zOSIPP Discussion Paper : DP-2001-E-004

Theories of Dynamic Pricing and the Japanese RetailGasoline

30 November 2001

Ujo Goto
Associate Professor, Faculty of Economics and Business
Administration, University of Kitakyushu

C.R. McKenzie
Professor, Osaka School of International Public Policy, Osaka University【Keywords】Gasoline; Collusion; Deregulation; Repeated game; Unexpected shocks【Summary】The purpose of this paper is to estimate models for retail price of gasoline based on theprediction deriving from the recent infinitely repeated game theories, supergame theories. The prediction
implies that both the future changes and the unexpected shock in the economic environment, where firms
faces, do have an impact on the current retail price of gasoline. Using monthly time series data on Tokyo andOsaka for the 1990’s, this paper shows evidence consistent with the implication of the theories. Some
evidence presented also suggests the behavior of retail prices has changed over the time period being
examined.

Theories of Dynamic Pricing
and the Japanese Retail Gasoline Market
Ujo Goto aaC.R. McKenzieb

andFaculty of Economics and Business Administration, University of Kitakyushu (ugoto@kitakyu-u.ac.jp)bOsaka School of International Public Policy, Osaka University, Japan (mckenzie@osipp.osaka-u.ac.jp)

Abstract: The purpose of this paper is to estimate models for retail price of gasoline based on theprediction deriving from the recent infinitely repeated game theories, supergame theories. The prediction
implies that both the future changes and the unexpected shock in the economic environment, where firms
faces, do have an impact on the current retail price of gasoline. Using monthly time series data on Tokyo andOsaka for the 1990’s, this paper shows evidence consistent with the implication of the theories. Some
evidence presented also suggests the behavior of retail prices has changed over the time period being
examined.
Keywords: Gasoline; Collusion; Deregulation; Repeated game; Unexpected shocks

1.

INTRODUCTION
The paper is organized as follows. In section 2, a

The purpose of this paper is to estimate thebrief survey of recent studies relating to the

behavior of the retail price of gasoline in Tokyo andJapanese and the North American oil industries are

Osaka using the predictions from several dynamic

presented. To examine how an interaction in longpricing models. These predictions are based on therun between gas stations influences the direction ofrecent infinitely repeated game theories, supergame

the behavior of retail price, the section 3 surveys

theories. The imprecation of these theories shows

several supergame theories including the situationthat the expected future changes and the unexpectedof imperfect monitoring. Section 4 details the

future changes in the economic environment, wheremodels to be estimated, while section 5 describes

firm face (for example, demand or cost conditions)the data used. Estimated results are presented inwill affect their current price setting if the firms

section 6.

engage in competition in a repeated game context[see, for example, Green and Porter, 1984;
Rotemberg and Saloner, 1986; and Haltiwinger andHarrington, 1991]. A second purpose of the paper is

2. RESEARCH ON THE OIL INDUSTRYAt the end of March 1996, the provisional law

to examine the impact of deregulation of the oilrelating to the importation of specified petroleum

industry on the behavior in Tokyo and Osaka inproducts (Tokutei sekiyu seihin yunyu zantei

Japan. Different responses to current and futuresochiho, called Tokusekiho) that restricted imports

economic conditions by firms in Tokyo and Osakaof specified petroleum products (gasoline, kerosene,

provide one explanation for differing behavior oflight oil) to a certain number of companies was

gasoline prices in the two prefectures.

abolished. As a result, the importation of specified2

petroleum products was liberalized. In June 1994, it

Vancouver have set a collusive price rather than abecame clear that the Tokusekiho would be

Nash equilibrium price. Borenstein and Shepard

abolished at the end of March 1996. Despite this[1996] using city level gasoline data for the United

liberalization, total imports of specified petroleum

States apply the ideas of Rotemberg and Saloner

products relative to total production in Japan have

[1986] and Haltiwinger and Harrington [1991] that,been very small, and the number of new importers

in a repeated game context, the future changes inof these products has remained rather small. At

the economic environment (for example, demandaround the same time the government made theand cost factors) will affect current collusive prices.

decision to abolish the Tokusekiho, the retail price

Their evidence indicates that expected futureof gasoline began to fall a little sharply. As a result,demand and cost changes do influence current

the media has often suggested the abolition of thegasoline prices, suggesting that gas stations are

Tokusekiho was a successful case of deregulations.

behaving in a manner consistent with a repeated
game.

There have been several recent studies of Japanese
oil industry. Prior to the actual abolition of theTokusekiho,

Chida[1996]

provides3.

MODELS OF DYNAMIC PRICING

somesimulation results that suggest that the wholesale

The purpose of this paper is to estimate models forprice of gasoline will fall as a result of theretail price of gasoline based on the prediction

Tokusekiho’s abolition. Onishi et al.’s [1997]

deriving from the recent infinitely repeated gamegraphical analysis of the national retail price oftheories,

gasoline suggests that the abolition significantly

implies that both the future changes and the current

reduced the retail price of gasoline. Goto’s [1999a]

unexpected shock in the economic environment,

analysis of the impact of the protection provided bywhere firms faces, do have an impact on the current

Tokusekiho showed that it was associated with anretail price of gasoline. Using monthly time series

upward shift in the cost function of several of thedata on Tokyo and Osaka for the 1990’s, this paper

major Japanese oil refiners. Goto [1999b] applies

shows evidence consistent with the implication of

cointegration analysis to the relationship between

the theories. Some evidence presented also suggests

the wholesale and retail prices of gasoline andthe behavior of retail prices has changed over theattempts to verify whether the relationship has beentime period being examined.

supergametheories.

The

prediction

affected by the abolition of the Tokusekiho. Gotoand McKenzie [2001] shows empirically how theIt is assumed that firms commit either to a price orretail gasoline price was influent by the change ofa quantity in Bertrand or Cournot competition

the expected future environment firms will face,

before unexpected shocks. In Cournot competition,using recent developments of supergame theories.

when firms commit to quantity, a shift (priceHowever, it is difficult for firms to expect theelasticity of supply is zero in the short-run), an

environment perfectly and it should be natural tounexpected increase (decrease) in demand merely

consider that the volatility of the retail gasoline

causes an increase (decrease) in the current priceprice is influent by the unexpected change of thewith consequential increases (decreases) in profits.

environment. This paper attempts to show how theIn the next period, while the unexpected increase in

future changes and the unexpected shock in the

demand in the previous period does not cause theenvironment contributes to the fluctuation of thetripping of the trigger strategy, the unexpected

retail or wholesale gasoline market in Japan.

decrease in demand in the previous period does
cause the tripping of the trigger strategy so that

In contrast, using detailed firm level data, Sladeprices could be expected to fall. That is ute >0[1987 and 1992] suggests that gas stations incauses pt ^ and pt+1 unchanged, ute <0 causes pt v

2

and pt+1 v, the response in period t is symmetric,

In order to estimate the price equations, it isbut the response in t+1 (and in the subsequent

necessary to calculate the expected values of future

periods

demand and wholesale prices in some way. Here,thetriggerstrategyistripped)isasymmetric.

we follow Borenstein and Shepard’s [1996]
approach of fitting equations for Q and W , andWhat about an unexpected increase (decrease) inthen using the computed predicted values frommarginal costs? In Cournot competition, provided

these equations as estimates of the expected values.

marginal cost does not increase above price, since

The estimated equations are of the following form:

the demand curve does not shift and firms havecommitted to a particular quantity, there is no11

Qit = β i 0 + β i1Qit −1 + β i 2 Pit −1 + ∑ θ ji Stjchange in price. As a result, the trigger strategy isj(2)

Wt = γ 0 + γ 1Wt −1 + γ 2Wt − 2 + error(3)

not tripped. That is, current and future prices do not+ β i 3t + β i 4 t + error2

respond at all to an unexpected change in thecurrent marginal costs!
4.

ESTIMATED MODEL

The model in section 3 indicates that when gas

wherestations are facing a state of mutual dependence,Stj

is a seasonal dummy for the jth month.

and behave cooperatively, the collusive price may

To save space, estimates of equations (2) and (3)resultare no presented.

from

firms

forecasting

their

futureeconomic environment and choosing their behavior
accordingly. To take account of this, the following

5.

DATA

price equation was estimated
The monthly data used in this paper run from
Pit = α i 0 + α i1Qit + α i 2Wt + α i 3UQit + α i 4UWt
+ α i 5 EQit +1 + α i 6 EWt +1 + uit

October 1990 to October 1999. Data on retail(1)gasoline prices at a prefectural level were obtained
from the Monthly Survey of the Market Situation of
Oil Products ( Sekiyu seihin shijo getsuji chousa)
produced by the Japan Energy Economic Researchwhere Pit is the retail price of gasoline for the ith

Institute’s Oil Information Center ( Nihon Enerugi
keizai kenkyusho Sekiyu joho senta). This data isprefecture at time t, Qit is the quantity of gasoline

obtained from surveys of the price of regulargasoline sold at gasoline stations. The surveys are

sold in the ith prefecture at time t, Wt is thecarried out on the tenth day of each month.

national wholesale price of gasoline, E is theData on wholesale gasoline prices were obtained

expectation operator, and uit is a disturbance. The

from the Nikkei NEEDS database using the pricediscussion of several dynamic model in thepaid by traders who purchase gasoline fromprevious section suggests the coefficients in (1)refineries and distribute it to gas stations. Data on

should have the following signs α i1 < 0 , α i 2 > 0 ,gasoline prices at the wholesale level are not

α i 3 > 0 , α i 4 > 0 , α i 5 > 0 , and α i 2 < 0 .

price is treated as being the same across Japan.

available at a prefectural level so the wholesale

Data on retail sales of gasoline at a prefectural level,3

data on a monthly basis severely restricted ourthe price of crude oil, and the number of gasoline-

attempts to investigate the possibility that it was

powered vehicles registered in Japan were also

misspecification of the equation that was causing

obtained from the Nikkei NEEDS database.

the significant diagnostic test results.

Although retail price and sales data is available forall 47 prefectures in Japan, the analysis in this paper

For Tokyo, all the signs of the estimatedis limited to the prefectures of Tokyo and Osaka.

coefficients,

An examination of the retail prices in these twoquantities, are consistent with the predictions of theprefectures suggests that there are some substantial

Rotemberg and Saloner [1986] model presented indifferences in the behavior of retail prices in Tokyosection 3. For all the sample periods, at least one ofand Osaka after mid-1994.

the expected future variables is statistically

excludingthe

expected

futuresignificant. This finding is consistent with game6.

theoretic models that suggest future changes in the

RESULTSeconomic environment will affect current price
Estimates of equation (4) for Tokyo and Osaka aresetting by firms if the firms are engaged inpresented in Tables 1 and 2, respectively. For bothcompetition in a repeated game context.

prefectures, retail price equations are estimatedusing three samples: all the data (1990:11-1999:10);

For Osaka, the signs of the estimated coefficients,

the first half of the data (1990:11-1994:5); and theexcluding the expected future quantities, are also

second half of the data (1994:6-1999:10). The time

consistent with the predictions of the Rotemberg

at which the sample is divided into roughly two

and Saloner [1986] model when the whole sample

halves, 1994:6, is when the abolition of theand the first half of the data are used. Both these

Tokusekiho was formally decided. Estimates using

signs are however reversed for the second half ofordinary least squares and instrumental variables

the data suggesting a structural change around theare presented; the latter takes account of thetime the abolition of the Tokusekiho was decided.

possibility that all the explanatory variables in (4)As with Tokyo, the signs of the estimatedmay be correlated with the equation’s error. The

coefficients for current and expected future

instruments used varied across the time periods andquantities are the opposite of those predicted by theprefectures being considered, but they were drawn

theoretical model. For all the sample periods, atfrom seasonal dummies, time trend (and its square),least one of the expected future variables islagged demand, lagged wholesale price, current andstatistically significant.

lagged rebate, current and lagged price of imported
gasoline, and current and lagged number of7.

ACKNOWLEDGEMENTS

registered gasoline-powered vehicles.
The authors wish to thank Masayoshi Matsui and
There are two reasons for computing the t-statistics

employees of the Fuel, Oil and Fats Newspaper

in all cases using Newey-West’s [1987] correction.

(Nenryo Yushi Shinbun) for providing detailed

First, the diagnostic tests in most cases provide

information on the Japanese oil industry.

evidence of strong serial correlation in the error.
Secondly, computing the fitted values of expected

8.

REFERENCES

future quantities and retail prices causes a generated
Borenstein, S. and A. Shepard, Dynamic pricing inregressor problem [see Pagan, 1986; and McKenzie
and McAleer, 1997] that, in general, induces serial

retail gasoline markets, RAND Journal ofcorrelation and heteroscedasticity in the equation’s

Economics, 27(3), 429-451, 1996.
Chida, R., Seikyu seihin no yunyu jiyuka ni tsuiteerror. Limitations on the availability of relevant4

(On the import liberalization of oil products),

generated regressors: a general approach,Nihon Keizai Research, 31, 276-298, 1996.

Japanese Economic Review, 48(4), 368-389,

Goto, U., Jigen hogo kikan to kigyou kodo-nihon

1997.
Newey, W.K. and K.D. West, A simple, positive

no sekiyu sangyo no keisu (Temporary
protection and firm behavior: the Japanese oil

semi-deficit

industry), International Public Policy Studies,

autocorrelation consistent covariance matrix,

3(2), 241-254, 1999a.

Econometrica, 55, 703-708.

Goto, U., Time series analysis on the Japaneseheteroscedasticity

andOnishi, K., T. Ueki, and S. Mizuguchi, kisei kanwa

gasoline price fluctuation, mimeo, 1999b.

no gasorin kakaku ni ataeru eikyo (The impact

Goto, U. and C. R. McKenzie, Price collusion andof deregulation on gasoline prices). Osaka

deregulation in the Japanese retail gasoline
market,Mathematics

andComputer

Economic Papers, 47(1), 132-133, 1997.
Pagan, A. R., Two stage and related estimators andintheir applications, Review of Economic Studies,

Simulation, forthcoming, 2001.
Green, E.J. and R.H. Porter, Noncooperative53, 517-538, 1986.
2

collusion under imperfect price information,

Pesaran, M. H. and R. J. Smith, A generalized R
criterion for regression models estimated by the

Econometrica, 52(1), 87-100, 1984.
Haltiwinger, J. and J. E. Harrington, The impact of

instrumental variable method, Econometrica,

cyclical demand movements on collusive

62, 705-710, 1994.
Rotemberg, J. and G. Saloner, A supergame-

behavior, RAND Journal of Economics, 22(1),theoretic model with price wars during booms,

89-106, 1991.
McAleer, M. and C.R. McKenzie, Keynesian andnewclassical

modelsofAmerican Economic Review, 76(3), 390-407,

unemployment

1986.
Slade, M., Interfirm rivalry in a repeated game: anrevisisted, CentER for Economic Research

empirical test of tacit collusion, Journal of

Discussion Paper No. 9006, 1990.
McAleer, M. and C.R. McKenzie, Keynesian andnewclassical

modelsofIndustrial Economics, 35(4), 499-516, 1987.
Slade, M., Vancouver’s gasoline-price wars: an

unemployment

empirical

revisisted, Economic Journal, 101, 359-381,

exerciseinuncoveringsupergamestrategies, Review of Economic Studies, 59(2), 27-

1991.
McKenzie, C. R. and M. McAleer, On efficient

276, 1992.

estimation and correct inference in models with5

Table 1: Estimated Retail Price Equations for Tokyo________________________________________________________________
1990:11-1999:10
1990:11-1994:5
1994:6-1999:10
Estimator
OLS-NW IV-NW OLS-NW IV-NW OLS-NW IV-NW________________________________________________________________
Qit

Wt

-0.24

-0.26

-.004

-0.016-0.023(6.02)(7.28)(3.50)(3.68)(3.12)

2.293

6.211

4.434

4.779

1.404

1.50

(5.00)(3.64)(6.24)(6.88)(16.69)(27.73)

e

UQit

0.020
(2.05)UWt

e

Qite +1

1.096

1.429

1.430

-.0.687 -0.583(2.37)(3.51)(3.33)(3.93)(5.56)-0.024-0.405-0.028(5.61)(4.61)(3.82)-1.12-5.095-4.671-4.979(2.66)(2.86)(4.81)(5.41)

s

1.921

1.932

0.969

1.007

1.87

1.97

R2

0.978

0.975

0.886

0.750

0.952

0.951

W et+1

SC
82.90* 71.86* 29.68* 28.33* 53.92* 42.70*
FF
26.73* 54.05* 0.73
16.42
2.38
26.16*
H
0.603
0.045
0.02
0.075
7.13*
0.51
ST
na
5.805
na
1.588
na
1.441
________________________________________________________________
Notes: OLS-NW and IV-NW denote estimation using ordinary least squares (OLS) and instrumental variables (IV), respectively, withthe t-statistics adjusted using the Newey-West (NW) correction. Figures in parentheses are absolute values of the t-statistics. s and R2
denote the standard error of the regression and the coefficient of determination [for models estimated by instrumental variables this is thegeneralized R2

measure proposed by Pesaran and Smith, 1994). SC, FF and H denote tests for 12th order serial correlation, functional

form misspecification and heteroscedasticity, and are distributed as

χ 2 variates with 12, 1 and 1 degrees of freedom under theirrespective null hypotheses. ST is Sargan’s general misspecification test for models estimated by instrumental variables. For these
diagnostic tests, a ‘*’ indicates significance at the 5% level. An entry of na, indicates that the ST are inapplicable for models estimatedby OLS. Estimates of the constant are not presented.

6

Table 2: Estimated Retail Price Equations for Osaka_________________________________________________________________
1990:11-1999:10
1990:11-1994:5
1994:6-1999:10
Estimator
OLS-NW IV-NW OLS-NW IV-NW OLS-NW IV-NW_________________________________________________________________-0.0184

Qit(4.91)
Wt

e

UQit

UWt

e

Qite +1

9.764

4.115

5.572

4.797

1.782

1.848

(2.48)(3.64)(5.96)(8.29)(4.01)(4.00)

0.253

0.276

0.172

0.152

(7.93)(4.38)(3.63)(3.63)

2.100

1.990

1.544

-1.662-1.573(2.27)(2.86)(2.72)(3.77)(4.44)-0.049-0.478-0.019-0.014-0.0745-0.061(2.27)(6.62)(2.93)(3.20)(2.23)(2.02)-8.927-3.058-6.194-5.171(2.17)(2.75)(4.51)(5.54)

s

4.934

4.961

1.296

0.646

5.298

5.282

R2

0.841

0.841

0.826

0.646

0.774

0.771

W et+1

SC
94.92* 94.54* 32.38* 33.56* 53.24* 53.03*
FF
45.63* 42.13* 2.21
5.30*
37.19* 36.91*
H
24.09* 24.70* 0.03
0.814
0.05
0.013
ST
na
2.537
na
13.38
na
22.80
_________________________________________________________________
Notes: As for Table 1.

7