Does a rebound effect exist in solid waste management - Panel

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					      Does a rebound effect exist in solid waste management?
                - Panel data analysis of unit-based pricing -


                                        Takehiro Usui∗†

                          Department of Economics, Soka university

                                         February 2008




                                            Abstract

          Municipalities introduced the pricing-by-the-bag policy expecting the emissions
      reduction effect, substitution effect of recycling, and financial benefits. However,
      several years after the introduction of this policy, some municipalities reported an
      increase in waste emissions. We clarify whether or not the rebound effect is statis-
      tically significant, using panel data with Japanese cities’ waste emission data under
      volume-based pricing. We find that the rebound effect canceled out the reduction
      effect of the pricing-by-the-bag policy approximately 19.8 years after its introduc-
      tion.


      JEL Classification: D12, C13


      Keywords: Pricing by the bag, Waste reduction, Rebound effect, Panel data analysis




∗
    1-236, Tangi-cho Hachioji, Tokyo 192-8577, Japan.
†
    Tel: +81(42)691-4016; E-mail address: usui@soka.ac.jp



                                                 1
1     Introduction
In Japan, the Ministry of Environment (MOE) had encouraged and supported the intro-
duction of the pricing-by-the-bag policy. Municipalities introduced this policy expecting
to achieve the emission reduction effect, the substitution effect of recycling, and financial
benefits. However, several years after the introduction of this policy, some municipalities
reported an increase in waste emissions, compared to the first year of introducing it. This
phenomenon is referred to as the “rebound effect.”
    The rebound effect is considered to comprise certain composite effects, namely, the
over-compression of the garbage bag when people dispose waste and the announcement
effect that arises when the city administration advertises the significant reduction in waste
emission that occurs in the first year since the policy’s introduction. However, this effect
was considered to be decreasing every year. Moreover, previous works have not clarified
this tentative theory. Since these works employed cross-sectional data, it was difficult to
detect the rebound effect. On the other hand, the rebound effect of pricing is relative to
the time series effect, however, the application of only a time-series analysis may not be
useful for detecting the rebound effect because of the differences in the waste policies of
various cities.
    The use of panel data analysis will be appropriate to detect the rebound effect because
this estimation method combines both the cross-sectional and time-series analyses. Lin-
derhof et al. (2001) employed the panel data analysis. However, they have not clarified
the number of years that have passed since the introduction of the pricing policy.
    We assume that the rebound effect of the pricing-by-the-bag policy involves the follow-
ing: (1) The announcement effect, which is believed to be the result of the first impression
made by intensive advertisement and persuasion by public bureaucrats; and (2) Seattle
stomping, a well-known phenomenon wherein people over-pack waste in the garbage bag
by stomping, thereby increasing the weight per bag (Fullerton and Kinnaman, 1995).
These concepts are illustrated in Figure 1. If the trend of waste generation is increasing,
the decreasing effect of waste generation owing to the pricing-by-the-bag policy exhibits
a downward shift in the upward-sloping curve, from left to right. If a rebound effect is
observed, it could be represented by a large slope drawn as a continuous line or, as in



                                            2
the alternative case the pricing-by-the-bag policy is not introduced, as a pathway on the
dashed line. Finally, the slope of the continuous line meets the pathway when the pricing
policy is not introduced, which implies that the rebound effect will overcome the effect of
waste reduction.
        It is difficult to detect the rebound effect because of the need to set the control variables
which means other relevant factors being equal; otherwise, it would merely identify the
increasing trend of waste generation. Econometrically, almost all previous works use
cross-sectional data, which is made available at certain intervals; however, there is no
dynamic information on the amount of time taken by the municipality to introduce the
pricing-by-the-bag policy.
        Then, we investigate whether or not the rebound effect is statistically significant, using
Japanese cities’ waste emission data obtained through a panel data analysis under volume-
based pricing. It is also useful to clarify the problem faced in designing the unit-based
pricing program.
        The paper is organized as follows. The next section provides information on the
relevant literature. Section 3 describes the econometric model employed and the type
of data used. Section 4 presents a detailed report of the model selection procedure in
the panel data analysis and the estimation results, and the final section contains the
concluding remarks.


2         The relevant literature
There is a considerable amount of empirical literature on waste reduction; notably, there
has been an increase in that on the practice of separating recyclables from waste, which
has provided an incentive to unit-based pricing (Hong and Adams, 1993; Saltzman et al.,
1993; Reschovsky and Stone, 1994; Callan and Thomas, 1997; Nestor and Podolsky, 1998;
Hong and Adams, 1999; Sterner and Bartelings, 1999; Kinnaman and Fullerton, 2000;
Jenkins et al., 2003; Callan and Thomas, 2006; Usui, 2008)1 . For example, Reschovsky
and Stone (1994) examined the recycling probabilities of households using a sample of
micro-data for recyclable materials. Kinnaman and Fullerton (2000) estimated the de-

    1
        Miranda et al. (1996) provide a survey of the unit-based pricing literature.



                                                       3
mand equations for solid waste and recycling in order to make the unit-price and curbside
recycling endogenous. Jenkins et al. (2003) investigated the recycling behavior of house-
holds using an ordered probit model with aggregated data on recyclable material.
      There are few works that have examined the effect of the time that has elapsed since
the introduction of the unit-price. Studies in energy economics have recently discussed
the idea of a “rebound effect” that is “usually assumed to have increased the search
for new energy-saving technologies where eventual gains in energy efficiencies will reduce
the real per unit price of energy services, and hence, the consumption of energy will
rise and partially offset the initial reduction in the usage of energy sources.”2 Bentzen
(2004), Hertwich (2005), and Mizobuchi (2007) detected and discussed this effect. The
rebound effect of the pricing-by-the-bag policy is not considered to fall under the field
of energy economics in terms of the change in energy prices owing to the improvement
in efficiency. Though it is not equivalent and directly comparison with energy situation,
gradually decreasing reduction effect of this pricing policy owing to the citizens’ growing
awareness of waste reduction technology like the over-compression of the bag to save using
the pricing bag.
      Only one work by Linderhof et al. (2001) applied the panel data analysis for a dy-
namic analysis. They clarified the short- and long-term price elasticities of household
compostable waste service demand. The effect of the long-term price elasticity was found
to be 30% more elastic than its short-term counterpart; moreover, they concluded that
the long-term effect of weight-based pricing in compostable waste would be sustainable
in the future. They explain that the introduction of weight-based pricing and the exten-
sive public debate that preceded it temporarily boosted people’s environmental awareness.
However, this effect was observed under the condition of weight-based pricing, which is not
the general method followed in the pricing-by-the-bag policy. It constitutes weight-based
pricing and not volume-based pricing and does not inform people regarding the disincen-
tives of stomping and compressing the bag in order to accommodate additional waste in
the bag. The same weight is considered regardless of whether or not people compress the
bag. Fullerton and Kinnaman (1996) reported the comparison between volume-based and
weight-based pricing methods. Further, they noted that the price elasticity of weight-
  2
      Referenced from Bentzen (2004) pp.123.



                                               4
based pricing is more inelastic than volume-based pricing, because volume-based pricing
encourages the compression and stomping of the bag. It is likely that the possibility of
stomping and packing greater volumes of waste than the capacity of the bag serves as a
disincentive to people.
    In the next section, we will explain the estimation method for the detection of the
rebound effect in the pricing-by-the-bag method.


3     Econometric method
3.1    Panel data analysis

A panel data analysis is superior to that using cross-sectional or time-series data. This
is because with cross-sectional data, it is not possible to determine when the policy was
introduced, whereas with time-series data, it is not possible to ascertain the difference in
effect of the policy across a number of cities. The panel data analysis has considerable
advantages over the cross-sectional and time series data analysis; it would be better to
test the method of model selection for tournaments among the following three models:
pooled OLS, the fixed effect model, and the random effect model. The selection of an
incorrect model would result in the estimated coefficient not being consistent. Therefore,
we introduce the F test, Breusch-Pagan test (BP test), and the Hausman test for model
selection. 1) To choose between the pooling OLS and the fixed effect model, we apply
the F test in order to determine whether or not the constant term of each observation is
same in the equation. In this case, H0 implies all αi = 0, i = 1, · · · , N where i is sample
number, αi is time-constant unobserved effect, and Ha implies all αi ̸= 0; moreover, we
employ the F test statistics. 2) To choose between the pooling OLS and the random effect
model, we apply the BP test to determine whether or not the variance of the constant term
is significantly different from zero. In this case, H0 implies Var(αi ) = 0 and Ha implies
Var(αi ) ̸= 0; moreover, we employ the χ2 test statistics. 3) To choose between the
                                        (1)

fixed effect model and the random effect model, we apply the Hausman test to determine
whether or not the random effect estimation method is biased. In this case, H0 implies
that the random effect is not correlated with the explanatory variables, and Ha implies
that the random effect is correlated with them. We choose the fixed effect model, if H0



                                             5
is rejected by the χ2 statistic, where k represents the number of variables except for the
                    (k)

time dummies and the constant term.
       This is demonstrated through the regression model of a panel data analysis. First,
to elaborate on the variables, we divide them into two parts: the first part comprises
policy variables such as the price of the bag in the various cities and the number of years
that elapsed since the introduction of the unit price, and the second part comprises the
socioeconomic variables. An equation is as follows:



        Wasteit = β1 P riceit + β2 Y earselapsedit × P riceit + β3 Y earselapsed2 × P riceit
                                                                                it

                                                                                    2
                   +β4 P opdit + β5 P opd2 + β6 Incomeit + β7 F amilyit + β8 F amilyit
                                          it
                                   ∑
                   +β9 Ageit 65 +      γt Yeart + αi + uit                                           (1)
                                     t

                                                                                  3
       Price is defined as the price per bag or tag (40-50 liter bag/yen).
       We choose the following independent variables: Yearselapsed, representing the number
of years that have passed since the introduction of the unit-price, which is important to
detect the rebound effect because it is believed to be dependent on the years that have
elapsed since the introduction of the pricing; Popd and Popd2 , representing population
density (1000 person/km2 ) and its squared value which may affect to illegally dispose
waste, because the rural (low-density) areas as well as the urban (high-density) is thought
of as dumping easily; Income, representing taxable gain per capita (million yen); Family
and Family2 , representing the average household size and its squared value which may
take positive. This may also include mixed effects. The first is the effect of decreasing
consumption. A large household size will increase household consumption but decrease per
capita consumption. The second is the effect of shared housework which occurs for large
households. We also want to see the turning point.; Age 65, representing the percentage
   3
     However, this price is perceived as being endogenous. Previous works such as Kinnaman and Fullerton
(2000) and Callan and Thomas (2006) have tested its endogeneity. This paper also tests the endogeneity
of this variable. The instrumental variable is Pop, which represents the population of the city; this
variable may affect the timing of the introduction of the policy and the magnitude of its price. We now
proceed to testing the instrumental panel data and the normal panel data models. The endogeneity
test should be conducted by applying the well-known Hausman’s endogeneity test. We apply this test
(Hausman, 1978) to each model, namely, the exogenous pooled OLS, fixed effect, and the random effect
models. Since all the chi-squared statistics are not significant, we do not reject the null hypothesis and
refrain from using the IV panel estimator of our model



                                                   6
of people aged over 65 which may be due to differences in consumption habits within this
age group, and; Yeart , representing the time dummy variable, which is 1 if the current
sample is in the reference year (t), and 0 otherwise.


3.2       Data

Solid waste comprises waste generated in households and business establishments4 . Al-
though they should typically be examined separately, in certain municipalities, they are
not always segregated from the other waste. There is an advantage to using joint data on
both solid and other wastes in terms of the fact that the waste pricing may lead citizens
to illegally transfer their household waste to business waste dumps. Therefore, combining
the waste data will help in maintaining consistency. This study also defines waste as the
sum of the amount of combustible waste, noncombustible waste, recyclable waste, and
recyclables collected by citizens. In addition, the municipal waste data has been derived
from the Japan Waste Management Association (1995-2002).5
       Panel data pertaining to the waste emissions of each municipality spanning an eight-
year period from the 1995 to 2002 fiscal years were provided by the Japan Waste Man-
agement Association (1995-2002). Although waste pricing data is not published by the
MOE, Yamaya (2006) gathered waste pricing data and the years that have elapsed since
the introduction of the pricing for all Japanese cities using questionnaires administered
through mail and telephone. The data collected pertained to the price of garbage bag for
40-50 liter (approximately 12 gallons) of waste per garbage bag or the corresponding tag
used to levy a fee on the waste generated in 712 cities and 23 wards of Tokyo in February
2005. Figure 2 presents the histogram of this pricing data. Histogram shows that mode
is 40 yen per bag. Note that waste pricing data is priced only for combustible waste;
further, the data does not include pricing for recyclable waste.
       Other socioeconomic data with respect to all municipalities was obtained from the
Asahi (2003). This data includes information on the taxable gain per capita, the average
household size, number of residents over the age of 65, and population density.
   4
     In Japan, municipalities collect solid waste called as general waste, which basically comprises both
household solid waste and waste generated from business activities.
   5
     The amount of waste does not include the following: (1) “the amount of self disposal” and (2) “the
amount of waste carried into municipal facilities.”



                                                   7
        Finally, we adopt the data for the eight-year period on 665 cities of the 712 cities, taking
into consideration the municipal mergers during this period and making the relevant
exclusions. The descriptive statistics and the definitions of the variables are presented in
Table 1.


4         Estimation result
We discuss the estimation results; however, we consider only the fixed effect estimates,
since we apply the model selection method discussed in subsection 3.16 .
        We show the Table of the estimation results (Table 2). Model 1, 2, 3, and 4 are the
estimated results of fixed effect model. Model 1 and 2 exclude Yearselapsed×Price and
its squared. Model 3 and 4 include them. Time dummy are included in model 1 and 3.
The number of years that elapsed since the introduction of the unit price are effective in
terms of model fitting because AIC in the model 1 and 3 are smaller than AIC in the
model 2 and 4. The coefficient of the Price whose models’ Yearselapsed×Price and its
squared are excluded is over estimated, but the difference isn’t so large. Also including
the time dummy, Year 1996 - Year 2002 is made improvement of the model fitting, since
controlling for the unobservable effects. Eventually, Model 3 is most desirable one. We
explain only Model 3 in next subsection.


4.1         Pricing by bag

The pricing-by-the-bag method comprises three terms, β1 , β2 , and β3 . The marginal effect
of the price depends on Yearselapsed and Yearselapsed2 . Prior to calculating the marginal
effect and its elasticity, we test the significance of the joint restriction. We are primarily
interested in the rebound effect. To test this effect, we employ the F test on the joint
restrictions of the coefficients as follows:

                      H0 : (β1 , β2 , β3 ) = (0, 0, 0),       H1 : (β1 , β2 , β3 ) ̸= (0, 0, 0)    (2)

    6
    First, we apply the F test of the pooled OLS model vs. the fixed effect model. As a result, we reject
the null hypothesis and select the fixed effect model. Next, we apply the BP test of pooled OLS vs.
the random effect. Based on the test results, we reject the null hypothesis and select the random effect
model. Finally, we employ the Hausman test of fixed effect vs. random effect. The result shows that we
should reject the null hypothesis and employ the fixed effect model.



                                                          8
If the null hypothesis is rejected and the sign of the β3 which is the coefficient of the
squared Yearselapsed, is statistically significant and the coefficient of the quadratic term
is positive whose the shape of the quadratic curve is convex in the downward direction,
the existence of the rebound effect is confirmed7 : F (3, 4626) = 9.58∗∗∗ . Then, the null
hypothesis is rejected, and the β3 is highly significant and positive. Thus, we find that
the rebound effect exists. If we differentiate equation (1) by P rice of equation (1) and
set it as zero, then


               ∂Waste
                       = −1.73 − 0.00447Y earselapsed + 0.0067Y earselapsed2                       (3)
               ∂P rice
       We solve the quadratic equation relative to Yearselapsed, Yearselapsed= 19.8 which
passed the F test. This implies that approximately 19.8 years after the introduction of
the pricing-by-the-bag policy, the rebound effect cancels out the reduction effect arising
from pricing by the bag. The first and second effects have been discussed previously; they
cancel out the reduction effect of the pricing; however, the third effect is considered to
enhance the waste reduction effect with each passing year. Summing up these effects, the
net effect will be positive.
       We interpolate the estimated value of β1 , β2 and β3 from equation (1) and derive the
shape of the rebound effect, as illustrated in Figure 3; the value of this effect is predicted
to be the same as the sample mean of the Price controlled by other variables.
       Then, we value Yearselapsed at the sample mean of the introduction of the unit-price
and derive the price elasticity of the waste emission, as follows:
                         ∂Waste
                                   = −1.73 − 0.0447 · (9.58) + 0.0067 · (9.58)2
                          ∂P rice
                                   = −0.939
                                              (       )
                  ∂Waste P rice                 35.75
                         ·         = −0.939 ·
                  ∂P rice Waste                 853.0
                            ϵprice = −0.039

where Price and Waste is sample mean of the unit-price cities. The estimated Price
elasticity, evaluated at the point of mean is −0.039. If we estimate the elasticity from the
                                                      (                 ) (         )
   7                                                     RSSR − RSSUR        RSSUR
    That is, a joint F test of the three restricts, F0 =                 /            , where RSSR is
                                                                p             n−k
the restricted sum of the squared residual; RSSUR is the unrestricted sum of the squared residual; p is
the number of restrictions; and n − k denotes the degrees of freedom.



                                                  9
Model 1 which is excluded the variable of Yearselapsed, Price elasticity is −0, 076 which
is over estimated. Our estimated value of the magnitude of price elasticity is smaller than
−0.226 in the case of volume-based pricing (Fullerton and Kinnaman, 1996), however this
one is included of substitution effect of recycling. The value of −0.25 in that of short-run
elasticity (Linderhof et al., 2001) is weight-based pricing system. Consequently, the effect
is not included “Seattle stomping”.
   Eventually, our estimation result is not so small. If their estimation considered the
Yearselapsed, their elasticities may be partially reduced due to the rebound effect.


4.2    Socio-economic variables

The values of population density, Popd and Popd2 , are determined depending on whether
or not the community tends to illegally dispose waste, because the rural (low-density)
areas as well as the urban (high-density) areas tend to dump easily. Although the t
test does not produce significant values for these variables, the joint F test is significant
and rejects the hypothesis wherein both coefficients are zero. We calculate the turning
                         ∂Waste
point using the variable           = −36.21 − 3.52P opd = 0, P opd = −10.29. It appears
                          ∂P opd
that the greater the increase in the population density, the more is the decrease in waste
emission, and there is no limit to this trend. Although this contrasts with the suggestions
of Fullerton and Kinnaman (1996) and Callan and Thomas (2006), it should be noted
that it is not easy to uncover illegal dumping activities in rural areas as compared to the
case in urban areas.
   The taxable gain per capita, Income, is a proxy variable for average per capita income
and represents the opportunity cost of time. The coefficient is significant and positive for
the fixed effect model. This income elasticity of waste demand is 0.29, which is evaluated
at the sample mean of waste (962.1) and income (1.37). Other works have estimated
the income elasticity, for example, at 0.26 (Kinnaman and Fullerton, 2000); however, the
elasticity in these cases captures the joint estimation of recycling.
   The average household sizes in each municipality, Family and Family2 are both highly
significant. Differenced by Family, we derive the turning value as 2.59, which is a concave
functional form. The greater the increase in the household size until 2.59, the greater
will be the waste generation; however, beyond 2.59, the waste generation will decrease.


                                             10
This result is different from that presented by Callan and Thomas (2006). In terms of the
lifestyle, collective consumption affects the waste reduction, for example, each household
subscribes to only one newspaper, whereas it is likely that a single-person household does
not subscribe to even a single a newspaper.
    The percentage of people aged over 65, Age 65, is significant and negative. A 1% point
increase of Age 65 reduces waste generation by 11.8 g per person per day. In the study
conducted by Kinnaman and Fullerton (2000), it was 24.9 g (this has been converted from
pounds per year to grams per day). Apparently, this results from the fact that elderly
people appear to have considerable time and can therefore reduce waste generation.


5     Conclusion
We apply the test of model fit among the three panel data models, based on which the
fixed effect model is selected. The estimation result reveals that the coefficient of price is
statistically significant and its marginal effect on the price is dependent on Yearselapsed
and Yearselapsed2 ; further, the value of the elasticity is −0.039 at the sample mean of
Yearselapsed. This magnitude is smaller than −0.226 of volume-based pricing (Fullerton
and Kinnaman, 1996) and −0.25 of short-run elasticity (Linderhof et al., 2001). We also
test the rebound effect and find that it does exist; moreover, we find that the shape of the
function is quadratic, and therefore, the greater the number of years that have elapsed,
the larger is the rebound effect.
    Our study is, however, not without some limitations. We were unable to determine
the effect relative to the recycling of waste. It is important to ascertain this effect and
to consider segregating recyclables and non-recyclables by using a multi-equation model
approach and applying a three-stage least squares estimation in the framework of a panel
data analysis.


References
 [1] Asahi Shimbun, 2003. Minryoku 2002 CD-ROM. (In Japanese).




                                           11
 [2] Bentzen, J., 2004. Estimating the Rebound Effect in US Manufacturing Energy Con-
    sumption. Energy Economics, 26, 123-134.

 [3] Callan, S.J., Thomas, J.M., 1997. The Impact of State and Local Policies on the
    Recycling Effort. Eastern Economic Journal, 23 (4), 411-423.

 [4] Callan, S.J., Thomas, J.M., 2006. Analyzing Demand for Disposal and Recycling
    Services: A Systems Approach. Eastern Economic Journal, 32 (2), 221-240.

 [5] Fullerton, D., Kinnaman, T.C., 1996. Household Responses to Pricing Garbage by
    the Bag. American Economic Review, 86, 971-984.

 [6] Hertwich, E.G., 2005. Consumption and the Rebound Effect: An Industrial Ecology
    Perspective. Journal of Industrial Ecology, 9 (1-2), 85-98.

 [7] Hong, S., Adams, R.M., 1993. An Economic Analysis of Household Recycling of Solid
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 [8] Hong, S., Adams, R.M., 1999. Household Responses to Price Incentives for Recycling:
    Some Further Evidence. Land Economics, 75 (4), 505-514.

 [9] Japan Waste Management Association, 1995-2002. Haikibutsu syori jigyo jittai chosa
    toukei siryou (general waste). Results for 1995-2002. (In Japanese).

[10] Jenkins, R.R., Martinez, S.A., Palmer, K., Podolsky, M.J., 2003. The Determinants of
    Household Recycling: A Material-Specific Analysis of Recycling Program Features
    and Unit Pricing. Journal of Environmental Economics and Management, 45 (2),
    294-319.

[11] Hausman, J. A., 1978. Specification Tests in Econometrics. Econometrica, 46 (6),
    1251-1271.

[12] Kinnaman, T.C., Fullerton, D., 2000. Garbage and Recycling with Endogenous Local
    Policy. Journal of Urban Economics, 48 (3), 419-442.




                                           12
[13] Linderhof, V., Kooreman, P., Allers, M., Wiersma, D., 2001. Weight-based Pricing
    in the Collection of Household Waste: The Oostzaan Case. Resource and Energy
    Economics, 23, 359-371.

[14] Miranda, M.L., Bauer, S.D., Aldy, J.E., 1996. Unit Pricing Programs for Residential
    Municipal Solid Waste: An Assessment of the Literature. U.S. EPA.

[15] Mizobuchi, K., 2007, Estimation of the Rebound Effects caused by an Improvement in
    Energy Efficiency: Japanese Household Consumption and Emission, Environmental
    Science, 20 (1), 61-70

[16] Nestor, D.V., Podolsky, M.J., 1998. Assessing Incentive Based Environmental Policies
    for Reducing Household Waste Disposal. Contemporary Economic Policy, 16 (4), 401-
    411.

[17] Reschovsky, J.D., Stone, S.E., 1994. Market Incentives to Encourage Household
    Waste Recycling: Paying for What You Throw Away. Journal of Policy Analysis
    and Management, 13 (1), 120-139.

[18] Saltzman, C., Duggal, V.G., Williams, M.L., 1993. Income and the Recycling Effort:
    A Maximization Problem. Energy Economics, 15 (1), 33-38.

[19] Sterner, T., Bartelings, H., 1999. Household Waste Management in a Swedish Munic-
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[20] Usui, T., 2008. Estimating Effect of Unit-Based Pricing under the Japanese Recycling
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[21] Yamaya, S., 2006. Katei-gomi Yuryoka no Genjo to Kadai, Life and Environment,
    51(1), 13-20. (In Japanese)




                                           13
waste emission




                                               Rebound effect

          Waste Reduction
         by pricing the bag




                                                          t

                    Figure 1: Rebound effect
      .025
      .02
       .015
 Density
      .01
      .005
      0




              0          50              100              150
                               PRICE




                  Figure 2: Histogram of price




                              14
                                           Table 1: Descriptive statistics
        Variable        Mean       S.D.     Definition                                                       N =
        Waste            962.1     202.6    Volume of solid waste collection (in gram per capita per day)   5314
        Waste            853.0     187.5    Volume of solid waste collection (in gram per capita per day)   823a)
        Price            35.75     16.42    Price per bag or tag (yen/40-50 liter bag)                       824
        Yearselapsed     9.580     10.31    Number of years since the introduction of the unit price         824
        Popd             1.704     2.314    Population density (1000 person /km2 )                          5313
        Income           1.370     0.304    Taxable gain per capita(million yen)                            5320
        Family           2.860     0.343    Average household size (number per household)                   5313
        Age 65           0.171     0.171    Percentage of people aged over 65 (% over 65 years of age)      5320


a) Number of observations with introducing pricing by bag.




                                            Table 2: Estimation results
                                                     Model 1     Model 2    Model 3      Model 4
                          Price                         -1.81       -1.75       -1.73       -1.71
                                                        (0.1)       (0.1)       (0.1)       (0.1)
                          Yearselapsed×Price                                 -0.0447      -0.0122
                                                                             (0.046)     (0.0464)
                          Yearselapsed2 ×Price                                0.0067      0.0072
                                                                             (0.002)      (0.002)
                          Popd                         -36.59      63.62      -36.21       63.08
                                                       (39.7)      (38.6)      (39.7)      (38.6)
                          Popd2                         -1.82       -5.34       -1.76       -5.21
                                                        (2.9)       (3.0)       (2.9)       (3.0)
                          Income                      217.49       75.83      206.12       74.08
                                                       (29.6)      (17.3)      (29.9)      (17.3)
                          Family                      712.32      541.14      685.84      522.57
                                                      (106.9)    (104.3)     (107.1)      (104.1)
                          Family2                     -137.14    -147.66     -132.41     -142.25
                                                       (16.6)      (16.5)      (16.6)      (16.5)
                          Age 65                    -1,195.78     914.16    -1,183.96     887.08
                                                      (270.9)      (184)     (270.5)      (183.7)
                          Constant                     -21.75     324.14       24.47      333.03
                                                      (217.4)    (196.8)     (217.7)      (196.3)
                          Observations                  5,307      5,307       5,307       5,307
                          Year controls?                 Yes          No           Yes        No
                          Adjusted   R2                 0.247      0.222       0.250       0.226
                          AIC                        59242.2     59399.3     59227.1     59375.9
                          Note : Standard errors in parentheses.




                                                            15
                             16
     Figure 3: Prediction of the rebound effect
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