Discussion Paper No. 709

YARDSTICK COMPETITION TO
ELICIT PRIVATE INFORMATION:AN EMPIRICAL ANALYSIS OF
THE JAPANESE GASDISTRIBUTION INDUSTRY

Ayako Suzuki

March 2008

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

Yardstick Competition to Elicit Private Information:
An Empirical Analysis of the Japanese Gas Distribution Industry†
Ayako Suzuki‡
Institute of Social and Economic Research, Osaka University, Japan†I am grateful to Matthew Shum for his suggestions and encouragement for the initial version of the paper.

I would like to thank Kazunari Kainoh for the discussion on the industry, and seminar participants at
Aoyama Gakuin University; GRIPS; JFTC; Keio University; KISER; Kobe University; Kyoto University;
Nagoya University; Osaka University; and University of Tokyo, for their useful comments. Nobuo
Hanafusa provided outstanding research assistance.
‡

Institute of Social and Economic Research, Osaka University, 6-1 Mihogaoka, Ibaraki, Osaka 567-0047,

Japan. Tel.: +81-6-6879-8581; fax: +81-6-6878-2766; e-mail: a-suzuki@iser.osaka-u.ac.jp.

(Abstract)
This study examines the effect of yardstick regulation in Japan’s gas distribution sector,
especially focusing on its effect of reducing the adverse selection problem. The Japanese
government has regulated the price of city gas supplies by a combination of fixed-priceregulation and ex-ante yardstick regulation. The yardstick compares a firm’s reported costs withthose of “similar” firms before the price is determined. Realizing that yardstick inspection willlead the industry to a full-information outcome if it works perfectly, we infer its effect from thedifference between the current and the counterfactual full-information welfare levels.
We estimate the cost function of retail gas distributors under the assumption ofasymmetric information between the regulator and the distributor in the efficient level of labor.
The estimation allows us to obtain informational parameters such as firms’ efficiency levels andeffort levels. Using the estimated cost structure and the firms’ behavior in response to theregulatory incentive, along with the demand system and the behavior of the regulator, we
calculate the current and the hypothetical full-information welfare levels, and examine whether
the discrepancy of the current level from the full-information one has been significantly reduced
since the introduction of yardstick regulation. Our results suggest that, on average, yardstick
regulation reduces welfare discrepancy, implying it is somewhat effective in reducing firms’
incentive to report higher costs. This effect, however, comes mainly from the very firstinspection conducted in 1995. There seems to be a dynamic problem, similar to the Ratchet
effect, because subsequent inspections cannot be effective for a firm that has learned the relative
position of its own cost in the comparison group.

Keywords: Adverse selection, Yardstick competition, Incentive regulation, Relative performance
evaluation
JEL Classification: L0, L12, L51, L95, K23

2

1. Introduction
Since the seminal work of Shleifer (1985), yardstick competition has been recognized as an
instrument for reducing the problems of asymmetric information, namely the adverse selection
and moral hazard problems, faced by regulators when regulating firms. This regulation has
gained increased attention in the debate about optimal incentive structures in retail distribution.
However, there have not been many empirical studies of such a relative performance evaluation
despite the increased number of formal applications of this measure, and the need for further
empirical evidence is not diminishing.12 The purpose of this paper is to contribute to the debate
on yardstick regulation. The paper examines the effect of yardstick regulation in Japan’s gas
distribution sector, especially focusing on its effect of reducing the adverse selection problem.
The Japanese government (the Ministry of Economy, Trade and Industry or METI) regulates theprice of city gas supplies. The price of gas is determined by a type of fixed-price regulation. As
is well known, while this type of contract has a high-powered incentive scheme to induce
regulated firms to exert the best efforts because the firms are residual claimants, it does not have
any truth-telling mechanisms. Presumably to improve such regulation, the METI introduced socalled “yardstick inspection” in 1995. This inspection system compares a firm’s reported costswith those of “similar” firms before the price is determined. Firms that report relatively higher
costs are subject to penalty. The reported costs are reduced and the price is determined based onthese adjusted costs. Such a relative performance system may effectively reduce the regulator’s
1

The yardstick competition has been implemented in utility industries in many countries, such as: theelectricity industry in the UK, Switzerland, Chile, and Germany; the water industry in the UK and Italy;
the bus industry in Norway and so on.
2

As exceptions, there exist some empirical studies related to yardstick competition. For example, Farsi

and Filippini (2004) measure the cost efficiency of electricity distribution utilities in Switzerland. Studies
such as Antonioli and Filippini (2001) and Yatchew (2001) discuss how benchmarks should beconstructed using the data from Italy’s water and Canada’s electricity distribution utilities, respectively.
Dalen and Gómez-Labo (2003) investigated to what extent different types of regulatory contracts affectcompany performance in Norway’s bus industry, and found that a yardstick type of regulation
significantly reduces operating costs. Our study differs from these previous studies in the way that it uses
a structural model that explicitly takes into account the information problem in the regulatoryenvironment. Moreover, most of the above studies focus on the discussion about firms’ incentive to
behave in a more cost-effective manner, but not about their incentive for information revelation. Our
study, however, focuses on the latter incentive.

3

ex-ante information disadvantage by inducing firms to compete against each others andeliminating firms’ incentive to report higher costs. Thus, the new regulation system, which
combines the fixed-price contract with yardstick inspection, should effectively eliminate bothex-ante adverse selection and ex-post moral hazard problems, the former by yardstick inspection
and the latter by the fixed-price contract.
However, several practical problems are associated with yardstick regulation. The main problem
is the comparability between agents (see Shleifer (1985), Yatchew (2001)). For basic yardstick
regulation to work, all distributors must produce under the same condition. This condition isunlikely to hold for regional monopolists such as Japanese gas distributors. The second problem
is the possibility of firms colluding (see Shleifer (1985), Tangerås (2002) and Potters et al.
(2004)). These problems may reduce the effectiveness of yardstick competition. Having
recognized these problems, the objective of the study is to assess whether and to what extent theyardstick in the Japanese gas distribution sector works effectively.
We show that, if yardstick inspection works perfectly, that is, the current industry exhibits
desirable conditions and does not face the problems pointed out above, the current welfare level
converges to the counterfactual full-information welfare level. On the other hand, if yardstickinspection does not work well, then the welfare difference should persist. The idea of this study
is to infer the effect of yardstick inspection by the difference between the current and the fullinformation welfare levels.

Using firm-level panel data of local distributors, we estimate the cost function of the Japanesegas retail distribution sector based on Laffont and Tirole (1986). This estimation procedure was
first introduced by Gagnepain and Ivaldi (2002). The estimation allows us to obtain
informational parameters such as firms’ efficiency levels and effort levels. Using the estimatedcost structure and the firms’ behavior in response to the regulatory incentive, along with thedemand system and the behavior of the regulator, we calculate the current and the hypotheticalfull-information welfare levels, and examine whether the discrepancy of the current level fromthe full-information one has been significantly reduced since the introduction of yardstickinspection. The results suggest that, on average, yardstick inspection reduces the welfare
discrepancy, implying it is effective in reducing firms’ incentive to report higher costs. Thiseffect is, however, mainly a result of the very first inspection conducted in 1995. There seems to
be a dynamic problem, similar to the Ratchet effect, because subsequent inspections cannot be4effective for a firm that has learned the relative position of its own cost in the comparison group.
The structure of the paper is as follows. The next section reviews the existing literature. Section
3 describes the existing regulation in the Japanese gas distribution industry. Section 4 considers
the application of the theory of Laffont and Tirole (1986) to the industry in order to construct
the structural model. Section 5 presents our empirical model and estimation method, and theresults are shown in Section 6. In Section 7, the welfare levels—current and full information—
are calculated and the welfare implications of the yardstick inspection are presented. The lastsection concludes the paper.

2. Previous Studies
The asymmetric information problems in the regulatory environment arise as follows. A firm’s
cost opportunities may be high or low based on its inherent attributes. Typically, the firm has
better information on its own cost opportunities. The firm would like to convince the regulator
that it is a “higher cost” firm than it actually is, in the belief that the regulator will then set
higher prices for the services it provides. Thus, the social-welfare-maximizing regulator faces apotential adverse selection problem as it seeks to distinguish between firms with high cost
opportunities and firms with low cost opportunities. Furthermore, a firm’s realized costs will
depend not only on its underlying cost opportunities but also on the behavioral decisions madeby managers to exploit these cost opportunities. While such managerial effort will lower thefirm’s costs, other things being equal, exerting more managerial effort imposes costs on
managers. The regulator cannot observe managerial effort directly and thus, faces a potential
moral hazard problem associated with variations in managerial effort in response to regulatory
incentives. For more than 20 years, there have been many theoretical studies to find the optimal
regulation when there is information asymmetry between a regulator and regulated firms. There
are two strands of such literature. One uses the principal–agent framework to assess the optimal
regulation, namely individual incentive regulation, while the other uses a relative performancemechanism, namely yardstick regulation. 3
The representative studies on the theory of individual incentive regulation are Baron andMyerson (1982) and Laffont and Tirole (1986), both of which examine optimal regulation when
the regulated firm has superior information about its costs. They differ in that the former focuses
3

See Chong (2003) for an extensive literature review of incentive regulation.

5

on the problem of hidden information while the latter considers both hidden information andhidden action problems. The optimal regulation is the one that maximizes social welfare under
the incentive compatibility and participation constraints.

Yardstick regulation was first introduced by Shleifer (1985) as an incentive regulation. Heshows that if there are multiple noncompeting but otherwise identical firms, an efficientregulatory mechanism involves setting the price for each firm based on the realized costs of theother firms. Then each individual firm has no control over the price it will be allowed to charge;
each firm effectively has a fixed-price contract and will exert the best effort. While Shleifer(1985) considers the case where there is no adverse selection and where the firm’s performance
depends deterministically on its effort, Tangerås (2002) shows that yardstick competition canhelp the regulator in compelling firms to reveal their private information. He uses the stochastic
structure in Auriol and Laffont (1992) where firms’ adverse selection parameter β i is comprisedof two parts: a common random variable m and an idiosyncratic one ε i , as follows:

β i = αm + (1 − α )ε i , i = 1,2,
where α is a measure of the correlation between firms, and subscript i represents a firm. In
Tangerås (2002), firms are first asked to submit a report on their common adverse selection
parameter. Because the regulator can dissuade any untruthful reports, information asymmetry is
reduced.
The empirical studies that explicitly consider the asymmetric information problems in theregulatory environments seem to have appeared much later, possibly because there areunobservable variables that play a key role in the model, but for which data cannot be obtained.
Recent empirical studies such as Wolak (1994) and Gagnepain and Ivaldi (2002) cope with suchdifficulties by using distributional assumptions on those variables. In the theory of individual
incentive regulations, it is usually assumed that the regulator at least knows the distribution of
the parameter responsible for the asymmetric information, and the recent empirical studies use
this assumption directly for their estimation. Both Wolak (1994) and Gagnepain and Ivaldi(2002) assume that there is information asymmetry in labor inefficiency. That is, the observed
physical labor is different from the efficient level of labor while the former determines theoperational cost and the latter determines the output level. The studies compare the estimation
results of the two models with different informational assumptions, one under the assumption ofasymmetric information and the other without it, and show that the asymmetric information
model can explain the data better. The difference between these two studies is the same as that6

between Baron and Myerson (1982) and Laffont and Tirole (1986): Wolak (1994) considers thecase of hidden information, while Gagnepain and Ivaldi (2002) consider both hidden
information and hidden action problems. Another main difference is that Wolak (1994) assumes
the optimality of the existing regulation while Gagnepain and Ivaldi (2002) do not. Wolak(1994) first presents the optimal regulation in the California water supply industry and assumes
the firms are acting under such regulation. He then tests whether the data can be explained bysuch behavior. On the other hand, Gagnepain and Ivaldi (2002) estimate the parameters of a costfunction for the French transit system treating the existing regulation as given. Then, using thoseparameters, they calculate and compare the welfare levels under the existing regulation and the
optimal regulation.

3. Overview and Data
In Japan, entry to the gas distribution business is regulated and therefore, to prevent the existing
distributors from charging an inappropriate rate, the price of gas supply is regulated by the
METI. This section provides a brief overview of the industry and associated regulation.
In 2006, the Japanese gas retail distribution sector consisted of 226 firms, most of which arevery small and local. While some distributors are partially or entirely vertically integrated, mostof them have no significant production of their own. The large vertically integrated distributors
import inputs such as liquefied natural gas or liquefied petroleum gas and vaporize them within
the country. The small independent distributors generally purchase vaporized gas from suchlarge integrated firms or use national natural gas in their local markets. Distribution is handled
by both private distributors and distributors owned by prefectures or cities. There were 174
private and 52 public distributors in 2006. They are regional monopolists and supply gas
services in a certain area. We consider each regional monopolized market during a time period
as a realization of a regulatory contract.
We use the data of the public distributors for our analysis. While it is certainly our interest to
analyze the private distributors, only the data of listed private distributors are available from thedatabase, which is a very small portion of the entire population. Furthermore, pooling private
and public distributors is not desirable because their size and input structure differ significantly.
Therefore, we decided to focus on public distributors in this study. We use the gas section of
Chiho Koei Kigyo Nenkan, which contains data on costs and production structure for all public

7companies in Japan. Unless otherwise noted, data are taken from this source. This provides us
with a sample of 76 public gas distributors for the period 1990–2005.
Our sample can be classified into three categories according to technology. The first type does
not have any vaporization or reformer systems and purchases vaporized gas from large
integrated distributors or uses national natural gas. The second type includes those withvaporization systems. They purchase liquefied natural gas from large distributors and vaporize it
on site. The last type owns reformer systems that enable them to convert liquefied petroleum gas
to city gas. The gas jigyo binran states how each distributor is classified. Because of thetechnological differences, the cost structures of the three types differ significantly. For example,
the first type incurs low input costs as vaporized gas is transported through conduits, while thesecond type transports liquefied natural gas by tank trucks, which is very costly. Therefore, forthe purpose of homogeneity, we use only the first type of distributors for the estimation of thecost function. This leaves us with an unbalanced panel of 59 distributors for the estimation in
the sample period.
Japanese gas retail distributors need to obtain permission from the METI when they change
price.4 Based on the expected future demand for a certain number of coming years (one year forthe existing distributors, three years for the new distributors), price P r is determined to satisfy
the equation below:

P r Y e = C (Y e ) + sB ,(1)

where Y e is the expected demand, C (Y e ) is the expected operating cost to meet the expecteddemand, s is the rate of return, and B is the rate base. Specifically, for private distributors, s is
the weighted average of the rates of return on equity capital and liability, and B is the sum ofoperational capital and fixed assets. For public distributors, sB is the interest expense on
enterprise loans, temporary loans and money transferred, plus less than 2 percent of the average

4This requirement has been abolished for voluntary price reductions since 1998. Distributors are only

required to report in the case of voluntary price reduction. (There have been, however, only two cases ofsuch voluntary price reduction among our samples during the sample period. Non-voluntary pricereduction includes those due to structural change such as calorific value change. In such cases withstructural changes, distributors still need to obtain permission for a price reduction). Furthermore, forlarge suppliers, entry and pricing have been deregulated since 1995. Our study focuses on small supply
services that are still under regulation.

8

of beginning and ending fixed assets. Thus sB can be considered a capital cost. Gas distributors
report each item of the above equation and the METI investigates whether the equation holds.
There is no ex-post inspection.
This regulation scheme does not have a truth-telling mechanism if there is asymmetric
information on the distributor’s costs.5 The distributor has an incentive to report higher costs
because that will make the regulated price higher and the profit allowed higher.6 On the other
hand, this regulation is the perfect mechanism to prevent moral hazard because the distributor isa residual claimant. Note that the regulation is different from the traditional average cost pricing
because price is determined based on expected costs, not on realized costs. Once the price isdetermined, the distributor can obtain higher profit as they increase effort to reduce costs. Thatis, the regulation is a type of fixed-price contract.
Presumably to mitigate the hidden information problem, the government introduced a so-called“yardstick inspection system”. The METI inspects the costs of each distributor and compares
them with similar types of distributors. The inspection procedure is as follows. First, thedistributors are categorized into 16 groups according to the size of markets (the number ofhouseholds in a market), the production system, inputs, location, and owner (public or private)of the distributor. Figure 1 shows this grouping. Then, the distributors in each group are gradedfrom 0 to 200 for their reported costs. Based on this grade, the distributors in each group areagain categorized into three groups: I, II, and III. Distributors with lower costs go into group I.
Distributors in groups II and III are subject to a penalty. The reported costs of the distributors inthose two groups are reduced and prices are determined based on the adjusted costs.7

5

Theoretical literature such as Lewis and Sappington (1988) assumes information asymmetry on the

demand side. That is, they assume that the firm has better information on the demand function than theregulator does. Although this assumption would be worth testing, in this version of the paper, we focus on
information asymmetry on the supply side. The METI have local offices throughout Japan and the local
offices are responsible for inspection of local distributors. We could argue that because of these local
offices, the METI is able to obtain good information on local demand and that there is little asymmetric
information on demand. If information asymmetry on demand is present, suppliers may have an incentive
to report lower expected demand.
6

More specifically, reporting higher costs leads to a higher (lower) regulated price if the demand

elasticity is enough low (high) (see Section 7).
7

For now, the reduction rates are 0.5% for group II and 1% for group III.

9

<<Insert figure 1 about here>>
Although Japanese yardstick inspection is not identical to the textbook type of yardstickcompetition, it does have its essence. If the penalty is large enough, the regulation reduces the
incentive of firms to report higher costs (given firms in each group are actually very similar)
because if a firm lies and others report the truth, then the firm that lied will be punished. Thus,
the current regulation, which combines a yardstick and a fixed-price contract, theoreticallyeliminates both adverse selection and moral hazard problems: yardstick inspection removes theadverse selection problem while a fixed-price contract removes the moral hazard problem. In
addition, because a yardstick system does not require the regulator to give firms aninformational rent to tell the truth, the current regulation may indeed lead the industry to thefull-information outcome.89
In practice, however, it seems difficult for the yardstick system to work perfectly to remove theadverse selection problem. First, it has often been discussed that the regulator is unlikely to finda large set of truly identical firms. In this Japanese system, distributors cannot be identical evenin the same group. Second, again as an often-discussed point, firms may collude. Third, thecurrent penalty seems to be ad hoc. It is unclear if it is sufficiently high to induce truth telling.
Furthermore, here, the extent of the punishment depends only on the order of the costs, not on
the difference in the costs. This may also reduce the effectiveness of the regulation.
Because yardstick inspection is unlikely to work perfectly, we do not assume optimality of thecurrent regulation. Therefore, our estimation follows Gagnepain and Ivaldi (2002) rather than
Wolak (1994). This estimation requires only ex-post realized data and we do not have to model
the firms’ ex-ante behavior under yardstick inspection. This suits us because we are not sure towhat extent the Japanese yardstick is effective and therefore, how the firms behave under such
regulation: we cannot model ex-ante behavior of the firms. As described before, we infer such
ex-ante behavior of firms, truth telling or not, by the welfare difference.

8

With an individual incentive regulation, the regulator cannot achieve the full-information outcome

because it needs to give informational rents to firms, and usually such rents are costly.
9

We mean, by full-information outcome, the counterfactual outcome that can be achieved if the regulator

does not face the information disadvantage. This differs from the often-discussed first best outcome
because the regulator here is not a welfare maximizer. See Section 7 for the discussion of the Japanese
regulator’s objective.

10

All the gas distribution companies were surveyed in the first yardstick inspection in 1995. They
were required to provide values for the variables in equation (1), regardless of whether they
were willing to change their current prices. Following the first inspection, only the distributors
that applied for a price change are subject to yardstick inspection. Among our sample of 59
distributors, there were 14 applications for price changes subject to the yardstick after 1995, oneeach in 2000 and 2003, two in 2001, four in 2004, and six in 2005. When only the distributors
that applied for a price change are inspected, the latest reported costs of firms that did not apply
for a price change (they did not report current costs) are used as a benchmark.
Figure 2 shows the average unit price of public firms over 1990–2005. The prices of public
firms have a downward trend after the introduction of yardstick inspection. There is a large dropin prices in 1996, following the introduction of yardstick inspection.
<<Insert figure 2 about here>>

4. Theoretical ModelIn this section, we consider a model of retail gas distribution services, which is still under priceregulation.10 To derive a structural model of the industry, we need a detailed account of thetechnological, informational, and regulatory constraints. We start this section by describing ourassumptions on these constraints.
For the technological constraint, we assume that, to provide the required level of services,
denoted by Y, the gas distributor needs to combine four inputs: labor (L), gas (G), materials (M),and capital (K). L includes all types of workers; G corresponds to gas inputs for distribution; K
refers to plant, infrastructure, and distribution networks; and M includes all materials used for
performing maintenance and management activities. The distribution process is then representedas:
Y = f ( L, G, M , K b) ,where b is a vector of parameters characterizing the technology in the production process.

10

As noted, prices for large supply services were deregulated in 1995.

11

(2)

Regarding informational and regulatory constraints, we follow the assumptions of Gagnepain
and Ivaldi (2002) (henceforth G&I). First, the gas distributor has private information about its
technology and its cost-reducing effort is unobserved by the authority. We assume that the
distributor is better informed about input efficiency than the regulator is. More specifically, we
distinguish between the observed and the efficient levels of labor and assume that the distributor
is better informed about labor efficiency. 11 Second, regulatory schemes and distributors’
efficiency levels are exogenous.12

Let L̂ be the physical amount of labor that is observable by the authority. L is the efficient levelof labor associated with the output level Y. We assume that the ratio of observed to efficientlabor quantities is a direct measure of informational discrepancies between the regulator and the
distributors. Following G&I:

Lˆ = L exp(θ − e) .

(3)

Parameterθ, the so-called “labor inefficiency parameter”, refers to variables that are not under
the control of the distributor. As θ becomes larger, the efficient level of labor is smaller given
the observed physical amount of labor. The variable e summarizes the behavioral decisions
made by managers to exploit the opportunities; e defines the effort level of managers. As e
increases, the discrepancy between L and L̂ decreases. The distributors cannot change theirtypes,θ, but can change the level of discrepancy between L and L̂ by increasing the effort levele. If the distributor sets the effort level so that e = θ , then the observed level and efficient level
coincide. 13 Both input inefficiency and cost-reducing activity are unobservable to the regulator
and to the econometrician. The efficient level of labor L determines the output level while costs
are incurred to cover physical labor L̂ .

11

For analytical simplicity, we assume that only one input is affected by this inefficiency although inreality all of the four inputs may be inefficient. Appraising efficiency by the observed quantity of physicalinput is more difficult in the case of labor and choosing labor input for the setting seems to be appropriate.
12

The assumption that the efficiency parameter is independent of time is debatable. This implies that

contracts are renewed each year independently of what the state of nature was in the past. In a dynamic
setting, inefficiency could evolve, and its evolution could be approximated by a trend. (See Cornwell,
Schmidt, and Sickles (1990) for such a model.)13

We assume that θ is always greater than e. As Gagnepain and Ivaldi stated, this assumption ismeaningful in the sense that the managers’ effort is aimed at reducing the inefficiency level, which cannot
be larger than θ.

12

Next, we interpret the distributors’ decision process after the price is set. The decision process
consists of choosing the optimal input and effort allocation. Note that this is an ex-post behavior
and does not involve an ex-ante decision process, such as which level of costs to report, underthe yardstick regulatory environment. We decompose this ex-post decision process into two
steps. The first step is to choose the optimal input and the second is to choose the optimal effort
allocation, given the regulated price and the demand associated with the price.

Assuming that the distributor is a price-taker in the market for input factors and has a costminimizing behavior for each level of effort, an operating cost function can represent thetechnological process. The operating cost faced by the distributor is:
C = ω L Lˆ + ωG G + ω M M ,where ω = [ω L , ω G , ω M ] are the prices of labor, gas, and materials, respectively. We assume that
K cannot be fully adjusted in the short run and is fixed. 14 From duality theory, the conditional

operating cost function is defined by:
C (Y , K , ω , e,θ β ) = min L ,G ,M ω L L exp(θ − e) + ω G G + ω M M ,(4)subject to:Y = f ( L, G , M , K b).

Equation (4) defines a “conditional” operating cost function because it still contains a level ofeffort. This is the first step in the distributors’ decision process.

The second step is to determine the level of cost-reducing activity under the given regulatoryenvironment. As seen in the previous section, the Japanese authority sets the price of gas
services so that it equals the expected average cost (see equation 1). There is no ex-postinspection to check whether the reported cost is actually equal to the realized cost. Under this
fixed-price regulation, the distributor is the residual claimant of effort. After the activity in thecontractual period, all the realized profit goes to the distributor. The utility of the firm is givenby:
U = P(Y )Y − C (Y , K , ω , e,θ β ) − sB −ψ (e),(5)

where ψ (e) is the cost of effort function; exhibiting effort is costly for the firm. The distributor

14

We also assume that the capital cost sB is fixed in the short term and therefore it is included not in theoperating costs but in the total cost.

13

maximizes utility in equation (5) with respect to the effort level, e , and the first-order conditionis:ψ ' (e) = −∂C / ∂e ,(6)which implies that the marginal cost of effort equals the marginal cost saving from the effort.

5. Empirical Model

5.1 Functional forms

We choose a simple Cobb–Douglas function to represent technology for the following reasons.
First, we use it for tractability. Although we could have used more elaborate functional forms
such as a translog for the estimation of the cost function, computations of welfare become
cumbersome with such functions. Second, because of the choice of the Cobb–Douglas function,
the two-step decision process above (the input allocation and effort level determination
problems) provides the same solution as if we had solved the two steps simultaneously. Under
Cobb–Douglas technology, the dual cost function is given by:βLβG

C = β 0 exp[ β L (θ − e)]ω L ω G ω M

βM

Kβ Yβ ,
K

Y

(7)

with the assumption of homogeneity of degree one in input prices, that is β L + β G + β M = 1 . We
should note that no constraint is imposed on the return to scale effect. As in previous studies, we
specify the cost of effort by:ψ (e) = exp(αe) − 1 ,(8)with α > 0.

Using these functional forms and the first-order condition (6), we can solve for the effort level
as:
e* =

β Lθ + ln β L β 0 − ln α + β L ln ω L + β G ln ωG + β M ln ω M + β K ln K + β Y ln Y.
α + βL(9)

From the equation above, we can see that the equilibrium effort level under this regulation
regime is an increasing function in the inefficiency parameter θ, the output level Y, and the input
prices ω L , ωG , and ω M . A distributor with the larger θ (less efficient distributor) needs to makea greater effort under this regulatory scheme. Moreover, e * is a decreasing function of α, thetechnological parameter of the internal cost function (8).

Substituting the optimal effort level e * into the cost function (7) and taking the logarithm, we

14

obtain the cost function as follows:
ln C = β ' 0 + ξ ( β Lθ + β L ln ω L + β M ln ω M + β G ln ωG + β K ln K + β Y ln Y ) ,

(10)

'

where ξ = α /(α + β L ) and β 0 = ln β 0 + β L (ln α − ln β L − ln β 0 ) /(α + β L ).

5.2 Estimation method and data

The key feature of G&I lies in the way a stochastic element is built into the classical Cobb–
Douglas cost function through the efficiency parameter. Assuming that parameter θ has adensity function f (θ ) defined over an interval [θ ,θ ] , where θ ( θ respectively) corresponds tothe most (least) efficient firm, provides us with the stochastic element required to perform theestimation.
Using equation (10), the stochastic cost function for distributor i at period t is given as:cit'= β 0 + ξ ( β Lθ + β L ln ω L + β G ln ωG + β M ln ω M + β K ln K + βY ln Y ) + ε itc
= c(Yit , K it , ωit ,θ it β ) + ε it

c

(11)

where c it = ln C and an error term ε c it is added to account for potential measurement errors. It
is assumed to have a normal density with mean zero and variance σ 2 c , and they are independentof each other. Moreover, we use a beta density function for f (θ ) , the distribution of theefficiency index θ , with scale parameters µ and ν. It is reasonable to choose this distribution forθ because the shape of the beta distribution is flexible depending on the scale parameters.

Furthermore, G&I sets out two additional advantages of using the beta density function. First,
the beta density function is defined over the interval [0,1] and therefore, the labor inefficiency
parameter is defined as a percentage. Second, we need a density function defined on a compact
support and the beta density function gives us this condition.

The conditional likelihood of θ i is:
Lit (θ it ) = L (c it | Yit , K it , ω it , θ i , β , σ c , µ ,ν ) =ε c 
φ  it θ i ,σ c  σ c 
1(12)where φ (.) denotes the normal density function. However, because the variable θ i is
unobservable, only the unconditional likelihood can be computed, that is:1

Lit = ∫ Lit (u i )uiν −1(1 − ui ) µ −10where Γ(.) is the gamma function.

15

Γ(ν + µ )dui ,Γ(ν )Γ( µ )(13)The sample consists of 76 public gas distributors for the period 1990–2005. As described in
Section 3, the sample can be categorized into three types according to their technology. For thecost estimation, we use 59 distributors of Type 1 for the purpose of homogeneity. Estimating the
Cobb–Douglas cost function requires measures of the level of operating costs, the quantity ofoutput, and the input prices. The output is specified as total volume (m³) of gas supplied by
distributors. The total length of the conduit (m) is used for the quantity of capital. Costs of labor
are specified as total labor expenditures including wages, salaries, pensions, and benefits. The
price of labor is calculated as labor costs divided by the number of employees. Costs ofmaterials are specified as nonpersonnel expenses for day-to-day operations and maintenance ofthe distribution network. The price of materials is calculated as the costs of materials divided by
the number of meters (that is, the number of households that have access to the gas supply
service) in each market. Because the costs of materials mostly arise from operating andmaintaining distribution lines to households, the number of households seems to be a suitablemeasure of material inputs. Costs of gas input are specified as total expenditure on raw material
inputs. The price of gas is calculated as the costs of gas divided by the total amount of gas used
for distribution.

For welfare analysis, we estimate the demand function in Section 7. We use all 76 samples forthe demand estimation. This estimation additionally requires measures of consumer prices. We
use the calorific value-adjusted price (yen/10,000 kcal) as the price measure. Furthermore,
welfare calculation requires the capital cost, sB in equation (1). Capital cost is specified asinterest expenses on enterprise loans, temporary loans, and money transferred plus 2 percent of
the average of the beginning and ending fixed assets.

Summary statistics of the variables categorized according to their technology types are given in
Table 1.

Table 2 compares the average operating costs and prices before and after the introduction ofyardstick inspection. We can see from the last row that, in our sample, both the mean average
operating cost and the mean price decreased after the introduction of yardstick competition.
These changes are statistically significant. The standard deviations of costs and prices also
decreased after the introduction of yardstick inspection, although the latter is statisticallyinsignificant. We examine these statistics in each group of the yardstick inspection; however,16

some groups show different changes. In group 15, the mean of prices increased, despite adecrease in the mean of costs, after the introduction of yardstick inspection. In groups 12 and 15,
the standard deviations of prices increased after the introduction of yardstick competition.
Furthermore, Table 2 compares the mean growth rates of average cost before and after the
introduction of yardstick inspection. We can see from the last row that, in our sample, theaverage operating costs were decreasing in the sample period. These decreases are notsignificantly different between the two periods at 5 percent level. In group 14, however, average
operating costs were increasing before the introduction of yardstick inspection, while they weredecreasing afterward.

6. Estimation Results

6.1 Estimation results of cost function
The estimated parameter values for equation (11) are reported in Table 3. Because we assumed
homogeneity, the parameter for β M is dropped. To capture the time trend, we add a year dummy
to equation (11), and β t denotes its coefficient.

All parameters are significant at least 10 percent level, except α and β t . In particular, this is true
for the scale parameters µ and ν characterizing the density of the inefficiency level. From theestimated µ and ν, it turns out that the density function is a decreasing function. More than 70
percent of the distributors have a θ of less than 0.5.

Along with the above model, we also estimate the alternative model. The alternative model is a
Cobb–Douglas cost function that does not take into account regulatory and informational
constraints. This model is referred to as the standard case, namely:cln Cit = β 0 i + β L ln ω L ,it + β M ln ω M ,it + β G ln ωG ,it + β Y ln Yit + β K ln K it + β t ln Year + ε it . (14)The standard case includes a time trend and a firm effect β 0 i to allow for a fixed-effectestimation procedure. To compare the fit of the two models, we conducted a Vuong (1989) test
whose null hypothesis is that the two models are equally far from the true data-generatingprocess in terms of Kullback–Liebler distances. The alternative hypothesis is that one of the twomodels is closer to the true data-generating process. We obtain a Vuong statistic of 2.67. This
statistically supports the asymmetric information model generated by the structural approachrather than the standard model.

176.2 Efficiency and effort levels
Estimates of individual efficiency parameters can also be recovered. From equations (10) and(11), the error term of the cost function has two unobservable, random, and independentccomponents, θ i and ε it . The error term can be written as:cuit = ε it + ξβ Lθ i ,where ξ = α /(α + β L ) . From a procedure by Jondrow et al. (1982), we recover an estimate foreach θˆi from the values of residuals ûit by considering the conditional distribution of θ i given
uit , that is, by computing θˆi = E (θ it | u it ) . For all distributors in our data set, the estimatedvalues of the efficiency levels are available from the authors. Once the estimate for θ i is
obtained, we can then also obtain the effort level using equation (9).

From equation (7), the cost distortion that measures the discrepancy between the theoretical
frontier and the observed cost is given by:
exp[ β L (θ − e)] .

(15)

The maximum cost distortion is achieved for a zero level of effort and an inefficiency level
equal to one. Figure 3 presents our set of distributors in 1996 ranked according to their costdistortions defined by equation (15). In addition, Figure 3 provides the level of the inefficiency
parameter for each distributor. Reflecting the high efficiency levels and the high-powered
incentive regulatory scheme (that is, fixed-price contract), the distortion is not very high. The
maximum distortion is about 10.1 percent, and most of the distributors exhibit a distortion levelof less than 5 percent.

<<Insert figure 3 about here>>

7. Welfare Implications and the Effect of Yardstick Inspection

7.1 Demand
Our objective is now to perform a comparison of current and full-information welfare. First, tocompute consumer surplus, the price elasticity of demand must be estimated.

Assume the demand function is log linear such that:ln Y = d 0 + d1 ln P + d 2 t + ε d ,

18

(16)

where a vector d 0 includes the fixed effects and t is a year dummy. Our model of costs and thedemand systems is sequential. First, the government sets a price and once the price is known,
the demand level is determined according to equation (16). Finally, the cost of running theservice is obtained through the cost model given by equation (10). This gives rise to a blockrecursive structure, so each equation can be estimated separately. We obtained the estimatedresults of price elasticity 0.275. See Table 4 for the results.

7.2 Regulator’s behavior
We now know the cost structure, the demand elasticity, the inefficiency level, the effort function,and the price level. Additionally, the behavior of the regulator must be specified. Here, we
consider the regulator’s pricing behavior, ignoring the existence of the yardstick regulation fornow. As noted in Section 3, the regulation requires the price to be equal to an expected average
cost as in equation (1): P r = (C (Y e ) + sB) / Y e . Therefore, we assume that the regulator’s
objective is to set the price equal to the average cost such that:P r Y = C (Y ) + sB ,(17)

where Y is the realized output level.15 Given the selected price is a point on the inverse demand
function, P (.) , when the authority has set the price, the associated demand Y is implicitly
determined, that is, the customers adjust their demand at this price. The regulator should takethis into account and therefore, equation (17) can be rewritten as:P(Y )Y= C (Y ) + sB
= C (Y , K , ω , e, θ β ) + sB

(18)

where the cost function in equation (4) is substituted. The regulator’s problem is to find thedemand level Y that satisfies the equation above, given K , ω , e,θ , β , and sB .

We assume that the regulator observes all the variables and the parameters in the above equation
except θ and e. Actually, however, from equation (9), once the level of Y is determined, thelevel of effort can be recovered if θ is recovered: e = e * (Y , K , ω , θ | β ) . The regulator isassumed to know this structure of the industry and therefore, the only unobservable for the15

Gagnepain and Ivaldi (2002) assume that the regulator is a welfare maximizer, given the regulatoryenvironment. However, because it is not welfare maximizing to set the price to be equal to the average
cost, we do not assume it here. Therefore, our full-information welfare is different from the first-bestwelfare unlike often discussed, and the current welfare may be larger than the full-information welfare.

19regulator is θ .

Given the above assumptions, the regulatory environment is reduced to the following. First, thedistributor reports the levels of K , ω , θ and sB , and the regulator sets the level of output so that
equation (18) holds, given the reported levels. Because K , sB and ω are observed by theregulator, we assume that the distributor reports the true levels of these variables; they are thesame as the observed data. On the other hand, because the regulator does not observe the levelof θ , we distinguish the true level of θ from the reported level θˆ . We assume that theregulator believes that θˆ = θ . Given the reported inefficiency level θˆ , the regulated output levelY r is determined so that:P(Y r )Y r

= C (Y r , K , ω , e* (Y r , K , ω , θˆ | β ), θˆ | β ) + sBββββ
= β 0 exp[ β L (θˆ − e* (Y r , K , ω , θˆ | β ))]ω L ωG ω M K β Y r + sB
L

where e* (Y r , K , ω ,θˆ | β ) =

G

M

Y

K

(19)

β Lθˆ + ln β L β 0 − ln α + β L ln ω L + β G ln ωG + β M ln ω M + β K ln K + βY ln Y r.
α + βLWe can see that the regulated output level can be expressed as a function of the reported
inefficiency level: Y r = Y (θˆ) .

7.3 Ex-post distributor’s behavior
Once the regulated output level Y r = Y (θˆ) is determined, the distributor conducts costminimization activity (4) given Y (θˆ) and for each level of effort e , and the cost function is
described as a function of both θ and θˆ , namely:
C (θ , Y (θˆ) | e) = β 0 exp[ β L (θ − e)]ω L ωG ω M
βL

βG

βM

K β Y (θˆ) β .
K

(20)

Y

Similarly, the distributor next maximizes utility with respect to the effort level given theregulated output level Y (θˆ) , and the first-order condition (9) gives us the effort level as afunction of both θ and θˆ , namely:β θ + ln β L β 0 − ln α + β L ln ω L + β G ln ωG + β M ln ωM + β K ln K + βY ln Y (θˆ)
e* (θ , Y (θˆ)) = L.
α + βL(21)

Therefore, the cost realization will be as the following,βββC (θ , Y (θˆ), e* (θ , Y (θˆ))) = β 0 exp[ β L (θ − e* (θ , Y (θˆ)))]ω L ωG ω M K β Y (θˆ) β
L

G

M

K

Y

(22)

7.4 Welfare implications
Given our knowledge of the demand and supply functions, we now calculate the welfare levels
20under the current and the hypothetical full-information situations to see whether the introductionof yardstick inspection reduces the information disadvantage of the regulator. Full-information
welfare is obtained by assuming the regulator observes all the variables and parameters.

We define social welfare as:
W = S − R +U

(23)

where S is the gross surplus and derived from the demand function, R is the distributor’s
revenue and obtained as the product of the price and the demand level, and U is the firm’s utility
defined in equation (4).

Substituting (21) and (22), the current (actual) welfare level W c can be expressed, given thereported inefficiency level θˆ and the true inefficiency level θ , as follows:
W c (θ , θˆ) = S (Y (θˆ)) − P(Y (θˆ))Y (θˆ) + [ P (Y (θˆ))Y (θˆ) − C (θ , Y (θˆ), e* (θ , Y (θˆ))) − sB − ψ (e* (θ , Y (θˆ)))] (24)This can be calculated by using the observed output level for Y (θˆ) and the inefficiency level θ
recovered in Subsection 6.2. The full-information welfare level W f , which can be obtained if a
distributor reports the true inefficiency level θ , that is, if θˆ = θ , is:Wf= W c (θ , θ )= S (Y (θ )) − P(Y (θ ))Y (θ ) + [ P(Y (θ ))Y (θ ) − C (θ , Y (θ ), e* (θ , Y (θ ))) − sB − ψ (e* (θ , Y (θ )))]

(25)

The problem with the fixed-price contract is that it does not have any truth-telling mechanism.
Therefore, the distributors may have an incentive to report θˆ , which is higher than the true levelθ , to obtain a higher permitted profit. Such a behavior either decreases or increases social
welfare away from the full-information welfare.16 Appendix A shows that reporting a higher
inefficiency level θˆ leads to a higher (lower) regulated price and lower (higher) output if theslope of the inverse demand curve is smaller (larger) than the average cost curve. It turns outthat with our estimated parameter values, all our observed markets exhibit a smaller slope of theinverse demand curve than that of the average cost curve. Figure 4 describes this situation. In
Figure 4, ACθ is the true average cost curve of a firm with inefficiency level θ , and ACθˆ is thefalse average cost curve the regulator believes that the firm has when the firm reports θˆ such

16

As noted, the full-information welfare is different from the often-discussed first best welfare. Therefore,

the current welfare can be higher than the full-information welfare.

21

that θ < θˆ . That is:ACθ (Y ) ==where e * (Y , K , ω ,θ | β ) =β Lθ + ln β L β 0 − ln α + β L ln ωL + β G ln ωG + β M ln ωM + β K ln K + βY ln Y
, and
α + βLACθˆ (Y ) ==where e * (Y , K , ω ,θˆ | β ) =C (Y , K , ω , e* (Y , K , ω ,θ | β ),θ | β ) + sBY,
β 0 exp[ β L (θ − e* (Y , K , ω ,θ | β ))]ω L β L ωG β G ωM β M K β K Y β YYC (Y , K , ω , e* (Y , K , ω ,θˆ | β ),θˆ | β ) + sBY,
β 0 exp[ β L (θˆ − e* (Y , K , ω ,θˆ | β ))]ω L β L ωG β G ωM β M K β K Y β YYβ Lθˆ + ln β L β 0 − ln α + β L ln ωL + β G ln ωG + β M ln ωM + β K ln K + βY ln Y.
α + βLP (Y ) is the inverse demand function. In the full-information case, price is determined so that
P = ACθ . This price and the associated demand are shown by P (θ ) and Y (θ ) , respectively, in

Figure 4. However, if the firm reports a higher θˆ , price and output are determined at the levelsof P(θˆ) and Y (θˆ) in Figure 4. In such a case, the firm’s true average cost is ACθ (Y (θˆ)) given
the regulated output level Y (θˆ) . The firm’s profit increases from zero in the full-informationcase to the area P(θˆ)adAC (Y (θˆ)) . The firm’s utility also increases, because the effort level
decreases because of the lower output. Consumer surplus decreases because of a higher priceand lower output.

<<Insert figure 4 about here>>
The introduction of yardstick inspection may reduce the incentive to report a higher θˆ , because
if a distributor reports a higher inefficiency level than the other distributors in the same group, it
is subject to penalty. In the next subsection, we show that if the yardstick inspection actually
reduces the discrepancy between θ and θˆ , the difference between W c in equation (24) and W f
in equation (25) should also decrease. We assess whether the introduction of yardstickinspection actually reduces the discrepancy between θ and θˆ by examining whether thediscrepancy between W c and W f has been reduced since its introduction.

7.5 The effect of yardstick inspection
The very first yardstick inspection was conducted in 1995. Under this first inspection, all gas
22

distributors were required to report values of the variables in equation (1), regardless of whether
they were willing to change their current prices at the time. Since the first inspection, only
distributors that apply for a price change have been subject to yardstick inspection. Among oursample of 59 distributors, there were 14 applications for price changes that were subject to theyardstick after 1995, one each in 2000 and 2003, two in 2001, four in 2004, and six in 2005.

We call the first inspection, in which all the distributors are targets, the “simultaneous yardstickinspection” and the subsequent cases, in which the distributor that applied for a price change isthe target, as the “individual yardstick inspection”. We examine the difference between fullinformation welfare W f in equation (25) and current welfare W c in equation (24) or∆W = W f − W c , with and without yardstick inspection. Equations (24) and (25) show that as areported inefficiency level converges to the true inefficiency level, the welfare difference
converges to zero. That is, as θˆ → θ , W c → W f and ∆W → 0 . Furthermore, Appendix B
shows that with our parameter estimates, current welfare W c (θ , θˆ) is a monotonicallydecreasing function of θˆ . Therefore, the welfare difference ∆W = W f − W c is always positive(when θˆ > θ ) and an increasing function of θˆ . Therefore, if yardstick inspection has the effectof reducing firms’ incentive to report higher inefficiency levels (that is, if yardstick inspection
has the effect of reducing the discrepancy between θ and θˆ ), it reduces ∆W .

We examine several measures of the effect of yardstick inspection, which are expected to take anegative value if yardstick inspection has the effect of reducing firms’ incentive to report higher
inefficiency levels. Now, let R be the indicator variable such that Rit = 1 if distributor i issubject to yardstick inspection in year t and Rit = 0 otherwise. Also, let I be the indicatorvariable such that I it = 1 if distributor i applied for a price change and obtained permission inyear t and I it = 0 otherwise. That is, when I it = 0 , a distributor preferred the status quo. Our
first measure of the yardstick effect is:
Effectave = Ei [ Diff i ] ,(26)

where Diff i = E[∆Wit | Rit = 1] − E[∆Wit | Rit = 0 & I it = 1] for each i . This is a simple average
difference in the welfare disparity with and without yardstick inspection. Next, we examine theeffect of simultaneous yardstick inspection:
Effect sim = Ei [ Diff sim ,i ] ,(27)

where Diff sim ,i = E[∆Wit | Rit = 1 & t = 1995] − E[∆Wit | Rit = 0 & I it = 1] for each i . This is an23average difference in the welfare disparity with and without simultaneous yardstick inspection.
Next, we examine the effect of individual yardstick inspection:
Effectind = Ei [ Diff ind ,i ] ,(28)

where Diff ind ,i = E[∆Wit | Rit = 1 & t ≠ 1995] − E[ ∆Wit | Rit = 0 & I it = 1] for each i .

The results are shown in Table 5. We calculate both per-household welfare and total market
welfare in each market and calculate the measures of improvement in welfare disparity defined
above. The negative values imply that yardstick inspection reduced the adverse selection
problem. The first row of Table 5 shows the measure defined in equation (26). We can see that,on average, yardstick inspection improved the per-household welfare disparity. On average, theper-household welfare disparity from the full-information outcome is 26.40 yen smaller underyardstick inspection. The second row shows the measure defined in equation (27). Again, we
can see that the per-household welfare disparity is 127.51 yen smaller under yardstickinspection. This implies that the simultaneous yardstick inspection in 1995 was somewhat
effective in reducing adverse selection. Measures (26) and (27) calculated with total market
welfare, however, show that welfare disparity was widened by yardstick inspection. Total
market welfare disparity is 5,604,000 yen larger under yardstick inspection. It is 3,367,000 yenlarger under simultaneous yardstick inspection. The result that per-household welfare disparity
was improved while total market welfare disparity was not may imply that simultaneous
yardstick inspection was effective only for firms in small markets. Because our estimated costfunction exhibits scale economies, firms in large markets have a cost advantage. Therefore, ourresults suggest that the simultaneous yardstick inspection was effective only for firms without acost advantage in reducing the adverse selection problem: firms with a cost advantage still have
incentive to report higher costs even under yardstick inspection, while firms without a costadvantage have a lower incentive to report higher costs. One possible reason for such aphenomenon is that firms are not identical in the yardstick comparison groups. Yardstickgrouping may not be appropriate here, and such a grouping may reduce the effect of yardstickinspection.

The measure of the effect of independent yardstick inspections defined in equation (28) shows adifferent result. On average, it can be seen from the third row that the individual yardstickinspection widened both per-household and total market welfare disparities. The per-household
and total market welfare disparities widened, by 647.11 yen and 23,700,000 yen, respectively.
This implies that subsequent individual yardstick inspections do not always have the power to24

reduce the adverse selection problem. Why might an individual case not work? One possible
reason is that, in such an individual case, the benchmark costs are already known for the firms
from the first inspection in 1995. Therefore, our results may give rise to a dynamic concern,
similar to the Ratchet effect, because the subsequent inspection cannot be effective for a firmthat has learned the relative position of its costs.

Finally, we calculate the additional two measures. The first measure simply looks at the average
difference in the welfare disparity before and after the introduction of yardstick inspection,
regardless of whether or not the firm is subject to yardstick inspection. Namely:
Effectbefore / after = Ei [ Diff before / after ,i ] ,(30)

where Diff beofer / after ,i = E[∆Wit | t ≤ 1995] − E[∆Wit | t > 1995] for each i . The second measure
looks at the average difference in the welfare disparity before and after the introduction ofyardstick inspection when firms choose the status quo. Namely:
Effect status.quo = E i [ Diff status.quo,i ] ,(31)

where Diff status.quo,i = E[ ∆Wit | t ≤ 1995 & I it = 0] − E[∆Wit | t > 1995 & I it = 0] for each i . We also
calculate these measures by groups. The results are shown in the last 12 rows in Table 5.

The fifth row in Table 5 (the measure defined in equation (30)) shows that, in general, thewelfare disparity from the full-information outcome widened after the introduction of yardstickinspection in 1995. Specifically, the welfare disparity widened by 8,954,000 yen, while the perhousehold welfare disparity widened by 341.27 yen after 1995. Similar results are observed inall groups except group 12. If we compare the cases where firms kept the status quo (themeasure defined in equation (31)), we again find that the welfare disparity widened after the
introduction of yardstick inspection. Specifically, as shown in the 11th row, the welfare disparity
widened by 9,215,000 yen, while the per-household welfare disparity widened by 385.63 yenafter 1995. Again, similar results are observed in all groups except group 12.

Because costs were decreasing during our sample period, keeping the status quo must have led
to larger welfare disparity. Moreover, the higher the rate at which costs decrease, the larger thewelfare disparity is when a firm keeps the status quo. Therefore, the above results of the larger
welfare disparity after 1995 may merely reflect the higher rate of cost decrease in the period
after 1995. However, the larger disparity after 1995 is observed even in the groups where thecost decrease rates are not significantly different between the periods before and after the25introduction of yardstick inspection (see Table 2 for the cost decrease rates). Therefore, ourresults may imply that the introduction of yardstick inspection reduced firms’ incentive to adjust
prices.

Why might firms have less incentive to adjust prices under yardstick inspection? This may be
explained by firms’ collusive behavior. If a firm with decreased costs keeps the status quo, thebenchmark cost will be kept high, while if it adjusts prices, the regulator will recognize lower
costs and the benchmark cost will be reduced. Therefore, firms may have incentive to collude tokeep the status quo.

8. Conclusion
This study is aimed at assessing the effect of yardstick inspection in the Japanese retail gas
distribution industry. Realizing that yardstick inspection will lead the industry to the fullinformation outcome if it works perfectly to eliminate the adverse selection problem, we infer
its effect from the difference between the current and the hypothetical full-information welfare
levels.

We estimate a cost function for gas distributors under the assumption of asymmetric information
between the regulator and the distributor for the efficient level of labor. It is assumed that theregulator does not observe either the inefficiency level or the effort level of each distributor. As
the existing regulation has an incentive mechanism to induce the distributor’s effort, thedistributor is assumed to maximize the utility with respect to the effort level. Therefore, theeffort level can be solved as a function of the parameters. Using distributional assumption
regarding the inefficiency level, maximum likelihood estimation is conducted to estimate theparameters, except the inefficiency level, and then, the inefficiency level is recovered by themethod in Jondrow et al. (1982). It was shown that most distributors were quite efficient.
Having obtained all the parameters, the welfare levels under the current and the full-information
situations are calculated. Our results indicate that the welfare difference between the current andthe full-information outcomes is somewhat reduced by yardstick inspection on average,
implying that the inspection reduced firms’ incentive to report higher costs.

Yardstick inspection was introduced in 1995. In that year, all the firms were required to reporttheir costs for comparison. Since then, only the firms that apply for a price change are subject to26

inspection and the most recent costs of the other firms (which do not apply for a price rise anddo not report costs) are used as the benchmark. Our results show that the initial inspection in
1995 reduced the welfare discrepancy, while the later individual cases did not. This may giverise to a dynamic concern, similar to the Ratchet effect, such that subsequent inspection cannot
be effective for a firm that has learned the relative position of its cost. Furthermore, theinspection seems to have discouraged firms from changing prices. Our results from this study
suggest that a better form of regulation, which takes into account firms’ dynamic incentive,
should be considered.

27

Appendix I
We show that if the slope of the inverse demand curve is smaller than the average cost curve,
reporting a higher inefficiency level θˆ leads to a lower regulated price and higher output.

As in equation (19), the regulator set the regulated price so that :P(Y r )Y r

= C (Y r , K , ω , e * (Y r , K , ω , θˆ | β ), θˆ | β ) + sBββββ
= β 0 exp[ β L (θˆ − e * (Y r , K , ω , θˆ | β ))]ω L L ω G G ω M M K β K Y r Y + sB

where

β θˆ + ln β L β 0 − ln α + β L ln ω L + β G ln ω G + β M ln ω M + β K ln K + β Y ln Y re * (Y r , K , ω , θˆ | β ) = L.
α + βL
By totally differentiating the above equation, we obtain:
dY
=
dθˆ

Therefore,

αβ LC
α + βLP ' (Y )Y + P (Y ) − β Y

βL
C
C
+
βy
Y α + βLY

dY
< 0 ifdθˆP ' (Y ) < −βL
C + sBCC+ βy 2 −βy 2
2α + βLYYY(30)

The left side of the above inequality is the slope of the inverse demand curve and the right sideis the slope of the average cost curve. Therefore, if the slope of the inverse demand curve issmaller than the average cost curve, reporting a higher inefficiency level θˆ leads to a lower
regulated price and higher output.

We confirmed that, with our estimated parameter values, inequality (30) indeed holds in all themarkets of our observation for a broad range of output level.17

Appendix B
In this appendix, we show that current welfare W c (θ , θˆ) is a monotonically decreasing functionof θˆ .

17

Specifically, we have checked the range from the half to the double of the current output level.

28

Differentiating equation (24) by θˆ , we obtain the following:βL
β Y 1 dY
dW c (θ , θˆ)1) − α exp(αe * )]= [ P(Y ) − β y C (1 −α + βL Y
α + β L Y dθˆdθˆ
But we know, from Appendix A, thatdW c (θ , θˆ)dY< 0 . Therefore,< 0 ifdθˆdθˆΦ (Y ) ≡ [ P (Y ) − β y C (1 −

βL
βY 1
1
) − α exp(αe * )]>0
α + βL Y
α + βL Y

The value of the left hand side of the above inequality Φ (Y ) depends on the level of Y . With ourparameter values, we graphically confirmed that Φ (Y ) is always positive for all Y suchthat Y < Y (θ ) . 18 That is,dW (θˆ)< 0 for all Y such that Y < Y (θ ) : welfare is monotonicallydθˆdecreasing in θˆ for the level of Y such that Y ≤ Y (θ ) .19

18

The graphs are available from the author upon request.

19

Because Appendix A shows that reporting higher θˆ decreases Y, we only need to consider the range ofY such that Y < Y (θ ) .

29

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31

Table 1: Summary statistics
OutputTotal cost Labor priceMaterial priceGas price
Capital Consumer price Capital cost
Number(1000 yen)(1000 yen)(1000 yen)(m)(1000 yen)of firms( m3 )(1000 yen/ m 3 )(yen/ m 3 )1
Mean
91294866735776869
14.8250.0443249432112.41413684259s.d.
14400000
9490491433
10.0690.005526241726.26396701
2
Mean
16400000
16814456990
20.1140.0347494968152.705
1051975
21s.d.
44000000
41982671424
9.413
0.00671112475
19.4723839283Mean15400000
18929047053
18.6450.0355848017170.8203872863s.d.
13700000
15685061457
8.999
0.0065615647
12.212446240Total
Mean
11100000
9669656906
16.2480.0418334483124.608
18032776s.d.
25000000
22627891432
10.1250.007261602931.346545884
Note: Production type 1 includes those without vaporization systems or reformers. Type 2 includes those with vaporization systems. Type 3 includes those withreformers.
The total number of firms is larger than the sum of the number of firms in each production type because some distributors switched their production type during thesample period.
Production
type

32

Table 2: Cost and Price before and after the introduction of yardstick
Average operating cost
Price
Annual growth rate of
(yen)
(yen)
average operating cost
(%)
Group
PeriodBeforeAfter
BeforeAfter
BeforeAfterGroup 12Mean
129.65 120.57 ***152.65 151.39-0.780 -0.284
23.83
20.56
24.71
25.95
0.851
0.896
S.D.
Group 13
Mean
82.05
73.02 ***
105.87 101.77 ***-0.191 -1.591
S.D.
26.31
14.89 ***
16.73
14.54 *
0.781
0.523 *
Group 14Mean
82.96
77.86 ***
101.6697.99
0.467 -1.239 *
S.D.
12.00
14.48 *
16.22
13.95
0.585
0.453
Group 15
Mean
86.81
83.18
123.00 124.05-2.453 -1.951
S.D.
6.16
24.57 ***
5.22
20.37 ***
1.084
1.714 *
Total
Mean
92.21
82.24 ***
115.12 109.69 ***-0.244 -1.310 *
S.D.
29.55
23.47 ***
26.61
25.34
0.466
0.346
Note: The differences of means and standard deviations are tested by T-test and F-test, respectively. Stars referto the significance. * = significant at the 10% level; ** = significant at the 5% level; and *** = significant at
the 1% level.

33

Table 3: Parameter estimates of the cost function
Type of model

Asymmetric information caseparameter

Estimate

Standard error

α
β0
βL
βG
βK
βY
βt
µ

45.31331.51220.07220.00850.2497

Standard case
Estimate

Standard error

0.01870.10000.02870.44210.02050.65800.03080.16760.00980.13710.01480.77080.00770.76430.0117–0.0005

0.0155–0.0005

0.02330.17700.10250.84450.4607

ν

1.96480.2385σc0.16240.0922Log likelihood
251.2
236.0
# of observations
754
754
Note: Because we imposed homogeneity of degree one in input prices during theestimation, β M does not appear in the Table.

34

Table 4: Demand Estimation
Log output
Coefficient Standard error
Log price-0.2750.143
Constant
16.005
0.708
Fixed effectYes
Year dummy
Yes
Number of Observation
1046
Adjusted R-squared
0.9696
F-test (91, 954)
367.6135

Table 5: Welfare disparity between current and full information
outcome:
Difference before and after the introduction of Yardstick
MeasureEffectave
Effect sim
Effectind
Effectbefore,after
Total
Group 12Group 13
Group 14Group 15

Per household(yen)–26.40(62.02)Whole market(thousand yen)
5604
(682)

–127.51(62.16)

3363

(372)

647.11(143.18)23700(2142)

341.27-19.47448.35162.081504.50(42.24)(206.65)(26.46)(48.95)(76.82)

8954
297
5183
8857
99300

(285)
(585)
(197)
(490)
(5236)

385.63-107.98542.25197.371527.86(48.97)(245.21)(28.48)(47.10)(83.12)

9215
-664
5664
9701
98900

(309)
(667)
(206)
(519)
(5698)

Effect status.quo
TotalGroup 12Group 13
Group 14Group 15

Note: Negative value implies reduction in incentive to report higher
cost. Inside the parentheses are standard errors.

36

Figure 1: Grouping for yardstick inspection

Private Gas Suppliers
Number ofhouseholds inmarket: more than
150,000
Hokkaido
Tohoku
Kanto
Chubu
Hokuriku
Kinki
Chugoku
Shikoku
KyushuOkinawa

From wholesale
supplier (suppliers
without vaporization
system)LNG satellite,
Petroleum
LPG air (with(suppliers with
only vaporization
reformer)system)Group 2
Groups 4 & 5Group 3
Groups 6 & 7Group 9Group 1

Group 10

Public Gas Suppliers
From wholesale
supplier (suppliers LNG satellite, LPG Petroleum
withoutair (with only
(suppliers withvaporization
vaporization system) reformer)
system)Hokkaido
Group 12
Tohoku
Kanto
Groups 13 & 14
Chubu
Hokuriku
Group 16
Kinki
Group 15
Chugoku
Shikoku
KyushuOkinawa* The first column in each table shows the names of districts.

37

Group 8Group 11

unit price

Figure 2: Recent average unit price of public firms
128
127
126
125
124
123
122
121
120
119
199

0

199

2

199

4

199

8
199
year

6

38

200

0

200

2

200

4

Figure 3: Inefficiency parameter and cost distortion
0.6
0.5

theta
distortion

0.4
0.3
0.2
0.1
0

39

Figure 4: Reported and True Inefficiency Levels and Price and Output:
With Inelastic Demand

P

P(Y )

a

P (θˆ)
ACθ ( Y ( θˆ ))P (θ )

ACθˆ

d

c

b

Y (θˆ)ACθY (θ )

40

Y