Ownership and Incentives
in Transportation Infrastructure Projects
~ a welfare comparison of PFI and joint ownership~
Koichiro TEZUKA,
Associate Professor
Faculty of Education and Regional Studies, University of Fukui
3-9-1, Bunkyo, Fukui-city, Fukui, 910-8507,Japan
[email protected]
Yukihiro YASUDA,
Associate Professor
Department of Management, Tokyo Keizai University
1-7-34, Minami-cyo, Kokubunji-city, Tokyo, 185-8502, Japan
[email protected]
Abstract
This paper compares the effects of the welfare of the PFI (Private Finance Initiative)
scheme and joint ownership by public and private sectors in transport infrastructure
projects. We construct a basic model and show that the advantages of PFI under a
competitive environment would exist although excess competition might bring some
welfare loss because it discourages a firm’s incentive for input effort (moral hazard).
Keywords: ownership, PFI, incentive, transport infrastructure project
1
Ownership and Incentives in Transportation Infrastructure
Projects ~ a welfare comparison of PFI and joint ownership~
1. Introduction
The amount of private sector involvement in public sector projects has been growing
recently. Especially, in many countries, many kinds of transport infrastructure projects
such as roads, railways and airports have been privatized.
With regard to private sector involvement in managing transport infrastructure, there are
two ends to the spectrum. One involves complete privatization with 100% flotation; the
other involves nationalized projects.
However, there are intermediates between these two extremes. For example, Graham
(2005) classified privatization into five categories: share flotation, trade sale, concession,
project finance privatization, and management contract. These categories could be
interpreted as intermediates; we sometimes recognize them as “public private
partnerships.”
In Japan, many transport infrastructure projects have been privatized. However, most are
not fully privatized in the sense that the government retains hold of the infrastructure
asset. That is, these privatized firms have not undergone 100% per share flotation.
In fact, most firms that provide transport infrastructure services in Japan are in joint
public and private sector ownership. This implies that, depending on the share,
government retains hold of the right to control assets. In Japan we call such joint
ownership schemes the “third sector.” Hence, some Japanese privatized railway
companies are still in joint ownership. Moreover, Japan’s main airports are in joint
ownership, whereas in the UK some airports have already been privatized.
Recently, the number of project finance based infrastructure projects, which is sometimes
called PFI (Private Finance Initiative) originated in UK, has been increasing. PFI is the
scheme with characteristics of project finance and concession. PFI scheme includes BOT
(build- operate-transfer), BOOT (build-own-operate-transfer), BTO (build- transferoperate) , ROT(rehabilitate-own-transfer) etc.
2
Over 200 facilities in Japan have been built and are operated using PFI schemes.
However, there are few transport projects included in the Japanese PFI projects, while
many kinds of transport infrastructure projects such as road and rail ventures have been
conducted in the UK.
The main difference between joint ownership and PFI is whether the government owns
and funds the firm that operates the project. The public sector funds the firm in joint
ownership. In this case, the government has the right to control the firm. Therefore, the
firm sometimes seems to be protected from a real competitive environment by the
government.
On the other hand, PFI firms appear to face more competitive environments and need to
satisfy a VFM (Value for Money) requirement. There is an aim to improve welfare by
PFI. The government, however, would have less flexibility for controlling such a firm
than one in joint ownership.
Additionally, problems with regards to an incomplete contract might arise. PFI schemes
are essentially based on contracts between the government and the private sector. If the
contract of the project between public and private sectors was incomplete and a fully
satisfied situation could not be achieved, then the PFI firm would not have sufficient
incentive to enhance welfare. That is, amoral hazard problem could arise.
A tradeoff between a competitive environment and a firms’ incentive appears to exist,
especially in monopolistic infrastructure projects. Accordingly, we focus on these
relationships. This paper aims to investigate the differences in welfare effects between
PFI and joint ownership projects.
The paper is organized as follows. In section 2, we model PFI and joint ownership,
respectively, and in section 3 we compare the welfare between the two schemes. Then we
interpret the model in section 4, and conclude in section 5.
2. The model
2.1. Formulation of a PFI firm
We propose a basic model to compare PFI and joint ownership. First, we formulate the
PFI firm. It is assumed that the profit of the firm consists of revenue from user and
3
government transfer.
We define the profit function of PFI firms:
 PFI  t  yxe  Ce ……….
(1)
where t denotes lump sum transfer from the government to the firm. y represents the
marginal monetary effects of welfare, and we interpret y as the unit benefit of
the
performance of effort x . While x is the parameter that represents the degrees welfare
increased and reflects cost reduction and effective products resulting from the input of
effort.
That is, we cannot observe x directly but can explicitly observe yx resulting from
effort 1. For example, revenue can be interpreted as increased profit by the efforts of cost
reduction.
We also assume that the performance parameter x involves uncertainty. In other words,
we define xe  e   where e  0, denotes the levels of effort and  is a


stochastic variable with N 0,  2 . In the last term of the right side in (1), C (e)
is a
cost function with respect to the effort of the firm. The cost function is assumed to be a
private cost function and cannot be observed by a third party.
 is an important parameter to compare PFI with joint ownership. It reflects degrees of
competition. The smaller  the more competitive the environment. If competitive
pressure exists, the firm might not receive enough resulting rent from the effort input. A
smaller  implies less rent extracted, while the rent would spread and redistribute
among society. We set yx as the explicit revenue the firm receives; hereafter, we see
the parameter  as the effect of competition and we set   0,1 2.
With regard to Japanese PFI projects, some schemes of competitive pressure seem to be
built into franchise bidding. Generally speaking, a PFI firm does not enjoy a
1
The revenue
yx which stems from the input of effort, and we assume yx
is represented in
monetary terms. This revenue can be interpreted as profit from the users of the service.
2 For the same setting, see Petersen and Rajan (1995)，Chan, Greenbaum and Thakor (1992). we
exclude the fully competitive case   0 and assume   0 .Because we assume a risk-averse firm,
which requires a risk premium, and the reservation profit would be higher than in a perfectly
competitive environment.
4
monopolistic position to extract a monopoly rent. In such cases, we might be able to see
that   1 holds in PFI schemes.
Now we assume that the purpose of government is to maximize the expected social
welfare by controlling lump sum transfer t . We can interpret the value t as an
operational subsidy or payment by the government.
We also assume that each firm is risk averse and has a constant absolute risk aversion
(CARA)
utility
function. We specialize in the utility function as
u( PFI )   exp( r PFI ) where parameter r shows the degrees of risk adversity.
Without loss of generality, we assume the reservation utility (profit) of a firm is  1 .
Then, we can derive the object function of the PFI firm using a certainty equivalent
function CEPFI from the profit function  PFI .
1
CE PFI  t  ye  C e   r 2 y 2 2
2
(2)
By using the equivalent function, we can define the expected social welfare function of
PFI as follows:
WPFI  S  1   t  CE PFI  1    ye
1


 S  1    ye  1   C e   r 2 y 2 2  ye  CE PFI
2


(3)
where S denotes the expected social surplus from conducting business and has a
constant number. We assume the value of S is large enough to operate. The second term
in (2) represents the marginal cost of public funds  that would occur when the public
sector pays for the firm.
The main feature of the expected social welfare function is as follows: If the competitive
mechanism could work well and  decreased, then all else being equal, it could
increase social welfare (see the second term in equation (3)).
Note that if the competition mechanism was over-worked, then the incentives for cost
reduction would reduce. As a result, the benefit of competition could be offset by the
disincentive (under-input of effort) of cost reduction.(see the third terms in (3)). This can
be interpreted as the costs and benefits of competitive pressure.
5
From the assumption, the object of the government is to maximize social welfare. Then,
we present our problem as follows:
Problem:
max
t 
s.t.
1


S  (1   ) ye  (1   )C (e)  r 2 y 2 2  ye  CE PFI
2


1
1
CE PFI  t  ye  C e   r 2 y 2 2  0 , e PFI  arg max t  ye  C e   r 2 y 2 2
2
2
, but
The problem describes that the government maximizes the expected social welfare
subject to constraints, which are called “participation constraint” and “incentive
compatible constraint”. Assuming that the government cannot directly observe the efforts
of the firm, incentive compatibility constraints could correspond to the conditions for the
firm’s profit maximization from a social welfare viewpoint.
That is, we specialize the firm’s cost function of effort as C e  
k 2
e where k  0 .
2
Under the incentive compatibility condition, the PFI firm sets its effort as e PFI 
y
k
.
From its functional purpose, it is optimal to set t PFI = CEPFI . That is, the government sets
its lump-sum transfer equal to the firm’s participation constraint (reservation profit).
Then the expected social welfare under a PFI scheme WPFI can be derived by
substituting the above solutions into its object function.
1
k

WPFI  S  1    ye  1    e 2  r 2 y 2 2  ye 
2
2

2
1   y  1 1    2 y 2  r 2  1 
S


k
2
k

(4)
Then we obtain the following proposition.
Proposition 1: If r 2 
1
 0 ， it does not hold that   0 can always enhance the
k
expected social welfare. In other words, increasing competition is not always preferable.
The expected welfare is maximized at  * 
1


2  1    kr 2  1
6
Proof：We define the right hand side of (4) as the function of  , F   . Then, we
obtain:
F    S 
If r 2 
1   y 2
k

2
 2

1
1    2 y 2  r 2  1    y  1 1   y 2  r 2  1  2  y   S
2
k
k 
k


k 2
1
 0 , the coefficient of  2 is negative. Then if there exist  such as
k
F    0 , it then maximizes F   . Q.E.D.
Corollary 1: The higher  , the lower the value of  * that maximizes the expected social
welfare.
An intuitive interpretation of the proposition is as follows: In the case where the PFI firm
is faced with uncertainty as r 2 
increasing 
1
 0 , the expected social welfare could increase by
k
in *    1 . Within this area, increasing competition and rent
exaggeration could enhance welfare.
Whereas the introduction of excessive competition would decrease social welfare in
0     * because there would be a lack of incentives for cost reduction 3. As we have
seen in corollary 1, all things being equal, the larger cost of  , and the more competitive
the environment (lower  alpha), the more the expected welfare we could obtain.
2.2.
Formulation of a joint ownership firm
To compare the PFI firm, we set the profit function of a joint-ownership firm,  JO as
follows:
 JO  t  yxe  C e
(5)
In our model, the main difference from a PFI firm is that the joint ownership firm could
have less competitive pressure. Because the public sector owns and control the asset in a
joint ownership situation (and the firm might face just soft budget constraints), the firm
can earn revenue without competitive pressure. We can express such a situation as   1 .
Then, the joint ownership firm has incentives to invest its efforts to cost reduction
3
The case where
k is large enough, expected welfare maximizes at   0 .
7
because all revenue as a result of input would belong to the firm.
We also assume that a joint ownership firm is also risk averse. To compare two types of
firms, all parameters except  , are the same. Then, the purpose of joint ownership is to
maximize the following certainty equivalent function:
1
CE JO  t  ye  C e   ry 2 2
2
(6)
We obtain the expected social welfare WSEC as follows:
1


W JO  S  1   t  CE JO  S  1   C e   ry 2 2  ye  CE JO
2


(7)
As mentioned above, the main difference between PFI and joint ownership is where
competitive pressure exists or rent extraction occurs.
We can also calculate the expected social surplus of joint ownership as follows:
1
1
1
k


W JO  S  1    e 2  ry 2 2  ye  CE JO  S  1    y 2  r 2  
2
2
2
k



(8)
Note that if the value of r, which represents the degree of risk aversion, is high enough,
the sign of the second term in (8) would be positive. This implies that additional effort
would rather decrease the expected social welfare.
3. Comparison of PFI with joint ownership
We model the PFI and joint ownership firms that are characterized by parameter  and
derive expected social welfare in each case. In this section, we consider the welfare
implications of ownership, incentive, and the competitive environment. We compare two
cases: PFI and joint ownership. To make the comparison easier, we assume each project
would bring the same fixed benefit S .
By
WPFI  S 
1   y 2  1 1    2 y 2  r 2  1  and W  S  1 1    y 2  r 2  1  , the difference of the


JO
k
2

k
2
expected social welfare between the two is:
8

k
WPFI  WJO 
1   y 2
k



1
1   y 2  r 2  1   2  1
2
k

(9)
We can evaluate the two schemes by the sign in (9) and derive the following proposition
(also see the figure).
Proposition 2: If r 2 
1
 0 ,and all else being equal, then a PFI of   1 is preferred
k
to a joint ownership of   1 .
where r represents the degree of risk aversion and 
represents operational
uncertainty. Therefore, it is shown that the more risk averse and the more variance (a
highly uncertain environment), the higher the expected welfare under PFI scheme is than
that under joint ownership. 4
Figure: Welfare comparison between PFI and Joint ownership
WPFI
WPFI  WJO
S
WJO
０

1


2  1    kr 2  1

１
4. Implications of the model
From the results, it is suggested that a PFI scheme under a competitive environment is
preferable tone of joint ownership in respect to social welfare. In this section we observe
the applicability of the model to transport infrastructure projects and some of the
implications.
4
Conversely if r 2  1  0 , there might be the case where joint ownership is preferable.
k
9
4.1. Features of transport infrastructure
To consider applicability, the features of transport infrastructures such as roads, railways
and airport usually have the following characteristics. 1) Consist of a network, 2)
involves a huge and lumpy investment, and 3) involves sunken costs etc. Because of
these features, transport infrastructures are frequently provided by monopoly firms along
with regulations; well-known as natural monopoly regulations. In particular, such an
arrangement is easily applicable to roads, railways, and airports.
4.2 competitive environments
The first point is whether a PFI firm would face competitive environments. In some cases,
even joint ownership firms can face such environments. However, it can be pointed out
that most PFI firms would experience the process of franchise bidding (Demsetz ,1968).
The process of selection would construct a competitive environment in the franchise
bidding. Additionally, joint ownership firms are sometimes considered as less risky by
investors. It can be expected that the government would like to avoid bankruptcies and
protect such firms, especially in the case of Japan.
Our model describes the trade off between the introduction of competition, the extraction
of rent and incentives in transport infrastructure projects. From proposition 1, we derive
the optimal level of extraction, i.e. the degrees of competition. Our model also implies
that excessive competition and rent extraction would decrease welfare by causing
disincentives. For example, it seems that some PFI transport infrastructure projects
cannot obtain sufficient welfare gainｓ because of severe competition in the bidding
stage.
In sum, the problem of how to create competitive environments can be related to the
problem how much rent can be allowed for the firm. In some cases, it might be preferable
for there to be joint ownership without competition.
4.3 Scale of the project and attitudes toward risk
As noted above, transport infrastructures usually are of a large scale and involve huge
and lumpy investments, which have large risks. Thus attitudes toward risk might differ
depending on the size of the project. It might be expected that a PFI firm would be more
risk averse than the one in joint ownership.
10
We compare the case when attitudes toward risk differ. The expected social welfare is as
follows:
WPFI  WJO 
1   y 2
k



1
1   y 2  2 rPFI 2  rJO 2  1 1   2 
2
k


(10)
rPFI denotes the degree of risk aversion of a PFI firm and rJO denotes that of joint
ownership. If rPFI is large enough and rJO is low, joint ownership would be preferable.
For example, that holds if   1 .
There are the following implications: In the case that a PFI firm is highly risk averse; the
firm would require high rent. As a result, the cost of introducing severe competition
would overwhelm the benefit. In fact, such an argument seems to be applicable because it
appears that the larger scale the project becomes, the more risk averse the PFI firm would
be. In this case, joint ownership or public provision might be preferable.
5. Conclusion and future research
In this paper, we constructed a model to compare the welfare effects of PFI and joint
ownership. We considered some implications. Our model described the trade off between
the introduction of competition, the extraction of rent, and incentives in transport
infrastructure projects. Our model implied that excessive competition and rent extraction
would decrease welfare by causing disincentives. For example, it appears that some PFI
transport infrastructure projects do not obtain enough welfare gains because of the severe
competition present in the bidding stage.
Some problems remain for future research. First, in this research we only provide a
model that compares PFI and joint ownership schemes. However, there are many types of
public-private partnership schemes. Thus we need to develop our model to compare these
as well. Second, to consider the practical applicability of our model, we will need to
collect real data and/or case studies. As other problems no doubt exist, there is much
potential for future developments of our model.
11
Acknowledgements
This paper is a revised version of a paper previously circulated ‘The possibility of the
PFI and the third sector approach for managing a transport infrastructure’ in Annual
Report on Transportation Economics 2004(in Japanese). We are grateful to anonymous
referees for helpful comments.
And the research of the first author, Tezuka, is supported by a Grant-in-Aid for Scientific
Research 19730171 of the Ministry of Education, Culture, Sports, Science and
Technology of the Government of Japan.
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