eration forces, measured through number of persons per
square kilometer; also a couple of education variables is
considered: the average schooling years (SCHOOL) and
the average government subsidies to public universities
(GSPU) by student in superior education measured at
real prices of 1993; finally, a location quotient of the
high-technology industries (LQHTI), as a measure of the
industrial concentration, is assessed. This last index was
built as the percentage state employment divided by per-
centage national employment in high-tech industries. We
contemplate patenting process as dynamic in the sense
that one patenting occurring in the past years could have
positive feedbacks in the future patenting. Also, the ac-
cumulation of patents suggests that effects of invents can
persist several years and they do not necessarily disap-
pear at all. If this is so, then patents accumulation process
should be taken into account.
As is well known there are much more variables af-
fecting the patenting activity, but we have decided to
choose this set for at least two reasons. First, they are
easily available for all economies, and second, we seek to
measure the impact and magnitude of these set of vari-
ables because often they are government targets to im-
prove the well-being of the population. Sources of data
are from official institutes as follows. POPDEN and
SCHOOL are figures provided by INEGI, meanwhile
GSPU is a factor published on year-to-year basis by
ANUIES (council of Mexican public universities); fi-
nally, LQHTI is an index of concentration calculated by
us with data on employment for high-tech industries of
the Mexican states also published by INEGI.
3.2. Econometric Specification
The dynamic panel data is a widely used methodology
when data are few in terms of time periods and individu-
als. Our database includes 13 time series and 31 cross-
sections (after excluding Distrito Federal),3 so we have in
all 403 pooled observations on patents and their factors.
Although estimations based in dynamic panel data
method loose two observations because lagged variables,
3Some statistics are not available for Distrito Federal (for instance, the
number of scientists is not published). Also, the statistics for this state
are quite elevated in comparison to the rest of states, which means that
Distrito Federal is a potential outlier biasing our estimations when
employing regression equations.
so in this case the database contains a total of 341 obser-
vations (31 × 11).
The estimations are conducted following three alterna-
tive regression equations: pooled regression, panel data
with fixed effects and dynamic panel data. In short, the
strategy to capture the impacts on patenting is as follows.
We start from the general modeling for analyzing
pooled regression:
it it
 
yαxβ (1)
where matrix it contains K regressors, it
is the
patents accumulation per each 100,000 inhabitants, β is a
vector of coefficients to be estimated and is a random
error term. Taking into account the asymmetry and het-
erogeneity problems expected from a set of individuals,
regressions, obtained from a pooled viewing, can be po-
tentially misleading. Therefore, a more realistic structure
can be done by panel data modeling:
iti it
yxβα (2)
where i is a set of individual variables which may or
not be observed. Existent heterogeneity among cross-
sections is captured through this matrix of individual
effects. If i may be observed for all cross-sections
then it is possible to fit the model by least squares. In not
few situations, like actual exercise, this is not the case,
because some variables such as ‘ability’ and ‘experience’,
among others, will be missing and unobservable vari-
ables; also, there are factors and decisions from firms and
individuals that are not possible to measure only from
observed variables. So, the phenomenon can be best han-
dled by panel data than other methods.
On the other hand if i is reduced to the constant
term, then ordinary least squares is enough to obtain con-
sistent and efficient estimates of the common and the
slope vector β. This case is equivalent to treat the model
as pooled regression. However, unobserved variables and
heterogeneity among cross-sections are expected from
both theory and empirics behavior suggesting that esti-
mators from least squares will be biased and inconsistent
as a consequence of omitted variable.
To fix this problem panel data literature considers two
ways, at least: fixed and random effects. The first one
assumes that unobserved variables are correlated with
regressors included in the model, meanwhile in the last
structure an uncorrelated relationship is assumed. As
consequence that patenting decisions –observed and un-
observed– are expected to be correlated the fixed effects
seems to be more convenient. Fixed effects method as-
sumes an estimable conditional mean in the model (2).
This formulation implies that differences across indi-
viduals can be captured through differences in the con-
stant term.
The Equation (2) may be estimated to see the rela-
tionship between patents accumulation and its factors.
However, it does not take into account the potential ef-
fects of the past patenting, in such a way that one econ-
omy with more patents trends to increase its patent ac-
tive- ity. Therefore, patenting would be better symbol-
ized as an accumulative process. A dynamic structure of
panel data suggests that one way to consider this possi-
bility is modifying the equation (2) as follows:
,1iti tit
it i
yxβyα (3)
where itt it
together with the assumption
x. The lagged dependent variable in the
right side of the equation converts the panel data struc-
ture in dynamic one. A difficulty with equation (3) is the
possible correlation of the lagged dependent variable
with the error term even in the case it
is serially un-
correlated ([22] and [8]). It means that estimated coeffi-
cients from ordinary least squares (OLS) are inconsistent
in small samples. Fixed effects estimator, which is a
mean of k estimators, also results unsuitable. Considers
as one vector containing the estimated coefficients from
equation (3), that is
θβ,α. Then, [27] prove that
OLS estimator is given as:
ii ii
ii iii
xMDx xMDy
xMDx xMDxb
 
 
 
 
 
 
 
 
where MD is the orthogonal projections matrix defined
from the dummies variables. Simplifying the equation (4)
we have,
From this representation it is possible to infer that es-
timated coefficients of fixed effects are result of a mean
of k estimators. It is equivalent to run a regression by
OLS using transformed data, but even so the mean of k
estimators is inconsistent.
Particularly, when lagged dependent variable is pre-
sent in the right side of the equation, fixed effects pro-
duces biased estimations and this problem is more ac-
centuated in the small T cases. [27] evaluate several
techniques created to estimate dynamic models and they
find great biases with fixed effects.
An alternative to fixed effects is the Generalized
Method of Moments (GMM) as [6]. This method re-
quires no knowledge concerning the initial conditions or
the distributions of the error term. In short, the GMM
estimator basically differences the model to eliminate the
individual specific effects. This also eliminates any pos-
sible endogeneity due to correlation among individual
Copyright © 2013 SciRes. TI
effects and the regressors. The moments consist in to use
the orthogonally conditions between errors –in differ-
ence– and lagged values of the dependent variable. The
model assumes that the original disturbances are serially
uncorrelated and for this reason it is supported in a set of
diagnostics concerning to significance of instruments.4
With the end to obtain efficient estimations through
GMM it will be necessary to include a set of instrumental
variables and to apply a transformation to remove cross-
section fixed effects. [7] suggest applying first differ-
ences or orthogonal deviations to the dynamic panel data
model. Orthogonal deviations strategy has the property
that if the innovations are i.i.d., the transformed innova-
tions are also i.i.d. Meanwhile, the set of instruments can
be a combination of lags and levels of the dependent and
predetermined variables.
With those econometric details in mind, and after to
give name to variables it and it , the empirical re-
search specification is due as follows:
y x
 
,1 2
34 ,
ln ln
ln ln
it it it
it it
 
 
 
 
for the case of pooled regression. Due to strong proper-
ties of correlation and heterogeneity imposing by this
equation in which all individual are taking as equal, a
more convenient specification would be given by fixed
effects method,
,1 2
34 ,
ln ln
ln ln
it iit it
it it
 
 
 
 
where t
denotes the dummies of time periods and ,it
is the random error term. If we also are interested in cap-
turing the past effects of patenting on the actual one then
the lagged dependent variable can be used as regressor in
the model. In this case we have a dynamic version of the
panel data structure:
,0 ,11,
,,, ,
ln ln
it itit
it it
itit itit
 
where .
~... 0,,~... 0,1
iidN iidN
Equation (8) can be obtained as an approximation of
the theoretical relationship between patenting with ag-
glomeration, education, and industrial concentration, in
which patenting in period t depends on patents in t-1. The
degree of patenting in t is measured by β0, which will be
positive if past patents effectively are influencing in pe-
riod t –that is, exists feedback. Furthermore, the other βi
coefficients should be positive due to convexity of the
explicative variables. Equation (8) captures the fact that
innovative activities behavior implies that past patenting
increase current one, holding the current values for ex-
plicative variables fixed.
To treat with patents accumulation has the advantage
that it is not a poor measure of the innovative activity
–such as could be the case if only we consider count of
patents–; however it is just to recognize some limitations
as for instance we cannot observe the potential effect of
other important domestic factors and our model considers
that all inventions have the same effect on innovation.
Nevertheless, we think that essay could be an acceptable
indicator on how patenting activity is evolving and how
the main factors are promoting.
4. Discussion of Results
4.1. An Exploratory Analysis
The Table 1 exposes the relationship between all vari-
ables. The correlations with patenting are all positive and
the greater correlation is on average schooling years.
This first approaching favors the existence of some rela-
tionship between the set of variables.
With the end to have a perspective of the variables
behavior the Table 2 shows some of the most relevant
descriptive statistics of data set. There is an average of
2.72 patents registered by the 31 federal entities along
the period 1994-2006; there is a population density of
89.78 inhabitants by square kilometer; the average
scholarly is 7.42 years and government subsidy has an
average of 12,295 pesos (national money in real terms)
by student. Taken together all the states have a mean of
location quotient of 0.78 < 1, indicating that the average
industrial concentration is minor to the national one. Ac-
cumulated patents show maximum and minimum values
of 18.78 and 0.055 with a standard deviation of 3.12
along the period. These same statistics for the rest of
variables are: 636.39, 4.84 and 114.04 (population den-
sity); 9.6, 5.0 and 0.92 (scholarly years); 41.38, 1.76 and
5.82 (government subsidy to public universities); and
2.32, 0.02 and 0.63 (industrial concentration index).
4.2. Results of the Regression Analysis
Three methods of regression are estimated: pooled re-
gression, data panel with fixed effects and dynamic panel
data. For dynamic panel data method we apply orthogo-
nal deviations transformation to remove cross-section
fixed effects. Dynamic panel data models are estimated
by GMM methods. [7] consider two alternatives: GMM
1-step and GMM 2-step. We use the last because we
consider that errors have time series correlation structure
that varies by cross-section.
A number of instruments must be used with the end to
obtain efficient GMM estimators. The discussion on
GMM estimators can be found in [4,6,12]. In our present
case some essays including it as instruments had not
efficient estimations. [7] consider that explanatory
4Formal details on this technique can be consulted in [5,7].
Copyright © 2013 SciRes. TI
Copyright © 2013 SciRes. TI
Table 1. Correlation matrix table.
Average Schooling
Accumulated Patents 1
Population Density 0.226 1
Industrial Concentration 0.445 0.422 1
Average Schooling Years 0.577 0.128 0.348 1
University Expenditure 0.285 0.280 0.284 0.255 1
Source: own estimations with data from INEGI, Conapo, ANUIES and IMPI.
Table 2. Global descriptive statistics of the database.
mean Maximum value Minimum value Standard deviation
Accumulated patents 2.72 18.78 0.05 3.12
Population density 89.78 636.39 4.84 114.04
Scholarly years 7.42 9.60 5.0 0.92
Government subsidy 12.29 41.38 1.76 5.82
Industrial concentration index 0.78 2.32 0.02 0.63
Source: own estimations with data from INEGI, Conapo, ANUIES and IMPI.
variables must be strictly exogenous with respect to re-
siduals for consistency. They also suggest using or-
thogonal deviations to allow suitably lagged endogenous
variables as instruments. Therefore, our estimates with
dynamic panel data model employs from two to six lags
of the dependent variable and it also combines levels of
the explanatory variables as instruments. The estimates
using cross-sec- tion effects were not sufficiently effi-
cient; in contrast dummies of time periods yield the bet-
ter results. All explanatory variables were measured in
logarithm terms except the average schooling years. This
variable yield best results when it was included in the
equation as first differences. The Table 3 shows the main
results with the three above commented methods.
It is clear a miss-specification between patents and its
factors in pool regression and fixed effects methods. All
variables were statistically significant except average
school years (SCHOOL), which also resulted with the
inverse sign when the fixed effects method was imple-
mented. Although adjustment was estimated in terms
quite acceptable –31% and 38%, respectively– the
Durbin-Watson index prevent us to take into account these
results because quite low values of this measure, indicat-
ing that a strong problem of autocorrelation is present in
those estimates. Conversely, dynamic panel data seems
to give best results according with the theoretical expec-
tative. Now, all the explanatory variables are highly and
statistically significant, moreover the list of instruments
used is valid and the J-Statistic suggests that the null hy-
pothesis of over-identifying restrictions is valid (see
p-value of 0.9231). This means that GMM method and
Table 3. Panel data estimates of the patenting factors
Variable Pool Fixed Effects Dynamic Panel Data
Constant 5.7112*** 4.8365***
PATi,t-1 0.9491***
ln(POPDEN)i,t 0.5804*** 0.5421*** 3.0766*
(0.1474)(0.1438) (1.8204)
Δ(CHOOL)i,t 1.0302 1.8391 0.8145***
(1.6739)(2.1863) (0.2925)
ln(GSPU)i,t 2.8605*** 2.6893*** 0.7854**
(0.3224)(0.3423) (0.3821)
ln(LQHTI)i,t 1.0074*** 0.9936*** 1.0003**
(0.1194)(0.1157) (0.4171)
R-SQR 0.31 0.38
Durbin-Watson0.04 0.03
J-statistic 12.8749
Instrument rank 31.00
p-value 0.9231
observations 372 372 340
Notes: standard errors in parentheses. Fixed effects method was estimated
with time dummy variables. Dynamic Panel Data was estimated by 2-step
GMM using orthogonal deviations and dummy variables of period. The
instruments are lags 2 at 6 of dependent variable and the levels of the ex-
planatory variables. The J-Statistic is simply the Sargan statistic and it tests
the null hypothesis that the over-identifying restrictions are valid. Super-
scripts***, **, and *, indicate significant at 1%, 5% and 10%, respectively.
the mixture of lags and levels variables provide a best
representation of the relationship among patents and do-
mestic factors.
It is observed from the Table 3 an estimated and
highly significant coefficient of 0.9491, indicating that
when index of patents increases in one patent per
100,000 inhabitants in the previous year then there is a
probability that in the next year almost a new patent can
be created. When subsidy of the government increases in
1% per student then the creation of patents arise to 0.78,
which implies that three quarters of a patent are being
created in average. However, the greatest effect came
from population density –agglomeration force. Results
highlight that if population density grows 1% then the
creation of patents is equal to 3.07 per 100,000 inhabitants.
This result is indicative that urbanization and the
spillovers arising from positive externalities in the cities
are becoming the most important forces to achieve major
standards of patenting. A second best place is obtained
by industrial concentration measured through the loca-
tion quotient. In this case, when the employment in
high-tech regional industries increases in 1% relative to
the national one, then inventive coefficient is increased in
approximately the same proportion. Scholarly also exerts
a positive effect in the patenting process. In this case, the
model estimates that this factor is highly and statistically
significant. The estimated coefficient indicates that ab-
solute variations of average scholarly years in the federal
entities help to increase the patents. Each average school-
arly year signify an increasing of almost four fifth parts
of patents. Also we can explain than for each 10 per cent
of increasing in the average scholarly years a total of
0.08 patents is being accumulated.
The exercise can be useful to know how education,
industrial concentration, population density and the ac-
cumulation of patents are performing. We think that gen-
eration of such estimates may be useful as a guide to im-
prove the achievements on economic development, such
a way that factors represent a technical change driving
appropriately the economic performance of a set of
5. Conclusions
Summarizing, this paper relates knowledge to a set of
“macro” level factors to characterize the patenting proc-
ess in Mexico. Using a dynamic panel data empirical
approach our results show that agglomeration, as meas-
ured by population density, exerts the bigger influence on
the accumulation of patents. This finding indicates that
innovation activities tend to be localized in those regions
where there are better market size related opportunities.
Additionally, other forces connected to agglomeration,
such as urbanization and spillovers must be interplaying
in to explain the patenting performance. Another factor
that resulted considerably important in explaining pat-
enting intensity is the concentration of employment in
high-tech industries.
Public education is also found to be relevant in deter-
mining innovation activities. When the federal subsidy
on public universities increases, so does the inventive
coefficient. Higher educational levels also imply higher
patents accumulated. Aiming to improve Mexico’s inno-
vation performance, we can state that a deeper effort in
terms of higher education expenditure must be carried
out. It should be complemented with schemes designated
to seize the advantage of agglomeration economies that
according to our study, are already present.
If theoretical arguments are correct and knowledge
based innovation is the key factor explaining economic
growth in recent years, we should expect a more explicit
effort by the national government in terms of enhancing
the federal states capabilities of capitalizing better tech-
nological opportunities. Nevertheless and making a quick
assessment of the matter, this does not appear to be the
case. Additionally, as economic growth has been ac-
knowledged as a more regional or local process, state or
local science and technology development programs
should become more prevalent. And again, there is not a
clear indication that this will be the path to follow in the
near future.
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