Spatial non-price competition in port infrastructure services
Soraya Hidalgo-Gallego
Ramón Núñez-Sánchezy
Pablo Coto-Millánz
April 26, 2016
Abstract
This study analyses spatial capacity competition in Spanish port authorities in order
to evaluate how e¤ective it has been the investment process in infrastructure for the last
twenty years. In this way, we propose the estimation of a dynamic two-stage model using
the NEIO approach. The main results show that shippers do not only take into account the
monetary costs of moving their cargo but also non monetary cost and substitutive ports’
charges and capacities. Moreover, we demonstrate that capacity competition exists but it
seems not to be too intense. Finally, using a counterfactual analysis, we simulate an scenario
of hypothetical alliances among di¤erent port authorities.
1. INTRODUCTION
In the last decades, ports over the world have been subject to structural changes, because
of the need to adapt to a constantly changing environment marked by globalization, growth
of international trade and the relocation of the main centers of production and consumption
Departamento de Economía. Universidad de Cantabria (Spain). Avda. Los Castros, s/n. 39005
Santander. Phone: +34942200868. Fax:+34942201603. E-mail: [email protected].
y
Departamento de Economía. Universidad de Cantabria (Spain). Avda. Los Castros, s/n. 39005
Santander. Phone: +34942206728. Fax: +34942201603. E-mail: [email protected].
z
Departamento de Economía. Universidad de Cantabria (Spain). Avda. Los Castros, s/n. 39005
Santander. Phone: +34942201653 Fax: +34942201603. E-mail: [email protected].
1
jointly with important technological changes in the sector; besides for European ports, the
entry into force of the European Single Market in 1993 presented new competitive challenges.
This has pushed ports to search for more e¢ cient organisational solutions. Speci…cally, the
Spanish port system have been transformed since 90s by four important port reforms (Law
27/1992, Law 62/1997, Law 48/2003 and 33/2010). These reforms have led the Spanish
port authorities to operate according to principles such as …nancial and operating autonomy,
quality and e¢ ciency, growing the participation of private sector in port activities by the
adoption of a landlord model and promoting intra and inter-port competition through higher
‡exibility in set port charges and investments. The result has been that, in the reality, an
e¤ective competition in prices has not occurred because there are not signi…cant di¤erences
between the port charges set by port authorities, so ports have used to compete other
strategies as capacity investments. The problem is that strong investments carried out
during the last twenty years have led to the overcapacity of the system, which implies
signi…cant losses of e¢ ciency and resources.
In this context, it is crucial to asses what has been the impact of such investments on
port demand, whether capacity expansions have been able to attract new tra¢ c to a given
port. This paper aims to evaluate the degree of non-price (capacity) competition of the
Spanish port authorities during the period 1992-2011 and determine the e¤ect of capacity
investment in port demand. To do this we carry out a model based in two di¤erent by
related approaches, game theory and new empirical industrial organization (NEIO). From
our model we are able to test and measure the degree of capacity competition, the generation
and deviation of tra¢ c caused by capacity expansions and using a counterfactual analysis
to simulate an scenario of hypothetical alliances among di¤erent port authorities.
Section 2 describes the Spanish port system paying particular attention to inter-port
competition and the investments in the sector. Section 3 o¤ers a brief review of the studies
which include port capacity in their analysis. In section 4, the theoretical model is developed
while section 5 shows the empirical speci…cation of our model. In section 6, data is described.
Finally, section 7 discusses the estimation results and some conclusions are given in section
8.
2
2. SPANISH PORT SYSTEM
Port privatization waves over the world during the 90s, the growth of maritime freight
and the entry into force of the European Single Market in 1993 showed the need to provide
the Spanish port system of a new regulatory framework in order to achieve greater agility
and ‡exibility to adapt to the changes and challenges that were to come. From this need,
the law 27/1992 arose with the aim of endowing Spanish ports with the tools to cope with
these new challenges.
Following the recommendations of the European Parliament (Resolution on port policy,
November 1988) on port management autonomy, competition between ports and cost coverage through port users’transfers, the Spanish government with this law created the Spanish
port authorities, began a liberalization process of port services with the introduction of private participation and set a new charge structure.
Port authorities were constituted as public entities with legal personality, autonomous
management and their own assets, independent of the state, which carry out their activity
according to business rules and procedures except in the exercise of the functions of public power that the law ascribes them. In turn, the public entity State Ports with global
responsibility for the entire port system is created in order to control and coordinate port
authorities.
On the other hand, this law designs the charges for port services as private prices so
as to provide ports more ‡exibility when they set their port charges. But this ‡exibility
is not complete because this reform imposes maximum and minimum boundaries to these
port charges, justi…ed by the self-…nancing of the whole system and prevention of abusive
practices on the captive tra¢ c.
Subsequently, the law 62/1997 delves into the functional autonomy and management
authorities, also establishes measures to increase the intensity of participation of regional
governments in the structure of authority in order to integrate more e¤ectively the interests
economic and territorial of the a¤ected regions. In addition, this law encourages further
private participation in the provision of port services and speci…es self-…nancing of port
3
authorities and not just of the overall system.
After a decade since the adoption of the law of 92, new developments and new economic
realities justify legislative renewal with the law 48/2003. During this decade, there has
been a signi…cant growth in demand accompanied by an increment of port competition,
both nationally and internationally, to attract international maritime tra¢ c and the intra
port competition between di¤erent providers of port services in a port has intensi…ed. In
this environment, the new law sets as main objectives: enhancing the competitive position
of Spanish ports guaranteeing the principles of free competition; setting criteria pro…tability and e¢ ciency in exploiting the public port space; promoting participation of private
companies in funding, construction and operation of port facilities and the provision of
port services; enhancing the quality and e¤ectiveness of port services delivery, reducing the
cost of passage of goods by the ports. Besides, this law goes a step beyond the target of
self-su¢ ciency and cost coverage by transferring them to users based in the recovery of
operating costs, external costs and the costs of new investments.
To meet these objectives, regulators again try to endow port authorities of greater ‡exibility to set public and private prices, respectively, by the use of port space and the provision
of port services. In this way, port authorities are allowed to have enough leeway to set the
speci…c amount of each charges and their bonuses depending on technical and market criteria and the pro…tability target which each authority negotiates with Puertos del Estado.
In this way, this law tries that port authorities can draw up their own business plan and
competitive strategies, but always conditional to the approbation by Puertos del Estado.
Finally, Law 33/2010 amends the previous legislative reform, seeking to provide to the
Spanish port system’s price model the ‡exibility which to date had not been reached, in
order to each authority could adapt its port charges to its economic actually.
Despite of being one of aims of the Spanish port reforms, in practice these reforms have not
allowed the existence of signi…cant di¤erences between the prices set by the port authorities,
which has not allowed the occurrence of an e¤ective price competition in Spanish port
system. If we add the fact that the weight of these port charges in the total cost of
transporting goods is relatively small (Martínez-Budría, 1996), the port authorities have
4
not found prices as a strategy to compete. This has led port authorities to seek other ways
to attract cargo tra¢ cs and extend their hinterlands, being the investment in port capacity,
the main competitive strategy developed (Haralambides, 2002).
The heavy investments made in recent years have endowed the Spanish port system an
important o¤er in terms of facilities, docks and deposit areas oriented to load / unload of
cargo. In many cases the growth of the infrastructures was higher than the evolution of cargo
movement (Gonzalez-Laxe, 2012), which has produced the existence of overcapacity in the
system (Hidalgo-Gallego et al. 2015). From 2010 these investments begin to lessen because
it is found that the o¤er does not necessarily create demand and due to the economic…nancial crisis. At this point, it could be important analizing what has been the impact of
these investments on freight tra¢ c and whether these investment have been able to divert
tra¢ c from one port to another. According Verhoe¤ (1981), González-Alonso and MartínBofarull (2007) and González-Alonso and Sánchez-Soriano (2007), the answer is that the
e¤ect of investments on tra¢ c is uncertain, i.e., improving port facilities no guarantee that
a port can compete successfully with other ports for tra¢ c.
2.1. Inter port competition
There are few studies that analyze the port selection and inter port competition in the
case of Spain. In this vein, García-Alonso and Sanchez-Soriano (2009) analyze the process
of port selection in Spain in order to identify the determinants in choosing a port. On the
other hand, García-Alonso and Sanchez-Soriano (2007) and Villaverde and Maza (2015) try
to delimit the hinterland of the ports and seafronts, respectively, as well as, the variables
behind it.
García-Alonso and Sanchez-Soriano (2007) compare the evolution of infrastructure investment with the evolution of province port selection. From the analysis of the origin and
destiny of the cargo ‡ows between Spain and the rest of the world, port’s hinterland can
be delimited. These authors …nd that the area of in‡uence of each port is formed by the
geographical environment of the province in which the port is located and Madrid, which
5
is part of the hinterland all of them. So, they conclude that the provinces tend to be linked
to the nearest port and that this trend has not changed over the years.
García-Alonso and Sanchez-Soriano (2009) try to determine the degree of importance of
distance in inter-port competition through the revealed port selection. They propose to
analyze the actual inter-port tra¢ c distribution using the explicative-stochastic approach
proposed by Chasco and Vicéns (1998), where de port-province distance is the main variable.
This approach is based in a hinterland perspective, i.e., studying port selection from the
provinces where the tra¢ c is generated, and uses discrete choice models, speci…cally, a
multinomial conditional logit model. By applying this approach to the main peninsular
container ports they obtain that distance plays an important role in the port selection
process.
Finally, Villaverde and Maza (2015) are able to delimit seafronts’ hinterland from the
data corresponding to the ‡ows of cargo between Spain and the rest of the word, as GarcíaAlonso and Sanchez-Soriano (2007) do for each port authority, achieving similar results.
Villaverde and Maza …nd that Spanish seafronts have a captive hinterland, being Madrid
the province that belongs all of them. Besides, these authors try to …nd those factors that
in‡uence in the delimitation of the hinterland through econometric analysis (parametric
and non-parametric). These analysis show that the main determinant of the hinterland is
the distance follow by the attractiveness of the port, being the relation between distance
and port tra¢ c not linear, since there is a limit beyond which the relationship between
these variables is null.
From these studies we can conclude that the main determinant of port selection in Spain
is the distance and other competitive strategies are constrained to port location. Therefore, we can assume that competition occurs mainly between those ports that are closer
in geographical distance, i.e., that belong to the same seafront. Additionally, because the
port regulatory framework does not allow signi…cant di¤erences between port charges and
the attractiveness of the port can a¤ect tra¢ c’s distribution, port authorities have used the
investment in capacity as competitive strategy to attract larger volumes of cargo tra¢ c.
6
2.2. Investment in Spanish port sector
Spanish port system has been characterized by its important investment e¤orts during
de period 1992 until the beginning of the world …nancial crisis in 2008, and example of
that is the investment achieved in 2008 almost triplicates the levels of 1992 as we can see
in Figure 25. The implementation of the landlord model that gave port authorities more
autonomy to plan their investments (García-Alonso et al. 2007), the increased intra and
inter-port competition, the growth of tra¢ cs and size of vessels and the coincidence with
a period of economic boom may explain that evolution. After the outbreak of the crisis in
2008, investments have dropped sharply to levels similar to those of the early 90s, which
could be mainly explained by falling of public spending.
The evolution of port investment and cargo tra¢ c have not always followed the same
trend as Figure 25 shows. By the use of index numbers, we can see that in the …rst years
of the sample, the growth trends of port investment and cargo tra¢ c were similar; from
2002 to 2008, the investment expense went o¤, growing faster than tra¢ c which produced
overcapacity and thus, loss of e¢ ciency; …nally, in the last years, as mentioned before,
port investment decreases while port tra¢ c increases after falling in 2009. So, there is a
breakdown in the evolution of both magnitudes since 2002.
With respect to the distribution of port investments, we can see in Figure 25 that the
70% of economic investment funds have been dedicated to increase capacity and improve
infrastructure. In the period of larger investor e¤ort, 2002-2008, 4,131 millions of euros have
been exclusively committed to the expansion of Spanish port capacity, this led Spanish port
system to duplicate its storage area, from 17 millions of square meters in 2002 to exceed 32
millions in 2008. So, at this point, it seems important to know what have been the e¤ect
of that economic e¤ort on Spanish port authorities’demands.
Finally, Figure 25 shows the expense in capacity expansion per authority during the
period 2000-2012. The di¤erence among authorities is clear: Algeciras, Barcelona y Valencia
(the largest ports) with Gijón, A Coruña and Las Palmas present higher levels of capacity
investment than the others authorities. The others island ports (Tenerife and Baleares)
7
with medium size ports as Bilbao and Tarragona presents levels of capacity investment
near 200 millions during this period. To end, it is key to point out that Cádiz, which is
a relatively important port in terms of size and tra¢ c, exhibit one of the lowest levels of
expense in capacity expansion. Indeed, only Pasajes presents lower levels of investment per
square meter of surface than Cádiz. In this line, Hidalgo-Gallego et al. (2015) test that
Cádiz is the only Spanish port authority that does not su¤er overcapacity.
3. STRATEGIC INTERDEPENDENCE IN PORT CAPACITIES
Game theory and industrial organization are powerful tools to analyze strategy interdependence in port industry decisions. They have been widely used in order to determine
optimal levels of port capacity and seek the factors are behind this. But, to date, there are
few studies that analyze explicitly the interdependence in setting port capacities.
Authors as De Borger et al. (2008), Xiao et al. (2010) and Tan et al. (2013) have
developed models which determine theoretically the optimal level of port capacity. The …rst
ones base their model in a two-stage competition game where in …rst stage governments
decide the levels of port and hinterland infrastructure capacity in order to maximize the
welfare of their respective regions. In the second stage, port managers choose port chargers
that maximize port’s pro…ts.
On the other hand, Xiao et al. (2012) analyze the optimal levels of port capacity and
port charges in function of port ownership through a one-stage integrated model, considering
both cases, competition and monopolistic situation.
Finally, Tan et al. (2013) model analyzes pricing, capacity and localization decisions of
an inland river port competing with road transport for spatial distributed customers, taking
into account congestion and heterogeneity in condition of the waterway.
In none of these models capacity decisions depend on the capacity decisions of its competitors, but on factors such as ownership, port charges, customers’localization. . .
In this way, Luo et al. (2012) and Anderson et al. (2008) explains the capacity investment
process of two ports in the East Asia, assessing whether ports should invest in capacity
8
taking into account investment decisions of their competitor in di¤erent scenarios. Both
models assume capacity expansion is in the same extend for both ports, common knowledge
and would be carried only if its gain, which depends on the strategy of the competitor, is
larger than its annualized cost. So, although these models explain when a port have to
enlarge its capacity, the strict assumptions imposed, as for example, that both capacity
expansion would be in the same extend, do not allowed measure how capacity expansion
could ‡uctuated in function rivals strategies.
As mentioned before only Luo et al. (2012) and Anderson et al. (2008) consider explicitly
strategic interdependence in setting non-price competition instruments (capacities), but
they do not derives functionally rival’s best responses to capacity strategies. The New
Empirical Industrial Organization (NEIO) approach o¤ers instruments to estimate it by
conjectural parameters. Although this methodology does not allow us to derive a functional
form of interdependence in non-price strategies, permits to obtain a measure of that when
the model is applied to data.
This methodology has been widely used in bank industry, where banks explicitly consider
their own network and their rivals’ expectative branch network when they take branch
decisions. They are models that allows banks take into account its rivals’future reaction to
its network extension and the e¤ects of such on demand or market shares (Kim and Vale,
2001).
In this research line, Kim and Vale (2001) analyze the strategic interdependence of branch
decisions in the market of loans. Moreover, their article evaluates the existence and e¤ects of
informational externalities on conduct, i.e., on rival’s reactions, and the impacts of changes
in bank sector on these reactions. The model is applied to a panel of Norwegian banklevel data. In their model, banks’sets its control variable, branches, in order to maximize
the discounted ‡ow of pro…ts subject to demand function which depends on the number
of branches (own and rival), interest rates on loans (own and rival) and a vector of exogenous macro variables. To set the number of branches for a given period use all the
information available at that time, in this case the number of branches of rivals bank. From
these maximization problem, they obtain a system of non-linear equations formed by the
9
demand equation and the …rst order condition equation where the conjectural parameter
appears. The conjectural parameter captures rival banks’conjectures next period reaction.
In the same way, Pinho (2000) and Valverde and Guevara (2009) analyze not only non-price
competition but also price competition, obtaining a speci…c conjectural parameter for each
competitive instrument. The …rst one applies the model to the Portuguese deposits market
and the second consider deposits and loans demand. Another important di¤erent is the
following one: while Pinho (2000) and Kim and Vale (2001) specify that all rival’s response
occurs in a national level, Valverde and Guevara (2009) use two di¤erent speci…cations for
loan and deposit market, national and regional.
In this article, we combine game theory and NEIO approaches, using a similar methodology than that used in these last papers, adapted to the behavioral characteristics and
structure of Spanish infrastructure port industry, in order to estimate and evaluate the
non-price competition in the sector.
4. THEORETICAL MODEL
We propose a dynamic two-stage model. In the …rst stage Spanish port authorities try to
maximize their present and future cargo demand ‡ows by setting port capacities in a given
period. In the second stage, shippers chose the amount of cargo which pass for each port
that minimizes their port generalized cost once they observe port charges and capacities.
Figure 25 displays model’s structure. The game is solved by backward induction.
4.1. Second stage: Demand for di¤erentiated port infrastructure services
In this stage of the game, we follow the approach proposed by Pinkse et al. (2002) to
develop port cargo demands.
Formally, suppose that there are n port authorities that supply horizontally di¤erentiated
port services. Port authorities and their respective port services are indexed by i= 1,. . . , n.
Their port services are measured as amount of cargo handled, q = (q 1 ; q 2 ; : : : ; q n )T : These
port services are o¤ered at port charges t = (t 1 ; t 2 ; : : : ; t n )T . Finally, each port service is
10
associated with a characteristic s i , which represents port capacity of each port authority.
On the other hand, there are k shippers who need to load/unload their cargo in a given
front of Spanish coast so they demand q, these shippers are indexed by k = 1 ; : : : ; K . Each
shipper is located at a point in geographic space and, therefore, has a unique cost function.
Shippers take port charges and capacities as given. This model, unlike other models such
as those proposed by Hotelling (1929) or Salop (1979), allows shippers use more than one
facility sharing their cargo among di¤erent ports and demands do not have to be unit, i.e.,
they can send di¤erent amounts of cargo to a given port.
We assume that the kth shipper wants to minimize its port generalized cost which includes:
total monetary cost of passing cargo throught a given port, where T = (T1 ; :::; Th )T is the
total unit cost of handling cargo in a given port in which port charges are included and
which can be interpreted as the total monetary price of using a given port; and cost of
time that cargo is on port. We do not include other transport costs due to we assume
that shippers’demand is a captive to the nearest front coast, so these transport costs are
implicitly taking into account. The cost of the time in a port depends on port capacity, so
the port cost function of the kth shipper is:
Pk = P [T; f (s)] = P (T; s)
(1)
where Pk is the port generalized cost of the kth shipper, T is the vector of total port
prices, f is the time cost and …nally s is the vector of capacities.
Without loss of generality, by treating a collection of price taking shippers as a single
price taking cost minimizing unit (Bliss, 1975 and Pinkse et al. 2002), the aggregate cost
function obtained is
P (T; s) =
X
Pk (T; s)
(2)
k
We approximate the aggregate cost function with a ‡exible functional form as the quadratic
cost function which is a second order approximation to an arbitrary cost function that places
11
no restriction on product substitution possibilities.
P (T; s) =
0
+
T
1T
+
T
2s
+
1 T 1
T B T + T T B 2 s + sT B 3 s
2
(3)
where P is the port generalized cost, t is the vector of total port prices, s is the vector of
capacities,
0
is the coe¢ cient associated to the constant term,
1
and
2
are n
1 vectors
of the …rst order coe¢ cients associated to prices and capacities respectively and …nally, B 1 ,
B 2 and B 3 are n
n symmetric matrices which contains the second order parameters of
the quadratic cost function.
Applying the Shephard’s Lemma, we can obtain the optimal demand for each port service,
i.e, the demand for cargo handled services of each port authority.
qi =
@P (T; s)
=
@Ti
1i
+
X
b1ij Tj + b2ij sj
(4)
j
We can see that the amount of port services demanded in the ith port authority depends
on their own total port price and capacity and the prices and capacities of their competitors.
4.2. First stage: Port capacity expansion
From second stage we know that the quantity of demanded handled services (qit ) faced by
a port authority in a given period is function on its own total port price (tit ), competitors’
total port prices (t
it ),
own capacity (sit ) and rival’s capacity (s
qit = q(Tit ; T
it ):
it ; sit ; s it )
(5)
Quantity of demanded services are expected to decrease with increments in its own total
port price (@qit =@Tit < 0) and rivals’capacity expansions (@qit =@s
it
< 0). Otherwise, port
authorities’demand will rise with increments in rivals’total port price (@qit =@T
own capacity investments (@qit =@sit > 0).
12
it
> 0) and
In this stage, port authorities set capacities in order to maximize cargo tra¢ c ‡ows subject
to achieve some level of pro…tability; so we assume that maximization target is subject to a
positive pro…t. Thus the principle of …nancial self-su¢ ciency in the context of the Spanish
port sector described in section 2 is re‡ected in our model. So, from demands obtained in
the second stage (5), the decision problem of a port authority can be described as follow:
maxsit Mi0 =
s:t: tit qit
P1
t=0 qit
Cit (w;qit )
(6)
0
where qit is the amount of cargo services provides by the ith authority in the period t,
tit is the port charge for those services, Cit is the total cost and w is the vector of inputs
prices.
In addition, we assume that port authorities use a feedback strategy (Kim and Vale,
2001), i.e., at period t port authorities set capacities based in the information available at
that time, in this case, rival’s capacity in the previous period. So the ith authority knows
that its competitors will react to its current capacity in the next period and this will a¤ect
its future demand. So ports authorities take into account rival’s reaction e¤ects on future
demand when they set their present capacity, expecting rivals to react with a lag of one
period. In this way, deriving the objective function by port capacity and equaling it to cero,
we obtain the following …rst order condition:
@Mi0
@qit
@qit+1 @s it+1
=
+
@sit
@sit @s it+1 @sit
The terms
@qit
@sit
and
@qit+1
@s it+1
@s it+1
@sit
@qit
@sit
@Cit @qit
@qit @sit
=0
(7)
re‡ect the e¤ect of changes in own and rivals’capacity on the
ith port authority’s cargo handled services demand,
ith in period t while
tit
@Cit
@qit
represents the marginal cost of port
capture the conjectural variation (or conduct parameter) showing
how port authorities react to their rival capacity strategies. Our model allow conjectural
parameter to take zero, negative and positive values. However, we do not expect negative
values of the conjectural parameter because port infrastructure’s characteristics. A negative
sign of the conjectural parameter would be interpretec as a signal of misspeci…cation.On
13
the other hand, a conjectural parameter equal to zero implies Nash equilibrium, i.e., port
authorities not take into account rivals’ decisions when they set their capacities. Finally,
positive values implies that competitors respond to increments of capacity, increasing their
own capacity, in this case, a value equal to 1 implies imitation of rivals strategy. So, we can
disguises two e¤ects of increasing capacity in given period: a direct e¤ect on current demand
represented by the derivative
@qit+1 @s it+1
@s it+1 @sit :
@qit
@sit
and an indirect e¤ect on next period demand measure by
Not taking into account this second e¤ect could led to under/overestimate
capacity e¤ects on demand.
5. EMPIRICAL SPECIFICATION
The empirical speci…cation of the above model is formed by a system of two equations
jointly estimated: cargo demand equation (5) and the …rst order condition (7) for the choice
of capacity.
The cargo demand function are speci…ed as log-linear relationship:
ln qit =
i
+
1 ln Tit
+
2 ln T it
+
3 ln sit
+
4 ln s it
+
t
+
where Tit is the ith total price of passing a unit of cargo for a given port, T
de average total port price of ith authority’s rivals, sit and s
average of rival’s capacities,
1
and
2
it
2
(8)
it
represents
are own capacity and the
are own and cross price elasticities,
3
and
4
are the
elasticity e¤ect of variations in own and rivals’capacity on port authorities cargo handled
services demand respectively and …nally, a quadratic trend ( ) has been added to account
for technological change.
The derivatives of cargo demand with respect the capacities could be displayed as follow:
@qit
@ ln qit qit
=
=
@sit
@ ln sit sit
@qit
@ ln qit qit
=
=
@s it
@ ln s it s it
14
3
qit
sit
4
qit
s it
(9)
(10)
To obtain the empirical speci…cation of the …rst order condition we …rst substitute previous derivatives (9) - (10) in equation 7 as we can see in 11.
3
qit
+
sit
4
qit+1 @s it+1
s it+1 @sit
tit
3
qit
sit
@Cit
@qit
3
qit
sit
=0
(11)
We take out common factors (12) and rearrangement (13)
3
qit
1
sit
Cit0
tit
+
4
qit+1 s
' =0
s it+1
(12)
s qit+1
4 ' s it+1
qit
=
sit
3 (1
(13)
Cit0 ))
(tit
Equation 13 represent the empirical speci…cation of maximization …rst order condition,
where 's is the conjectural parameter, i.e., the expected rivals’ responses to change in
capacities,
is the Lagrange’s multiplier from the positive pro…ts constraint and Cit0 is the
marginal cost of cargo. In order to be able to estimate equation 13, we need to include an
intercept which varies across port authorties in order to collect the inobserved heterogeinity
of port authorities. Thus, the resulting equation is:
s qit+1
4 ' s it+1
qit
=
sit
3 (1
Cit0 ))
(tit
i
+
(14)
3
Finally, to estimate the marginal cost of cargo, we specify a quadratic cost system formed
by the cost equation (15) and the input expenditure equations (16). All variables of the
system are deviated from their means.
Cit =
i+
q (qit
q) +
1
2 qq (qit
q)2 +
R
X
r (writ
w)+
r=1
R X
R
X
rs (writ
w)(wsit
w) +
qr (qit
q)(writ
w)+
r=1
r=1 s=1
t+
R
X
1
2
2
t
+
R
X
r
(writ
r=1
15
w)
t
+
q
(qit
q)
t
+
it
(15)
The input expenditures equations can be obtained by applying the Shephard’s Lemma
to the cost function.
Erit
@Cit
= writ
= writ
@writ
"
r
+
R
X
rs (wsit
w) +
qr (qit
q) +
r
t
+ vrit
s=1
#
(16)
where C is the total cost, q is the amount of output, wr is the price of variable input
r (r = 1; 2; 3), Er is the input r expenditure,
is a time trend representing non-neutral
technical change.
Finally, i = 1; : : : ; N relates to the i
th authority amd t relates to the time period .
Those variables which have a bar on the top correspond to the sample means.
6. DATA
The model is estimated with data from a sample of 21 Spanish port authorities over
the period 1992-2011. We do not include those authorities located in an island; Seville,
which is a river port and Ceuta and Melilla, which are strategic ports on the north of
Africa. We remove them because we consider that these authorities, due to the described
characteristics, do not follow the same competitive patterns than the other ones. Hence,
the sample used consists of 420 observations.
The data is collected from the annual reports published by Puertos del Estado (several
years, a and b) which provides homogeneous information about the performance of Spanish
port authorities.
In the demand equation (8) the quantity of output for each authority, i.e. total cargo
tra¢ c, qi , is measured by the sum of tons of solid bulk, tons of liquid bulk, tons of containerized cargo and tons of no containerized cargo. Due to the information about total
cost of passing a unit of cargo for a given port (total port price) is not avaliable, it is
approximated by port authorities’charges since in practice the variability of port charges
and total port costs seems to follow the same pattern. To build the variables corresponding
to port charges, tit and t
it ,
we make two assumptions: …rst, we consider port charge as
16
the total amount that a shipper have to pay to port authority for moving one ton of their
cargo through a given port; second, we assume that owners of vessels directly charge their
client all paid prices, including port charges to vessels. From these two assumptions and
the data available, we build this variable as the sum of the authorities’ average revenues
per ton from handled cargo services and vessel. Finally, capacity, s, is approximate by the
squared meters of the storage area.
As speci…ed in equation 4, the demand of cargo services of each port depends not only on
its own charges and capacities but also on its rivals. This enlarge, signi…cantly, the number
of parameters to be estimated. For practical reason, we believe convenient reducing the
dimensions of the problem. To his end, instead including all rivals’charges and capacities,
we use their mean. As mentioned in section 2, we consider competitor of a given port, any
port which is located in the same seafront. This classi…cation comprises the nearest ports.
In the …rst order condition equation (13), C 0 represent the marginal cost of cargo which
is estimated by a quadratic cost system (15)-(16). The dependent variable in equation 15
(ctr) is the total cost calculated as the sum of labour, capital and intermediate consumption
costs. The input variables prices used in the estimation of the cost system are: labour price
(w1 ), variable capital price (w2 ) and intermediate consumption price (w3 ). Labour price is
de…ned as the ratio of annual labour expenses by total employees. Variable capital price
has been approximated by multiplying a building index price of public works (obtained
from the reports of Confederación Nacional de la Construcción, SEOPAN) by the sum
of long-term interest rate and the depreciation rate the port’s property and equipment.
The depreciation rate is calculated as the annual depreciation expenditures of each port
authority over the total assets. Finally, intermediate consumption price is de…ned as the
ratio resulted by dividing intermediate consumption expense by intermediate consumptions
measured in physical units. For the expense equations of the system, we need also labour
(E1 ), capital (E2 ) and intermediate consumptions (E3 ) expenses.
Table 1 shows the descriptive statistics of the variables included in the model. All economic
variables have been de‡ated and are expressed in constant euros of 2001.
17
7. ESTIMATION AND RESULTS
The procedure of estimation is as follow: …rst, the quadratic cost system (15) and (16) is
estimated by three stage least squares (3SLS) model, applying a …xed e¤ects estimator. Due
to the endogeneity of the cargo (q) we instrument it using one-period lag of the variable.
Additionaly, variables from the cost system have been transformed in order to correct
the serial correlation. In this sense, we have applied the Cochrane and Orcutt (1949)
transformation. This approach had been appliedbefore in cost system estimations by Sung
and Gorth (2000) and Botasso and Conti (2010) The parameters obtained in this …rst
estimation are used to calculate the marginal cost of cargo services. Secondly, we estimate
jointly the demand equation (8) with the …rst order condition for capacity equation (14),
where the estimated marginal cost in the …rst stage are included as an input. In the second
estimation que use a nonlinear three-stage least squares estimator (N3SLS) which applies
the Gauss-Newton algorithm. Starting values have been obtained from the estimation of
the equations separately. Parameter standard errors are robust to heteroscedasticity.
Table 2 displays the results of the quadratic cost system estimation; while in table 3, the
port authorities’average marginal costs for the studied period are presented. The estimated
parameters show the expected signs. The mean of the marginal cost of cargo across the
420 observations is 0.268 with a standard deviation of 0.194. In the period covered, for all
observations, the average cost lie above marginal cost, so Spanish port authorities operate in
a region of scale economies; speci…cally, the economies of size in the mean of the sample are
equal to 0.182. This …nding suggest that capturing new tra¢ cs has a double attractiveness:
…rst, it increases revenues and second, reduce average costs taking advantage of those scale
economies.
We now use the constructed marginal cost from previous estimation to estimate the
nonlinear system formed by the …rst order condition (14) and the demand equation (8). In
both equations, we allow for di¤erent intercepts for all authorities in order to control time
invariant heterogeneity among them. This individual dummies have not been display in
order to simplify the presentation of the results. As we can see in table 4, three di¤erent
18
estimations are carried out to test the robustness of the model, in the …rst speci…cation we
do not include technical change, in the second one we include a lineal trend and …nally, we
include a quadratic trend. The estimated coe¢ cients in the three speci…cations are very
similar so the robustness of the model is checked.
In the demand equation the coe¢ cients of lti and lt
i
which represent price elasticity
and cross price elasticity have the expected signs, positive and negative respectively, being
both signi…cant at 1% level. We …nd unit price elasticity since the coe¢ cient associated is
statistically equal to 1 in the three speci…cations. The cross-price elasticity is always smaller
than the absolute own-price elasticity, thus cargo demand is more sensitive to variations
in the own price rather than rivals’. The elasticities associated to the capacities have the
expected sign and both are signi…cant at 1% level. The own capacity elasticity is positive
what means that shippers respond positively to increases of capacity; on the other hand,
increases in rivals’capacities decreases the demand of a given port, this fact is represented
by the negative sign of cross-capacity elasticity. This result shows, as our model explains
in section 4, that shippers not only take into account the monetary costs of moving their
cargo but also non monetary cost, such as time cost, which depends on capacity since the
more capacity the less probability of su¤ering congestion problems (Basso and Zhang, 2006;
De Borger and Van Dender, 2006).
Due to the joint signi…cance F test does not allow to reject the null hypothesis that the
parameters associated to the quadratic trend in speci…cation 3 are jointly equal to zero,
from now we focus in speci…cation 1.
Conjectural variation or conduct parameter re‡ect the intensity of non-price competition.
We can see that the conjectural parameter is signi…cantly di¤erent from zero, so port authorities take into account the capacity strategies of their rivals when they set their own
capacity. Thus, our results show that capacity competition exists but it does not seem
too much intense if we compare our result with those achieved by Kim and Vale (2001)
and Valverde and Guevara (2009) in bank industry. So let’s check this fact with …gures:
an average port authority, which current capacity is 849,199.3 square meters and moves
an average of 14,389,150 tons of cargo in period t; expands its capacity in 10,000 square
19
meters, which implies increasing its capacity by 1.177%. An expansion of 1.177% implies
increasing demand by 0.134%, i.e., 19,305.91 tons. On the other hand, this capacity expansion has a response in period t + 1, rivals’increase their average capacity in 1,549.93 square
meters (0.15%) which reduces demand by 0.033% (4,689.82 tons, approximately). Hence
the expected net e¤ect on an average port authority’s demand if it expands its capacity by
10,000 meters is an increase in its demand by 0.102% (14,616 tons).
Once we have analyzed the e¤ect of capacity competition in port authorities’ demand,
we ask what would happen whether this authorities instead competing, allying when they
set the extend of their facilities. We carry out a counterfactual analysis to estimate what
happen in that framework. To model this we have to change one of our assumptions, the
procedure of response of rival authorities. In this case, our new assumptions required that
authorities arrange to set the capacity and the variation in capacities are in the same extend.
So the new conjectural parameter is de…ned as follow:
@s it
=1
@sit
' =
(17)
This changes the …rst order condition (13), which is transformed as follow:
@Mi0
@qit
@qit @s it
=
+
@sit
@sit @s it @sit
tit
@qit
@sit
@Cit @qit
@qit @sit
=0
(18)
Thus, the econometric speci…cation of equation 18 is:
qit
=
sit
qit
4 s it
3 (1
(tit
Cit0 ))
+
N
X1
i=1
i
di
(19)
3
Then we estimate a new nonlinear equation system formed by equation 8 and 19. Table
5 shows the results of the contrafactual analysis using the same speci…cations than table 4.
In the …rst speci…cation we do not include technical change, in the second one we include
a lineal trend and …nally, we include a quadratic trend. As we can see the coe¢ cients of
demand equation do not vary too much with respect those displayed in table 4, with the
20
exception of the parameters associated to the capacity. If we assume that port authorities form alliances to set capacities, i.e., decide at the same time with their ’competitors’
to change their capacity in the same extend, the cross-capacity elasticity decreases considerably, so shippers demand of a given port became more inelastic to changes in rivals’
facilities.
Now, using a simulation, we approximate the net e¤ect of capacity changes in an alliance
framework. As we did before, we take our average port authority which increases its current
capacity in 10,000 square meters, i.e. an increment by 1.177%. This increment of capacity
implies demand increases by 0.096% (13,784 tons) in a direct way. On the other hand, the
capacity of my rivals increases too in 10,000 which implies a reduction of my demand by
0.029% (4,218.47 tons), so the net e¤ect of capacity changes on the cargo demand of our
average authority is an increment of 0.066% (9,565.61 tons). Comparing with competition
frame, gains of expansion are lower when competitors become allies, i.e., the incentives
to invest in capacity are reduced. These results must be interpreted carefully, they lie on
very restrictive and general assumptions such as all authorities in the same front joint the
alliance or the alliance implies set the same capacity expansion.
8. CONCLUSIONS
During the last decades Spanish port legislators have tried to set the instruments to
promote competition among ports allowing higher ‡exibility in making decisions about
port charges or giving autonomy to port authorities to plan their investments. But reality
seems to show that an e¤ective competition in prices has not been reached, either because
the port laws in order to achieve self-su¢ ciency in the system has imposed limits on the
setting of port prices reducing the power of decision of the authorities or because the weight
of these port charges in the total cost of transporting goods is relatively small. This has
led port authorities to seek other ways to compete and attract new cargo tra¢ c, …nding
in capacity expansion a competitive strategy. The problem has been that the capacity
expansion not always has been accompanied by the growth of cargo tra¢ c, which have led
21
the port system to su¤er of overcapacity problems.
This study analyses the non-price competition in Spanish port authorities in order to test
if it actually exists and tries to evaluate how e¤ective it has been by estimating its e¤ect on
ports’demands. Moreover, by a counterfactual analysis, we evaluate the capacity expansion
strategy when rivals become allies.
To do this, we use the NEIO approach, building a dynamic two-stage dynamic model.
In the …rst stage, Spanish port authorities try to maximize their present and future cargo
demand ‡ows by setting port capacities in a given period. In the second stage, shippers chose
the amount of cargo which pass for each port that minimizes their port generalized cost once
they observe port charges and capacities. The main results show that shippers do not only
take into account the monetary costs of moving their cargo but also non monetary cost and
rivals’ port charges and capacities have an important e¤ect on demand. We demonstrate
that capacity competition exists but it is not too intense comparing with the results of other
papers that estimate conjectural parameter to non-price competition strategies and we test
it by a numerical simulation. As we mentioned before, we carry out another simulation using
counterfactual analysis which results that the net e¤ect of capacity expansion on demand
is reduced when port authorities located in the same front behave as allies, this result have
to take carefully since the imposed assumptions are too restrictive.
Until now, there are not similar studies to as in port literature. This study is the …rst one
that explicitly measure and evaluate port capacity competition by a novelty methodology
based in two di¤erent approaches. Other advantage of our model is that it tries to re‡ect
as much as possible the Spanish port legislative context. In our opinion, this study has
important implications in terms of transport policy. First, our model allows to obtain a …rst
approximation of the e¤ect of port infrastructure investment on generation and deviation
of port tra¢ c, key elements in a Cost Bene…t Analysis (CBA). Second, the counterfactual
analysis allows evaluate the e¤ects of alliances and mergers in the Spanish port system,
which were proposed in 2011 but …nally were rejected after the general elections.
We are conscious about the limits of this research based in some restrictive assumptions
imposed in order to simplify our model or because the data available, but we believe that
22
this work is a good starting point for future research in this topic.
Acknowledgements This research is part of a Phd thesis. The authors would like to
express their gratitude to Álvaro Rodríguez, Pedro Álvarez Causelo, José Luis Gallego
Gómez and Luis Orea for their helpful comments.
REFERENCES
1. Anderson, C. M., Park, Y. A., Chang, Y. T., Yang, C. H., Lee, T. W. and Luo, M.
(2008) A game-theoretic analysis of competition among container port hubs: the case
of Busan and Shanghai. Maritime Policy & Management35(1), 5-26.
2. Basso, L. J., and Zhang, A. (2007). Congestible facility rivalry in vertical structures.
Journal of Urban Economics, 61(2), 218-237.
3. Bliss, C.J. (1975) Capital Theory and the Distribution of Income, Amsterdam: NorthHolland
4. Bottasso, A., and Conti, M. (2010). An assessment on the cost structure of the UK
airport industry: ownership outcomes and long run cost economies. Department of
Economics and Public Finance "G. Prato" Working paper Series No. 13. University
of Turin.
5. Castro, J. V., and Fernandez, A. M. (2015). Competencia y Competividad portuarias: Una aplicación a las fachadas marítimas españolas. Revista de Evaluación de
Programas y Políticas Públicas, 1(4), 55-81.
6. Cochrane, D., and Orcutt, G. H. (1949). Appliation of least squares regression to relationships containing auto-correlated error terms. Journal of the American Statistical
Association, 44(245), 32-61.
7. De Borger, B., and Van Dender, K. (2006). Prices, capacities and service levels in a
congestible Bertrand duopoly. Journal of Urban Economics, 60(2), 264-283.
23
8. De Borger, B., Proost, S. and Van Dender, K. (2008) Private Port Pricing and Public
Investment in Port and Hinterland Capacity. Journal of Transport Economics and
Policy 42(3), 527-561
9. De Pinho, P. S. (2000). The impact of deregulation on price and non-price competition
in the Portuguese deposits market. Journal of banking & …nance, 24(9), 1515-1533.
10. García-Alonso, L. and Sánchez-Soriano, J. (2007). Evolución de la inversión vs. evolución de la actividad portuaria en España. Investigaciones Regionales, 11, 115-130
11. García-Alonso, L. and Martin-Bofarull, M. (2007). Impact of port investment on
e¢ ciency and capacity to attract tra¢ c in Spain: Bilbao vs. Valencia. Maritime
Economics and Logistics, 9, 254-267.
12. García-Alonso, L., Sánchez-Soriano, J., and Vallejo-Pinto, J. A. (2007). La competencia interportuaria: Análisis del caso español. Lecciones de economía marítima, 13,
163.
13. García-Alonso, L. and Sanchez-Soriano, J. (2009). Port selection for the hinterland
perspective. Maritime Economics and Logistics, 11( 3), 260-269
14. Hidalgo-Gallego, S., Núñez-Sánchez, R., & Coto-Millán, P. (2015). Demand uncertainty and overcapacity in port infrastructure: the role of passengers. Revista de
Evaluación de Programas y Políticas Públicas, 1(4), 17-35.
15. Kim, M., and Vale, B. (2001). Non-price strategic behavior: the case of bank branches.
International Journal of Industrial Organization, 19(10), 1583-1602.
16. Laxe, F. G. (2012). El marco regulatorio de los puertos españoles: resultados y
conectividad internacional. Economía industrial, 386, 27-38.
17. Luo, M., Liu, L. and Gao, F. (2012) Post-entry container port capacity expansion.
Transportation Research Part B: Methodological, 46(1), 120-138.
24
18. Pinkse, J., Slade, M. E.,and Brett, C. (2002). Spatial price competition: a semiparametric approach. Econometrica, 70(3), 1111-1153.
19. Puertos del Estado. Several years a. Anuario estadístico, Ministerio de Fomento,
Madrid.
20. Puertos del Estado. Several years b. Informe de Gestión del Sistema Portuario de
Titularidad Estatal, Ministerio de Fomento, Madrid.
21. Sung, N., and Gort, M. (2000). Economies of scale and natural monopoly in the US
local telephone industry. Review of Economies and Statistics, 82(4), 694-697.
22. Tan, Z., Li, W., and Wang, T. (2013). Service Fee and Capacity Choice of an Inland
River Port. In International Forum on Shipping, Ports and Airports (IFSPA) 2013:
Trade, Supply Chain Activities and Transport: Contemporary Logistics and Maritime
Issues.
23. Valverde, S. C., and de Guevara Radoselovics, J. F. (2009). Estimating the intensity
of price and non-price competition in banking. Fundacion BBVA.
24. Verhoe¤, J. M. (1981). Seaport competition: some fundamental and political aspects.
Maritime Policy & Management, 8(1), 49-60.
25. Xiao, Y., Ng, A. K., Yang, H., and Fu, X. (2012) An analysis of the dynamics of
ownership, capacity investments and pricing structure of ports. Transport Reviews
32(5): 629-652
25
3
2.5
Index 1992=1
1.5
2
1
1990
1995
2000
year
Port investment
2005
2010
Cargo traffic
Port investment vs tra¢ c evolution (1992-2012)
Equipment and facilities
Logistic activities and intermodality
Infrastructure and capacity
Others
Port investment distribution (1992-2012)
26
27
Theoretical model’s structure
Villagarcía
Vigo
Valencia
Tener ife
Tarragona
Santander
Pontevedra
Pasajes
Málaga
Melilla
Las Palmas
Huelva
Gijón
Ferrol
Cádiz
Ceuta
Castellón
Cartagena
Bilbao
Barcelona
Baleares
Avilés
Almería
Alicante
Algeciras
A Coruña
Million Euros
1,000
800
600
400
200
0
Capacity investment per authority (1992-2012)
Table 1: Descriptive statistics
Variable
Mean
Units
q
1:44E + 07
Ton
ti
1:41
1:40
t
i
si
Standard deviation
Min
Max
1:47E + 07
515442
7:72E + 07
Constant Euros 2001
0:74
0:27
3:99
Constant Euros 2001
0:51
0:64
2:99
849; 199:3
Squared-meters
958190:4
60395
4824550
852; 641:5
Squared-meters
716849:4
143046
4824550
ctr
1:99E + 07
Constant Euros 2001
1:56E + 07
2768417
9:39E + 07
w1
31278:69
Constant Euros 2001
5922:206
14166:57
57664:24
w2
5:87
Constant Euros 2001
2:24
1:38
16:46
w3
43:14
Constant Euros 2001
31:50
2:45
215:76
E1
6; 819; 902
Constant Euros 2001
4731022
1449932
2:73E + 07
E2
7; 988; 428
Constant Euros 2001
6529388
779807:3
3:62E + 07
E3
5; 054; 906
Constant Euros 2001
4969310
353238:3
3:64E + 07
s
i
28
Table 2: Cuadratic cost system estimation
Parameter
Coe¢ cient
Constant
9294310
Parameter
Coe¢ cient
w1 w3
0:00003
(8:5)
w1
192:71
(1:88)
w2 w3
0:45
(32:01)
w2
796973:9
(3:4)
w1 q
0:000009
(15:04)
w3
6:28
(13:01)
w2 q
0:04
(13:93)
q
0:26
(7:3)
w3 q
0:00000005
(3:27)
trend
60704:28
(0:43)
trend2
( 0:81)
w1 2
0:002
(1:06)
w1 trend
( 2:53)
w2 2
4:013:05
0
w2 trend
0
w3 trend
12:51
(5:35)
R2
Cost eq.
Standard dev.
R2
0:59
( 5:12)
qtrend
(0:09)
w1 w2
118208
( 5:5)
( 1:01)
q2
12:97
( 6:05)
( 0:31)
w3 2
45848:67
0:03
(2:23)
Individual
Included
dummies
0:84
E2 eq.
2857432
E1 eq.
Standard dev.
0:79
0:46
3497413
E3 eq.
1601477
0:40
2673459
Number of observations
29
t-statistics for the parameter estimates in parenthesis (
at 1% level;
441
= signi…cant
= signi…cant at 5% level; = signi…cant at 10% level)
Table 3: Port authorities’average marginal cost (1992-2012)
Port authority
Marginal cost
Con…dence intervals
Algeciras
0:23
0:18
0:27
Alicante
0:33
0:24
0:42
Almería
0:24
0:20
0:28
Avilés
0:28
0:22
0:33
Cádiz
0:25
0:20
0:30
Barcelona
0:30
0:26
0:35
Bilbao
0:39
0:34
0:43
Cartagena
0:26
0:21
0:31
Castellón
0:31
0:25
0:37
Ferrol
0:31
0:23
0:38
Gijón
0:30
0:25
0:36
Huelva
0:33
0:26
0:41
A Coruña
0:23
0:19
0:28
Málaga
0:25
0:20
0:30
Pasajes
0:33
0:28
0:39
Pontevedra
0:23
0:18
0:28
Santander
0:34
0:25
0:43
Tarrgona
0:27
0:22
0:31
Valencia
0:33
0:27
0:38
Vigo
0:24
0:20
0:29
Villagarcía
0:35
0:27
0:42
= signi…cant at 1% level;
at 5% level;
= signi…cant
= signi…cant at 10% level
30
Table 4: Nonlinear system estimation
Parameter
Speci…cation 1
Speci…cation 2
Speci…cation 3
Demand equation
Constant
lti
lt
i
si
s
i
17:77
17:60
17:05
(39:38)
(25:45)
(23:17)
1:03
1:03
1:02
( 17:57)
( 17:11)
( 16:98)
0:32
0:30
0:32
(5:19)
(4:19)
(4:38)
0:11
0:12
0:13
(3:59)
(3:33)
(3:55)
0:18
0:17
0:15
( 5:23)
( 3:76)
( 3:16)
trend
0:0018
0:02
(0:33)
(1:68)
trend2
0:0013
( 2:11)
Individual
Included
Included
Included
dummies
First order condition equation
Conjectural
0:15
0:17
0:21
parameter
(2:54)
(2:00)
(1:91)
Lagrange
0:50
0:50
0:50
multiplier
(1426:34)
(1426:45)
Number of observations
420
t-statistics for the parameter estimates in parenthesis (
1% level;
(1438:30)
= signi…cant at
= signi…cant at 5% level; = signi…cant at 10% level)
31
Table 5: Counterfactual analysis estimation
Parameter
Speci…cation 1
Speci…cation 2
Speci…cation 3
Demand equation
Constant
lti
lt
i
si
s
i
16:21
15:82
15:53
(50:65)
(43:73)
(40:96)
0:96
1:04
1:02
( 16:61)
( 16:97)
( 16:85)
0:38
0:24
0:27
(6:13)
(3:45)
(3:87)
0:08
0:14
0:15
(2:58)
(3:96)
(4:10)
0:02
0:04
0:04
( 2:16)
( 2:88)
( 2:88)
trend
0:01
( 3:58)
trend2
0:02
(1:40)
0:00
( 2:77)
Individual
Included
Included
Included
dummies
First order condition equation
Lagrange
multiplier
0:50
(1722:16)
0:50
(1641:14)
Number of observations
(1605:49)
420
t-statistics for the parameter estimates in parenthesis (
1% level;
0:50
= signi…cant at
= signi…cant at 5% level; = signi…cant at 10% level)
32
33