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Measuring the value of plastic andreusable grocery bagsJarod Dunna, Arthur J. Caplanb & Ryan Bosworthb

a SWCA Environmental Consultants, 257 East 200 South, Suite 200,Salt Lake City, UT 84111, USAb Department of Applied Economics, Utah State University, 4835Old Main Hill, Logan, UT 84322-4835, USAPublished online: 02 Jan 2014.

To cite this article: Jarod Dunn, Arthur J. Caplan & Ryan Bosworth (2014) Measuring the value ofplastic and reusable grocery bags, Journal of Environmental Economics and Policy, 3:2, 125-147,DOI: 10.1080/21606544.2013.870052

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Measuring the value of plastic and reusable grocery bags

Jarod Dunnay, Arthur J. Caplanb* and Ryan Bosworthb

aSWCA Environmental Consultants, 257 East 200 South, Suite 200, Salt Lake City, UT 84111,USA; bDepartment of Applied Economics, Utah State University, 4835 Old Main Hill, Logan,

UT 84322-4835, USA

(Received 30 July 2013; accepted 25 November 2013)

Using data from an online survey of grocery store customers in Logan, Utah, weestimate willingness to pay (WTP) for continued use of plastic grocery bags, andwillingness to accept (WTA) for switching to reusable grocery bags. We find evidenceto suggest that, on average, individuals have a greater aversion to plastic-bag taxes thanan affinity for reusable-bag subsidies. All else equal, older and lower-to-middle-incomeindividuals, as well as larger-sized households, are more likely to switch to usingreusable bags exclusively when faced with a tax on plastic bags. Lower-to-middle-income individuals, as well as women in general, are more likely to switch away fromusing plastic bags when provided with a subsidy for reusable bags. Our results helpquantify the extent to which plastic-bag taxation and reusable-bag subsidisation mightinduce shoppers to switch from plastic to reusable bags for their grocery trips.

Keywords: plastic grocery bags; willingness to pay; willingness to accept

JEL codes: Q24, Q51, Q53

1. Introduction

Plastic grocery bags are ubiquitous. According to FMI (2012), Roach (2012), and Reuseit.

com (2012a), anywhere from 500 billion to 1 trillion plastic bags are consumed world-

wide each year, and roughly 1%–3% of these bags end up in the litter stream outside of

landfills.1 In the USA alone, an estimated 100 billion plastic shopping bags are consumed

annually at an estimated cost to retailers of $400 million (The Wall Street Journal,

February 25, 1985; Reuseit.com, 2012a).2 Akullian et al. (2006) estimate the external

costs associated with the production and use of plastic bags, which account for damages

from CO2 emitted during production, as well as litter, landfill, and improper recycling

disposal costs, totaling $0.11 per bag.3

In an effort to reduce these external costs, several cities in the USA, as well as coun-

tries worldwide, have implemented outright moratoriums or per-bag taxes in an effort to

reduce the demand for plastic grocery bags. These taxes and moratoriums reflect the fact

that, by themselves, educational programmes targeting litter and overuse of disposable

containers have been ineffective in inducing adequate community-wide levels of control.4

To our knowledge no study has yet attempted to systematically estimate determinants of

welfare – at the individual or household levels – associated with the use of plastic or reus-

able bags, in particular willingness-to-pay (WTP) for continued plastic-bag use and

*Corresponding author. Email: arthur.caplan@usu.eduyCurrent address: Department of Agricultural and Resource Economics, Colorado State University,Fort Collins, CO 80523-1172.

� 2013 Journal of Environmental Economics and Policy Ltd

Journal of Environmental Economics and Policy, 2014

Vol. 3, No. 2, 125–147, http://dx.doi.org/10.1080/21606544.2013.870052

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willingness-to-accept (WTA) for switching to reusable bags. This stated-preference study

is a first attempt at generating such welfare estimates empirically, estimates that might

serve as quantitative benchmarks against which to compare actual plastic-bag tax and

reusable-bag subsidy rates.5

WTP is perhaps the most commonly derived welfare measure in the economics litera-

ture, both for private and environmental (public) goods. This measure represents the

maximum amount of money an individual would willingly forgo in order to purchase

the good in question, and thus, by direct implication, is based upon the presumption that

the individual does not own a property right to the good (Freeman 2003). WTA, on the

other hand, represents the minimum amount of money an individual would willingly

accept as monetary compensation for giving up the property right to the good in question

(Freeman 2003).

Plastic-bag moratoriums have been most popular in the USA, while taxes have been

implemented more frequently throughout the rest of the world (Westervelt 2012). For

example, in 2007 San Francisco became the first US city to ban the use of plastic bags in

large supermarkets and pharmacies. The California cities of Santa Cruz, Santa Clara, and

Santa Monica have since followed suit with their own bans, as have three counties in

North Carolina (Koch 2010). More recently, Portland (OR) and Seattle (WA) have imple-

mented plastic grocery bag bans in concert with fees of $0.05 per paper bag (Yardley

2011; Slovic 2011).6

Since the 1990s, the governments in Australia, South Africa, Ireland, Canada, New

Zealand, Denmark, and the Philippines have imposed taxes on plastic bags (Cherrier

2006).7 For example, in 2002 Ireland introduced a 15 Euro cent tax per plastic bag, which

resulted in a 90% reduction in use (Convery, McDonnell, and Ferreira 2007). A lower tax

levied in South Africa in 2003 of approximately $0.06 per bag similarly resulted in an

80% reduction (Hasson, Leiman, and Visser 2007).8 In the USA, Washington, D.C. intro-

duced a $0.05 fee per plastic bag in 2009, which resulted in an estimated 87% reduction

in their usage (Craig 2010). Luis and Spinola (2010) report a potential reduction of 64%

in plastic-bag usage as a result of a 2 Euro cent fee imposed by supermarkets in Portugal.

These estimated reductions in plastic-bag usage, while indicative of aggregate

responses to alternative tax rates, leave unanswered two important questions. First, at

which levels (or within which intervals) might the tax/subsidy rates be set in order to

nudge individuals in their private lives toward achieving what are ultimately collective

reduction targets?9 Alternatively stated, should we expect tax rates as low as Washington,

D.C.’s to be a threshold above which the marginal effect on the individual’s bag choice is

negligible? Second, what determines response rates at the individual (or household) level,

not only with respect to a tax on plastic bags, but also with respect to a subsidy for reus-

able bags? Local policy-makers considering the implementation of a tax or subsidy will

find this type of information useful when it comes to publicly promoting the efficacy of

these types of market interventions.

In answer to the first question, we find both parametric and non-parametric evidence

suggesting that, on average, individuals have a greater aversion to plastic-bag taxes than

an affinity for reusable-bag subsidies. Our non-parametric evidence is manifest in Turn-

bull WTP estimates for plastic-bag use that are generally lower than corresponding Turn-

bull WTA estimates for reusable bag use, i.e. on average the tax per plastic bag necessary

to induce a plastic-bag user to switch to using reusable bags is lower (or has a lower

threshold) than the subsidy per reusable bag to induce the same switch. As Carson (2004)

points out, the Turnbull estimator uses individuals’ responses to the dichotomous-choice

WTP (or WTA) survey question to construct an interval estimate of the inherently latent

126 J. Dunn et al.

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WTP (or WTA) implied by each individual’s response. Our parametric evidence – based

on spike-model WTP and WTA estimates – generally concurs with the Turnbull results.

As discussed in greater detail in Section 3, our consideration of solely infra-marginal

changes in a household’s plastic and reusable bag use (e.g. shifts from using solely plastic

bags to using solely reusable bags rather than shifts from using solely plastic bags to using

a combination of plastic and reusable bags) is premised on two assumptions. First, we

have assumed respondents more easily envision their households making a complete

rather than partial switch (i.e. it is easier for respondents to consider a change in price

that drives their demand for plastic bags to zero, as opposed to potentially complicated

‘intermediate tradeoffs’ between price and quantity demanded), thereby enhancing the

accuracy of their corresponding WTP and WTA responses. Second, we have assumed

that this type of ‘complete-shift’ visualisation is consistent with what policy-makers

believe is necessary to achieve community-wide plastic-bag reduction goals.10

In answer to the second question, we find parametric evidence suggesting that a host

of household-level demographic variables can explain the variability in WTP and WTA

across households. As expected, providing reusable bags free-of-charge increases the

probability that certain types of shoppers will switch away from using plastic bags when

they are simultaneously faced with a tax. Certain types of individuals similarly switch

away from using plastic bags when provided with a subsidy for reusable bags. As with a

plastic-bag tax, providing reusable bags free-of-charge increases the probability of shop-

pers switching away from using plastic bags when simultaneously faced with a subsidy.11

The next section develops a theoretical framework within which WTP and WTA for

infra-marginal changes associated with a household’s plastic and reusable bag use (as

mentioned above) can be distinguished and understood in an abstract sense. Section 3

presents our survey methodology and the empirical model used to estimate marginal

effects on WTP and WTA from the data. Section 4 discusses the data obtained from the

survey and presents our empirical results. Section 5 concludes.

2. A simple methodology for estimating WTP and WTA

To begin, WTP is represented in Figure 1 by distance AB on the vertical axis, which in

this case is a small enough amount relative to the per-bag tax rate t > 0 to induce the indi-

vidual to completely switch from using plastic bags (i.e. the individual’s consumption of

plastic bags is driven to zero in response to the imposition of t). To see this, first note that

the horizontal line t ¼ 0 represents the individual’s status quo budget constraint, where no

tax has yet been levied on plastic-bag consumption, and thus the individual effectively con-

sumes the bags for free. The individual’s corresponding indifference curve, I1, is purposely

drawn flat to reflect the relatively minor contributions additional plastic bags make to utility.

This curve becomes horizontal (and thus coincident with the budget line t ¼ 0) at point C,

which in turn corresponds to q0, the individual’s plastic-bag satiation level.

Imposition of the tax rate t > 0 causes the individual’s budget line to rotate downward

(clockwise), and creates a new tangency (with an indifference curve I2) at point A, corre-

sponding to zero plastic-bag consumption. In this instance, WTP to avoid having to pay

the per-bag tax rate of t is represented by distance AB along the vertical axis.

The story is similar for WTA. In Figure 2, WTA is represented by distance AB

on the vertical axis, which in this case is a small enough amount relative to the subsidy

rate s > 0 to induce the individual to switch completely to using reusable bags (i.e. the

individual’s consumption of plastic bags is driven to zero, and thus the consumption of

reusable bags is driven to its satiation level at q0 in response to the provision of s). To see

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this, first note that the line s ¼ 0 represents the individual’s status quo budget constraint,

where no subsidy has yet been provided for reusable bags. The line is negatively sloped,

reflecting the fact that reusable bags are purchased by the individual at a positive (pro-

rated) cost (in terms of an explicit price per bag and/or the (monetised) time it takes the

individual to gather the bags prior to making a shopping trip). The individual’s corre-

sponding indifference curve, I1, is again drawn flat to reflect the relatively minor

Figure 1. WTP for continued use of plastic bags.

Figure 2. WTA for switching to reusable bags.

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contributions additional reusable bags make to utility. The curve also becomes horizontal

(and coincident with the budget line s ¼ 0) at point D, which in turn corresponds to q0,

the individual’s reusable-bag satiation level.

Provision of the subsidy rate s> 0 causes the budget line (drawn horizontal for conve-

nience) to rotate upward (counterclockwise) and creates a new tangency with the indiffer-

ence curve I2 at point C, corresponding to (satiated) q0 reusable bags consumed, i.e. the

point at which the household no longer consumes plastic bags. WTA is correspondingly

represented by distance AB along the vertical axis.

3. Survey methodology and empirical model

A hard copy of the survey, which was made available online to survey participants

through Survey Gizmo (surveygizmo.com) during the months of October and November

2011 is provided in Appendix A. The survey begins by providing participants with a brief

summary of plastic-bag estimates for Logan, Utah, and mentions the option of switching

from plastic to reusable grocery bags (the term ‘reusable bags’ is carefully defined).12

Logan is Cache County’s largest city, located in the northeast corner of Utah (see the red

highlighted areas in Figure 3). In 2009 Logan had a population of 46,000 people residing

in 16,000 households (US Census Bureau 2010).

Next, a routing question is asked regarding the respondent’s prior knowledge of reus-

able bags. Contingent upon the respondent’s answer, the respondent is routed in one of

two directions – those who have previous knowledge of reusable bags and those who do

not. This selection procedure is consistent with what Caplan, Aadland, and Macharia

(2010) have labelled a ‘between-subject survey design’, whereas in our case respondents

are asked either a WTP or WTA question, but not both.

We chose to implement this design for two reasons, both of which address the overrid-

ing concerns of construct and internal validity. First, we believed that asking respondents

to answer separate WTP and WTA questions within the same survey would lead to confu-

sion and thereby compromise the accuracy of their responses. Second, we believed that

Figure 3. Locations of Cache County (left-hand map) and Utah (right-hand map).

Journal of Environmental Economics and Policy 129

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individuals who had at least some experience using reusable bags would more accurately

envision what the subsidy rate would need to be in order to induce a shift to using reus-

able bags exclusively. Similarly, those who solely used plastic bags would more accu-

rately envision the tax rate necessary to induce a shift away from using plastic bags.

Respondents with no prior knowledge of reusable bags are first provided with a ‘cheap

talk’ reminder statement in an attempt to mitigate the incidence of hypothetical bias

(Aadland and Caplan 2006; Caplan, Jackson-Smith, and Marquart-Pyatt 2010; Cummings

and Taylor 1999). The four randomised bid or hypothetical tax values (tj) selected for

individual j’s ensuing WTP question are $0.05, $0.10, $0.25, and $0.35. These values

were chosen to form a rough distribution around Akullian et al.’s (2006) previously men-

tioned external cost estimate of $0.11 per bag, beginning with the level of Washington,

D.C.’s existing tax of $0.05 per bag, which is among the lowest rates currently levied in

the USA. Following Champ et al. (1997) and Berrens et al. (2002), a ‘certainty follow-up

question’ then offers a range from 0% to 100% on how certain the respondent is of the

answer provided to WTP question.

If instead a respondent indicates prior knowledge of reusable grocery bags, s/he is

routed to a separate set of questions, which focus on the respondent’s knowledge and

use of reusable bags. These questions ultimately route the respondent into one of two

groups – those who use reusable bags for each shopping trip and those who do not.

Respondents who are unsure about the extent to which they use reusable bags are routed to

WTP question for continued use of plastic bags, while those who are aware of their reus-

able-bag usage, and who use reusable bags for only some shopping trips, are asked a

dichotomous-choice WTA question prefaced with cheap talk. To be consistent with the

bid-value interval used for WTP question, the bid values for WTA question, sj, are likewise

drawn from the interval ($0.05, $0.10, $0.20, $0.35). The question asks if the randomly

drawn subsidy value is large enough to induce the respondent to use reusable bags for each

grocery trip. A follow-up certainty question is also asked of these respondents.

Respondents who use reusable bags for each grocery trip are instead routed to a quali-

tative question that asks about any known compensation they receive from their grocer as

a result of using reusable bags. These respondents are then routed to a set of demographic

questions – questions each respondent, regardless of how s/he has been routed, is asked in

the final section of the survey.

Before the survey was administered to the public, it went through three rounds of pre-

testing. Pre-testing in the form of cognitive interviews, where various types of individuals

participate in and evaluate the survey instrument, was used to mitigate any confusion

associated with the question format (Beatty and Willis 2007). Between three and five

environmental consultants, academicians, and college students each participated in the

pre-testing of the instrument. Several of these individuals had no prior knowledge of

using reusable bags for grocery shopping, while some identified themselves as current

users of reusable bags for some or all of their shopping trips.

As mentioned above, the survey was administered online through Survey Gizmo. To

recruit participants, 1400 postcards were distributed to grocery shoppers in a variety of

ways (described below). The cards included instructions on how to login to the survey at

surveygizmo.com (see Appendix B). As an incentive to participate in the survey, each

postcard included a unique alphanumeric code for the respondent to type in upon comple-

tion of the survey. Respondents were instructed to visit a separate website on a prear-

ranged date at the conclusion of the survey (7 November 2011) in order to see if their

code number was chosen at random for a $100 gift card to a local merchant (paid for by

the study’s authors).

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Participants were solicited in two different ways. First, 700 of the 1400 postcards were

randomly delivered door-to-door to households located in the two primary zip-code areas

of the city during October 2011. Second, the remaining 700 postcards were handed out to

customers in front of two of Logan’s largest grocery stores (350 postcards each) – Lee’s

Marketplace and Fresh Market – during the weekends of 8 and 22 October 2011. These

two stores were geospatially selected in order to recruit participants from different areas

of the city. Our various sampling frames (door-to-door in the city’s primary zip-code

areas and two of the city’s largest grocery stores) were thus simple random samples,

where each individual in a given sampling frame had an equal chance of receiving an

invitation to participate in the survey.

Approximately 4% of the 700 shoppers who approached in front of the two grocery

stores refused to accept the postcards, indicating that an overwhelming proportion of

those approached had the opportunity to participate in the survey. Overall, 216 surveys

were completed, for a total response rate of roughly 15%.13

For the parametric analysis, an interval regression approach is used to calculate mar-

ginal effects on WTP for continuing to use plastic bags, as well as marginal effects on

WTA for switching to reusable bags (Woolridge 2002).14 The analysis is premised on the

theory that, based on his/her response to a given bid value, a respondent’s latent WTP

falls in one of two regions: (�1, tj] in the event of answering ‘no’ to WTP question and

[tj, 1) in the event of answering ‘yes’. WTP for individual j (in its reduced form, as a

solution to a standard random utility model) is assumed linear in both its deterministic

and random components:

WTPj ¼ X jbþ ej; ð1Þ

where Xj represents a vector of explanatory variables, i.e. individual j’s demographic

characteristics and b is a vector of corresponding (constant) coefficients to be estimated.

An i.i.d. error term, ej, is appended in order to account for the unexplained variation in

the respondent’s estimated WTP.

For estimation purposes, a binary choice variable, accept_WTPj, is defined, which

equals 1 if the respondent accepts tj and zero if not. Thus, accept_WTPj ¼ 1 responses

imply WTPj > tj and accept_WTPj ¼ 0 implies WTPj � tj (Caplan, Jackson-Smith, and

Marquart-Pyatt 2010). Using Equation (1), the probability that respondent j accepts bid tj is

Pj ¼ Pr½accept WTPj ¼ 1� ¼ Pr½WTPj > tj� ¼ Pr½ej > tj � X jb� ¼ FðX jb� tjÞ; ð2Þ

where F(�) is the standard normal cumulative distribution function, with the last equality

following from F(�)’s symmetry. Using (2), the associated loglikelihood function defined

over all individuals j ¼ 1,. . ., N, is

Log L ¼XNj¼1

�accept WTPj

�ln�Pj

��þ �1� accept WTPj

��lnð1� Pj

��� ð3Þ

where, again, Log L is estimated as an interval regression model (Woolridge 2002).

Although the marginal effects obtained from this model provide reliable estimates of

change in the probability that the average household will accept the bid amount (i.e. either

accept_WTPj ¼ 1 or accept_WTAj ¼ 1) due to a 1% change in a given explanatory variable,

a combination of three well-known caveats suggests why mean WTP and WTA estimates

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obtained from this model are often problematic (Azevedo 2009; Haab and McConnell 2002,

1997; Kristr€om 1997). First, the regression model imposes a standard normal distribution on

the predicted WTP and WTA estimates (see Equation (2)), thus allowing for negative pre-

dicted values (which in our case – for plastic and reusable grocery bags – makes little to no

sense). Second, our sample sizes for both WTP and WTA regressions are relatively small,

which in turn hampers hypothesis testing of our WTP and WTA estimates; estimates that

are derived from preference space (Train and Weeks 2006). Third, there is a preponderance

(or spike) of zeros for the accept_WTPj variable (54 of 63 survey participants responded

accept_WTPj ¼ 0), and a spike of 1s for the accept_WTAj variable (83 of 97 survey partici-

pants responded accept_WTAj ¼ 1), thus drawing into question the appropriateness of the

standard probit specification for the interval regression model.

As we will see in Section 4, because of these three problems the randomised bid

values in WTP regressions are all found to be statistically insignificant, while the bid

values in WTA regressions are statistically significant only at the 10% level. Lack of

statistical significance of the bid value obviates estimation of the mean WTP and WTA

parametrically from the standard interval regression models.15 As a result, we instead

calculate (non-parametric, lower-bound) Turnbull and (parametric) spike-model

estimates of both the mean WTP and the mean WTA. Being non-parametric, Turnbull

estimates are resistant to the four problems mentioned above; again, problems that

typically plague mean welfare measures calculated from the interval regression model

(Haab and McConnell 1997, 2002). In contrast, spike-model estimates can suffer from

the first, second, and fourth problems because they are derived parametrically. As its

name suggests though, the spike model is expressly designed to correct for the third

problem (Azevedo 2009; Kristr€om 1997). See Appendix C for both the general form of

the spike model and the specific functional form used in this study.

4. Data, empirical results, and discussion

Definitions and associated descriptive statistics for the variables ultimately used in our

parametric analyses are presented in Table 1. Comparing the statistics in Table 1 (along

with statistics for some of the variables not ultimately included in the econometric analy-

ses) with corresponding US census data helps to identify characteristics of our sample

that both align with and diverge from associated characteristics in Logan’s general popu-

lation. For example, the average household size for respondents included in our sample is

roughly three members.16 In 2010, the average family size in the Logan city was also

roughly three members (US Census Bureau 2010). In our sample, approximately 89% of

the respondents identify themselves as ‘white’, while the US census reports 84% (US

Census Bureau 2010).

The percentage of male respondents in our sample is 29%, while the US census reports

49%. However, a recent survey estimates that, nationwide, women are responsible for

approximately 64% of their households’ shopping trips (Goodman 2008). This suggests

that the lower percentage of males in our survey aligns more closely with what one would

expect based on national data concerning the allocation of grocery shopping responsibilities

within a typical household. With respect to the education level, 93% of our total respond-

ents are high school graduates, compared to the US census information suggesting that 91%

of Logan residents are high school graduates. In our sample, 31% report household incomes

between $25,000 and $75,000 per year. Between the years 2005 and 2009 the median

income for Logan was estimated to be $34,466 (US Census Bureau 2010). Overall, it there-

fore appears that our sample compares quite favourably with US census data.

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Table 1 also reveals that a great majority of respondents who were asked whether they

would continue using plastic grocery bags in the face of a tax indicated that they would

not (accept_WTP ¼ 0.14). Likewise, a great majority of respondents who were asked

whether they would switch to using reusable bags if provided with a subsidy indicated

that they would (accept_WTA ¼ 0.84).17 Interestingly, both groups of respondents are rel-

atively certain of their WTP and WTA responses (certtax ¼ 0.82 and certsub ¼ 0.83,

respectively, where certtax and certsub are defined in Table 1 specifically as the ‘degree

of certainty associated with [an individual’s] answer to WTP and WTA question’).18

Large percentages of respondents also report that they would use reusable bags more

often if they were free (rbfree ¼ 0.81) and believe increased use of reusable bags

decreases the need for larger landfill size (rblandf ¼ 0.90). These descriptive statistics

suggest a strong stated inclination among our sampled households to switch from plastic

to reusable bags for grocery shopping, an inclination that concurs with the results

obtained from our empirical analyses presented below. We say ‘stated inclination’

because rbfree reflects respondents’ attitudes rather than actual behaviour. As Wright and

Klyn (1998) point out, stated intentions are typically unreliable predictors of the future

behaviour.

Table 2 presents our parametric results for the marginal effects associated with WTP,

obtained by estimating Equation (3) using the subsample of respondents who currently do

not use reusable bags.19 The first section of the table reports the marginal effects associ-

ated with a set of explanatory variables taken from Table 1 that explain the variation in

the probability of a typical respondent accepting the (average) bid.20 As indicated, older

and lower-to-middle-income individuals are, all else equal, more likely to switch to

Table 1. Variable definitions and descriptive statistics.

Variable Variable definition Mean (SD)

accept_WTP ¼ 1 if an individual accepts ti, 0 otherwise 0.143 (0.353)accept_WTA ¼ 1 if an individual accepts si, 0 otherwise 0.843 (0.365)Taxbid ti 2 {$0.05, $0.1, $0.2, $0.35} 0.169 (0.119)Subbid si 2 {$0.05, $0.1, $0.2, $0.35} 0.173 (0.105)Pbrecy ¼ 1 if an individual recycles plastic grocery bags, 0

otherwise0.745 (0.437)

Certtax Degree of certainty associated with an answer to a WTPquestion (%)

0.817 (0.181)

Certsub Degree of certainty associated with an answer to a WTAquestion (%)

0.834 (0.196)

Rbfree ¼ 1 if an individual would use reusable bags more often ifthey are free, 0 otherwise

0.806 (0.397)

Rblandf ¼ 1 if an individual believes increased use of reusable bagsdecreases the need for larger landfill size, 0 otherwise

0.903 (0.297)

Sex ¼ 1 if male, 0 if female 0.288 (0.454)Lowinc ¼ 1 if the household income is in the interval $0–$25,000, 0

otherwise0.546 (0.500)

Midinc ¼ 1 if the household income in the interval $25,001–$75,000, 0 otherwise

0.309 (0.464)

Young ¼ 1 if an individual’s age is in the interval 18–32, 0otherwise

0.432 (0.497)

Middle ¼ 1 if an individual’s age is in the interval 33–55, 0otherwise.

0.346 (0.477)

Totnhh Total number of individuals living in the household 3.131 (1.637)

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reusable bags when faced with a tax on plastic bags. As with the lower-to-

middle-income respondents, a possible reason for older individuals being more respon-

sive to a tax is that their incomes are more likely to be fixed, and thus the imposition of a

tax is perceived to have a larger impact on their purchasing power, leading to a reduction

in demand for plastic bags. Larger-sized households are also more likely to switch to

using reusable bags when faced with the tax, perhaps for the same ‘income-effect’ reasons

that lower-to-middle-income and older individuals are likely to switch. As expected, pro-

viding reusable bags free-of-charge also increases the probability that shoppers will

switch away from using plastic bags when faced with a tax.

The second section of Table 2 presents goodness-of-fit measures and summary statis-

tics for the overall model. The X2 statistic is significant at the 1% level of significance,

indicating that the estimated marginal effects are not simultaneously equal to zero. The

model also predicts accept_WTP ¼ 0 responses more accurately than accept_WTP ¼ 1

responses. This reflects the fact that a great majority of respondents rejected their rando-

mised bid offers, thus inducing the interval regression model to overpredict rejected bids.

Table 3 presents mean WTP estimates based on three different categorisations of the

accept_WTPj variable. The first estimate (denoted by WTP1) is based on the dataset as is,

i.e. the dataset in its pristine form. The second and third estimates (WTP2 and WTP3,

respectively) use re-coded data along the lines of Champ et al. (1997) and Berrens et al.

(2002). Following Champ et al. (1997), for WTP2 we have re-coded respondents who

have accepted the randomised bid value (i.e. accept_WTPj ¼ 1), yet have reported a cer-

tainty level less than 50% (i.e. certtaxj < 0.5), to accept_WTPj ¼ 0. For WTP3 we instead

Table 2. Marginal effects for WTP model (dependent variable ¼accept_WTP).

Explanatory variable Marginal effectsa

Taxbid �0.050 (0.101)Rbfree �0.371�� (0.243)Pbrecy �0.001 (0.009)Young �0.006 (0.014)Middle 0.413�� (0.315)Sex 0.005 (0.015)Totnhh �0.013�� (0.026)Lowinc �0.241��� (0.187)Midinc �0.018��(0.033)

Summary statistic Value

N 59c

Loglikelihood �10.150X2(9) 22.68���

Pseudo R2 0.528%Correct (accept_WTP ¼ 0)b 98%Correct (accept_WTP ¼ 1)b 14

aStandard errors are in parentheses.bThe model correctly predicted accept_WTP ¼ 0 (1) responses for pre-dicted values less (greater) than 0.5.cTwo observations from the original 61 were dropped due to missing vari-able values.���Significant at the 1% level.��Significant at the 5% level.�Significant at the 10% level.

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re-code respondents who have rejected the randomised bid value (i.e. accept_WTPj ¼ 0),

yet have reported a certainty level less than 50% (i.e. certtaxj < 0.5), to accept_WTPj ¼1. As a result, we expect to find WTP3 > WTP1 > WTP2, i.e. WTP3 (WTP2) represents

our more liberal (conservative) measure of consumer welfare.

Typically, only recoding akin to WTP2 is undertaken. This is because of a nuance

associated with the extent to which the setting in which WTP question is asked is ‘all-or-

nothing’. In the typical situation, the respondent answers WTP question in a strict all-or-

nothing setting, i.e. a ‘yes’ answer means the respondent obtains the environmental good

in question, while a ‘no’ answer means the good remains unobtainable. In our case, a

‘yes’ answer means the respondent continues using plastic bags, while a ‘no’ means the

respondent switches to using reusable bags. Either way, the respondent continues to go

grocery shopping. Thus, we are compelled to derive conservative as well as liberal WTP

estimates a l�a Champ et al. (1997) and Berrens et al. (2002). With respect to WTP2, we

presume that uncertain respondents will in fact not accept their respective bids and thus

switch to using reusable bags. With respect to WTP3, we presume the opposite, i.e. those

who are less than 50% certain of their ‘no’ responses will in fact accept the bid and thus

continue using plastic bags. We calculate the same liberal and conservative estimates

for WTA.

Two sets of WTP1, WTP2, and WTP3 measures are reported in Table 3. The first set

includes our Turnbull estimates of the mean WTP, which range from approximately

$0.01 to $0.03 per bag.21 Although these estimates are each statistically different from

zero at the 5% level of significance and WTP3 > WTP1 > WTP2, Snedecor and

Cochran’s (1989) two-sample t-tests for paired data indicate that WTP1, WTP2, and

WTP3 are not statistically different from one another. In other words, recoding does not

result in statistically different estimates of WTP1, WTP2, and WTP3. The most likely rea-

son for this result is that the average respondent is roughly 82% certain of his/her

response to WTP question, with a relatively small standard deviation of 18% (Table 1).

Few respondents’ certainty levels therefore have fallen beneath the respective 50%

thresholds necessary for recoding a l�a Champ et al. (1997).

Similar to the Turnbull estimates, our spike-model estimates of WTP1, WTP2, and

WTP3 in Table 3 range from approximately $0.01 to $0.03 per bag. The estimates are each

statistically different from zero at the 10% level of significance, and, again, WTP3 >WTP1 > WTP2. Further, Snedecor and Cochran’s (1989) two-sample t-tests for paired data

indicate that WTP1, WTP2, and WTP3 generated from the spike model are not statistically

different from one another, thus corroborating the Turnbull results. Poe, Giraud, and

Loomis (2005) find evidence that t-tests such as Snedecor and Cochran’s (1989) tend to

produce upwardly biased estimates of the difference between two WTP non-normal distri-

butions relative to methods of convolutions. In our case, because the t-test finds no

evidence of statistical differences between the spike-model WTP1, WTP2, and WTP3

Table 3. Mean WTP estimates.a

Turnbull Spike model

WTP1 0.018�� (0.0069) 0.023� (0.012)WTP2 0.012�� (0.0059) 0.018� (0.009)WTP3 0.028�� (0.0079) 0.025� (0.013)aStandard errors in parentheses, N ¼ 63.��Significant at the 5% level.�Significant at the 10% level.

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distributions, the question of biasedness in the assessment of these differences is averted. In

other words, because we find no evidence of statistical differences across the three spike-

model WTP distributions using the t-test, Poe, Giraud, and Loomis’s (2005) results suggest

that we are assured of finding no statistical evidence of differences across the distributions

using a convolution test.

Table 4 presents our parametric estimates of marginal effects for WTA model. Similar

to the plastic-bag tax, we find that lower-to-middle-income individuals are more likely to

switch from using plastic bags when provided with a subsidy for reusable bags. Unlike with

a plastic-bag tax, we find no statistical evidence suggesting that older individuals and larger-

sized households will switch to reusable bags when provided with a subsidy. However,

women are more likely to respond to a reusable-bag subsidy by making the switch, suggest-

ing that women are more responsive to subsidies than taxes, for reasons we are unsure of.

As with the plastic-bag tax, providing reusable bags free-of-charge increases the probability

that shoppers will switch away from using plastic bags when faced with a subsidy.

Also, as indicated in the second section of Table 4, the X2 statistic is significant at

the 1% level of significance. Unlike WTP model, WTA model predicts accept_WTA ¼ 1

responses more accurately than accept_WTA ¼ 0 responses. This reflects the fact that a

majority of respondents accepted their randomised bid offers for using reusable bags.

Because the number of accept_WTA ¼ 1 responses relative to accept_WTA ¼ 0 is not as

large as the corresponding number of accept_WTP ¼ 0 relative to accept_WTP ¼ 1

responses, WTA model accurately predicts a relatively large percent (60%) of the

accept_WTA ¼ 0 responses.

Table 4. Marginal effects for WTA model (dependent variable ¼accept_WTA).

Explanatory variable Marginal effectsa

Subbid 0.729� (0.327)Rbfree 0.269��� (0.116)Pbrecy 0.070 (0.085)Young �0.131 (0.123)Middle �0.210 (0.159)Sex �0.168�� (0.092)Totnhh 0.017 (0.019)Lowinc 0.134� (0.082)Midinc 0.117� (0.062)

Summary statistic Value

N 90c

Loglikelihood �28.589X2(10) 23.92���

Pseudo R2 0.2950%Correct (accept_WTA ¼ 0)b 60%Correct (accept_WTA ¼ 1)b 88

aStandard errors are in parentheses.bThe model correctly predicted accept_WTA ¼ 0 (1) responses forpredicted values less (greater) than 0.5.cTwelve observations from the original 102 were dropped due to missingvariable values.���Significant at the 1% level.��Significant at the 5% level.�Significant at the 10% level.

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Table 5 presents our Turnbull and spike-model estimates of the mean WTA. The

Turnbull estimates range between $0.08 and $0.09 per reusable bag, while, surprisingly,

the spike-model estimates range between $0.20 and $0.33 per bag. It is difficult to know

why the spike-model and Turnbull estimates diverge so dramatically for WTA. Similar to

WTP spike model, rbfreej ¼ 0 proxies for WTA > 0, since if individual j will not switch

to reusable bags even if they are free (i.e. rbfreej ¼ 0), then his WTA for using reusable

bags can safely be assumed to be greater than zero.22 Thus, even though we are uncertain

as to why the spike-model estimates of the mean WTA are so high, we feel confident that

the model is correctly specified.

Similar to WTP estimates, Table 5 indicates that (1) the Turnbull and spike-model

WTA estimates are each statistically different from zero (in this case at the 1% level of

significance), (2) WTA3 >WTA1 > WTA2, and (3) Snedecor and Cochran’s (1989) two-

sample t-tests for paired data indicate that WTA1, WTA2, and WTA3 are not statistically

different from one another in either model.

5. Conclusions

This study reports results from an online survey of customers at two major grocery stores

located in Logan, Utah, used to estimate (1) the marginal effects on WTP for continued

use of plastic grocery bags, (2) the marginal effects on WTA for switching to reusable

grocery bags, and (3) the mean WTP and WTA. Our results suggest that, on average,

individuals have a greater aversion to plastic-bag taxes than an affinity for reusable-bag

subsidies, i.e. their mean WTP to continue using plastic bags (Table 3) is less than their

mean WTA for switching to reusable bags (Table 5). All else equal, older and lower-to-

middle-income individuals, as well as larger-sized households, are more likely to switch

to reusable bags when faced with a tax on plastic bags (Table 2). Lower-to-middle-

income individuals, as well as women in general, are more likely to switch away from

using plastic bags when provided with a subsidy for reusable bags (Table 4).

These results provide at least initial answers to the two questions originally posed in

Section 1 concerning (i) what might be the threshold tax/subsidy rates that nudge individ-

uals in their private lives toward achieving what are ultimately collective reduction tar-

gets and (2) what determines individual responses to plastic-bag taxes and reusable-bag

subsidies. With respect to question (i), our results suggest that the threshold plastic-bag

tax may be less than the $0.05 rate currently in effect in Washington, D.C., which in turn

suggests that tax rates may not have to be set as high as Washington, D.C.’s to elicit the

desired level of reduction in plastic-bag usage. With respect to question (ii), our results

indicate that certain types of individuals are likely to respond differently to plastic-bag

taxes and reusable-bag subsidies. This type of information is particularly important for

educational campaigns that might accompany the introduction of a new tax or subsidy

programme.

Table 5. Mean WTA estimates.a

Turnbull Spike model

WTA1 0.088��� (0.0034) 0.282��� (0.0874)WTA2 0.084��� (0.0036) 0.197��� (0.0585)WTA3 0.089��� (0.0033) 0.325��� (0.1062)aStandard errors in parentheses, N ¼ 102.���Significant at the 1% level.

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Two limitations of this study are apparent. First, our online survey was self-adminis-

tered and based on a convenience sample frame of shoppers. Although several of our

sample’s mean demographic characteristics compare favourably with US census data,

its relatively low sample size and response rate draw into question its generalisability

beyond the local area in which the survey was conducted. Second, setting the lower

bound on our interval of randomised bids at $0.05 per bag has precluded us from

directly measuring consumer responses to even lower bid levels, e.g. at $0.03 or $0.01

per bag. As a result, we can only conjecture what actual threshold tax and subsidy rates

might be. Overcoming these shortcomings is an obvious starting point for future

research.

Acknowledgements

The authors express their appreciation to an anonymous journal reviewer and their colleagues in theDepartment of Applied Economics, Utah State University, for helpful comments on earlier drafts ofthe paper. Any remaining errors are of course the authors’ responsibility.

Notes

1. These estimates are based on a highly cited but to-date unobtainable 2001 report by the USEnvironmental Protection Agency (EPA).

2. Henceforth, the ‘$’ symbol refers to US dollars.3. To our knowledge, Akullian et al. (2006) provide the only empirical estimate of the external

cost attributable to plastic shopping bags. Reuseit.com (2012b) provides a nice outline of thevarious components of this cost.

4. For example, in Austin (TX) officials recognised that educating residents about the negativeenvironmental consequences associated with using plastic and paper grocery bags would notbe sufficient to curb consumer demand. The officials therefore decided to couple an educationcampaign with a ban on plastic and paper grocery bags and distribution of free reusable bagsin lower-income areas of the city (Lisheron 2012). Similar approaches have been used inTucson (AZ) (Kelly 2013). For a concise summary of specific policies and programmesimplemented across the USA, see NCLS (2013).

5. Because grocery stores in our study area (as with most areas worldwide) provide shopperswith free plastic bags, we are precluded from assessing the shoppers’ revealed preferences forthese bags.

6. Cities are not the only entities implementing plastic bag bans and taxes in the USA. Retailgiants Trader Joe’s and Whole Foods Market have banned the use of plastic bags in their out-lets, while Ikea charges $0.05 per plastic bag (Horovitz 2008). It is important to note that typi-cally not all forms of plastic bags are banned under a plastic-bag ordinance. For example, SanFrancisco’s ordinance does not apply to fresh produce bags, bags handed out at the meatcounter, or bags for prescription medications (Save The Bay 2013).

7. We thank an anonymous referee for pointing out that Australia also has multiple plastic-bagbans in place.

8. Dikgang, Leiman, and Visser (2011) point out that the initial 80% reduction achieved in SouthAfrica dwindled considerably within a year. Dikgang and Visser (2012) note that a similar taxlevied in Botswana had a longer-lasting effect than that experienced in South Africa becauseBotswana’s initial tax was set at a higher rate, and then maintained for a longer period oftime. We thank an anonymous referee for alerting us to these two articles.

9. Subsidisation of the purchase price of reusable grocery bags is common throughout the USA(Ebencamp and Hein 2008); however, statistics on the extent to which subsidisation occurs atcheck-out in the USA (e.g. small subsidies of the order of a few cents per bag) are currentlyunknown.

10. In reality, our notion of a ‘complete shift’ from plastic to reusable grocery bags must of coursebe tempered by the fact that from time to time even the most resourceful individuals forget tobring their reusable bags on shopping trips.

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11. We acknowledge that provision of reusable bags free-of-charge is a counterfactual situationused in this study solely for the purpose of avoiding the introduction of any possible confound-ing effects on the measurement of an individual’s WTA for switching to reusable bags. In real-ity, individuals are typically required to purchase their reusable bags.

12. Links to two Internet sites are also provided regarding (1) Washington, D.C.’s experience withits plastic bag tax and (2) the pros and cons associated with using reusable vs. plastic grocerybags. Respondents voluntarily chose whether to follow one or both of the links.

13. This response rate is roughly half the average rate reported by Cook, Heath, and Thompson(2000) based on their meta-analysis of a wide range of web-based surveys. According toLindhjem and Navrud (2011b), response rates for online, stated preference (SP) surveys tendto be more variable than those for online surveys in general. For instance, the authors cite sev-eral published studies based on web-based SP surveys with response rates as low as 5% and ashigh as 40%. Our response rate is admittedly on the lower end of this interval.Lindhjem and Navrud (2011) also find that stated preferences obtained via an internet-basedsurvey are not significantly different or biased in comparison with face-to-face interviews.Therefore, to the extent that the sample size, survey method, and response rate in generalcorrelate with the generalisability of a given survey’s results, the broader representativenessof our findings should be weighed accordingly. For example, our relatively low response ratemay reflect an oversampling of shoppers who are more interested than average in grocery bagchoices, or who feel more strongly about government or retailer taxes and bans in general.

14. We refer only to WTP in our discussion of the interval regression model for expository conve-nience. The same model is used for calculating the mean WTA, with the subsidy sj dulysubstituted for the tax tj.

15. Because bid values for WTA regressions were found to be weakly significant, we estimatedKrinsky and Robb (1986) mean WTA estimates and found these estimates to be negative andinsignificantly different from zero.

16. Of the 216 completed surveys, 17 included ‘unsure’ responses to WTP and WTA questions.These observations were removed from the sample for the estimation of the dichotomous-choice model (i.e. Equation 3), but included in the sample for the estimation of the ordered-probit model (see note 19 below). An additional 36 surveys were deemed sufficiently incom-plete and also removed from the samples for both the dichotomous-choice and ordered-probitmodels.

17. In cases where a respondent knows, or believes, s/he is already receiving a subsidy from thegrocery store for using reusable bags, the subsidy described in this study can be thought of asbeing in addition to the pre-existing one. Interestingly, although approximately 100% of therespondents in our sample indicate that using reusable bags for grocery shopping is possible,only 62% report having ever used a reusable shopping bag. Only 6% and 29%, respectively,report using reusable bags all the time or half the time, where ‘all’ effectively includes thefew exceptions when the respondent did not have a reusable bag(s) available. We unfortu-nately did not question respondents about whether, and to what extent, they reuse plastic gro-cery bags in the household, e.g. as garbage bin liners.

18. We did not include any controls in our study to detect protest responses among respondentswho were asked whether they would continue using plastic grocery bags in the face of a tax.As pointed out by Jorgensen et al. (1999, 133), ‘in practice there does not appear to be anyagreement over what constitutes a protest response, let alone a comprehensive rationale’.Jorgensen and Syme (1995) echo this sentiment, and Halstead, Luloff, and Stevens (1992)argue that censoring protest bids likely biases aggregate willingness to pay estimates in unpre-dictable ways.

19. For this model, 17 respondents who answered ‘unsure’ to WTP question were removed fromthe sample. However, an ordered-probit model was estimated with these 17 respondentsincluded to compare results, where accept_WTP ¼ 0 indicates a ‘no’ response, accept_WTP¼ 1 indicates an ‘unsure’ response, and accept_WTP ¼ 2 indicates a ‘yes’ response (anordered-probit model was similarly estimated for WTA model). The results from these respec-tive ordered-probit models, which are qualitatively similar to those for WTP and WTA esti-mated via Equation (3), are provided in Appendix D. Stata IC/11.0 for Windows (32 bit) wasused to derive all statistical results reported in this section.

20. Additional versions of WTP model (and of WTA model presented in Table 4) were run withvarious variables listed in Table 1. Results from these model runs are available upon request

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from the authors. The results presented in Table 3 are generated from what the authors believeto be the best-fitting model.

21. These estimates are derived following Kristr€om (1990) and Boman, Bostedt, and Kristr€om(1999). The ‘Turnbull’ command in Stata was used to obtain them. See Haab and McConnell(2002) for further details on the Turnbull estimator.

22. See Appendix C for further discussion on the proxy role of rbfreej ¼ 0.

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Luis, I.P., and H. Spinola. 2010. “The Influence of a Voluntary Fee in the Consumption of PlasticBags on Supermarkets from Madeira Island (Portugal).” Journal of Environmental Planningand Management 53 (7): 883–889.

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Appendix A: The Online Survey Instrument

I. Introduction

Hello and welcome to the survey regarding reusable and plastic bag use in Logan, Utah. This surveyshould take approximately 10–20 minutes to complete, depending upon your awareness level andinterest in this issue. The survey has been designed by a graduate student in the Department ofApplied Economics at Utah State University (USU). The results will be analyzed in fulfillment ofthe student’s Master’s thesis. Since nowhere in the survey is your name, address, phone number, oremail requested, your responses will be confidential. The information will be used solely for aca-demic analysis at USU. We request that you be 18 years or older, and that you are the person inyour household who is either responsible, or shares in the responsibility, for doing the household’sgrocery shopping on a regular basis.

One lucky respondent will win a $100 gift card to Lowe’s Home Improvement Store just bysuccessfully completing the survey and being randomly drawn from the survey’s pool of respond-ents. The winner of the $100 gift card will be drawn on November 7, 2011 (the last question on thissurvey provides instructions on how to enter the drawing and how you can find out if your house-hold is the lucky winner).

II. Background Information

Cache Valley businesses currently use over 100,000 plastic bags per week (personal correspondencewith the Managers of Lee’s Marketplace, Fresh Market, Smith’s, and Wal-Mart during the summerof 2011). According to a recent study published by Convery, McDonnell, and Ferreira (2007), plas-tic bags are a major source of litter in cities across the US and throughout the world. In response tothis problem, there have recently been programs implemented in places such as Washington DCand Ireland that have applied a per-bag fee to try and discourage their use. Other programs havebeen proposed in Oregon and California (Koch 2010). A plastic bag fee is applied at the time gro-ceries are purchased on a per bag basis.

An alternative to charging a fee per bag has been for grocers to promote the increased useof reusable bags by giving customers per-bag credits for using their own reusable grocery bags forgrocery shopping. Reusable bags are defined as bags meant for multiple use that are made of canvas,cloth, or some other washable fabric. The average cost of a reusable shopping bag in Cache Valleyis around $1.25 per bag. A reusable bag credit or subsidy is currently occurring at local grocerssuch as Fresh Market, Lee’s Marketplace, and Smith’s here in Cache Valley.

If you are interested in learning more about existing plastic bag ordinances, here is a link dis-cussing the pros/cons of reusable bag use:

http://plasticvpaper.weebly.com/reusable—pros–cons.htmlHere is a link explaining the Washington DC plastic bag policy:http://abcnews.go.com/Politics/washington-dc-charge-disposable-bag-fee/story?id¼9456761

III. The Survey

We begin the survey by asking you questions regarding your household’s current use of reusable bagsat the grocery store. Again, by ‘reusable bags” we mean only bags that are designed and manufacturedfor multiple reuse, and made of fiber, cloth, or another machine-washable fabric.

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0. Before participating in this survey, had you ever heard of using reusable bags for groceryshopping?

� Yes� No� Unsure

If question number #0 is answered “No” or “Unsure.”The next question asks you about your household’s willingness to switch from using plastic

bags to using reusable grocery bags instead. As you consider your answer to this question, pleasekeep in mind that sometimes what people say their households are willing to do in a hypotheticalsurvey like this one differs from what they actually do when given the opportunity to do it in a realsituation. Therefore, as you read the next question, please imagine your household actually facingthe situation described in the question.

N1. If your grocer begins charging you ti per plastic bag used at the checkout to bag your gro-ceries, would you switch to using reusable bags brought with you from home in future trips to thegrocery store?

� No, my household would pay the ti per plastic bag.� Yes, my household would switch to reusable bags.� Unsure

N2. On a scale from 0% to 100% (with 0% indicating “completely unsure” and 100% indicating“completely sure”) how sure are you of the answer you have provided to the previous question?(Please provide a whole number i.e. 35,50, 75, etc.)

If question #0 is answered “Yes.”Y1. Have you or anyone in your household ever used, or are currently using, reusable shopping

bags for grocery shopping?

� Yes� No� Unsure

If question Y1 is answered “No” or “Unsure” the respondent is routed to question N1.Y2. Approximately how often do does your household use reusable bags for grocery shopping?

� All shopping trips.� More than half of shopping trips.� Less than half of shopping trips.� My household does not use reusable bags.� Unsure

If anything but “All shopping Trips” is answered, continue to question Y3. Otherwise, skip toquestion Y8.

Y3. Do you think using reusable bags helps to reduce the amount of non-reusable bags (plasticor paper) that end up in the Logan/Cache Valley landfill?

� Yes� No� Unsure

Y4. If reusable bags were available free-of-charge from your local grocer or another source intown would your household use them more frequently?

� Yes� No� My household already uses reusable bags for all grocery transactions

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Y5. Does your household currently recycle the plastic bags that are provided by your grocer atthe cash register?

� Yes� No� Unsure� My household does not use any plastic bags provided by the grocer.

Grocery stores such as Lee’s Marketplace and Smith’s offer incentives to get customers to usemore reusable bags. These incentives have traditionally been small amounts (e.g., 5 cents per reus-able bag) subtracted from your grocery bill. Before you answer this question, please think about 1)your household income, 2) your household’s monthly grocery budget, and 3) how many reusablebags your household currently uses at the grocery store on shopping trips.

Y6. If your grocer provided a subsidy of si per reusable bag that you would bring from yourhome would your household switch to using reusable bags for all grocery shopping trips?

� Yes� No� Unsure

Y7. On a scale from 0% to 100% (with 0% indicating “completely unsure” and 100% indicating“completely sure”) how sure are you of the answer you have provided to the previous question?(Please provide a whole number i.e. 25, 50, 75, etc.)

Y8. Local grocery stores such as Lee’s Marketplace and Fresh Market provide their customerssubsidies for using reusable bags in the form of either cash (e.g., a per-bag cash credit on your gro-cery bill) or credits (e.g., points added to a customer loyalty card). Is your household currentlyreceiving a subsidy like these for using reusable bags?

� Yes� No� Unsure

Question Y9 is only asked of those respondents who originally answered “All shopping Trips”to question Y2.

Y9. Do you think using reusable bags helps to reduce the amount of non-reusable bags (plasticor paper) that end up in the Logan/Cache Valley landfill?

� Yes� No� Unsure

Demographic InformationWe conclude this survey with a few questions about you and your household that will aid in the

statistical analysis of the information you and all the other participating households have provided.You are under no obligation to answer a question that you might feel uncomfortable with. Again,all of your responses to the questions on this survey are anonymous and confidential.

1. What is your gender?� Male� Female

2. In what year were you born? ___________________

3. What is the highest level of education you or anyone else in your household has completed?(Please check only one category.)� 0–8 years, no high school diploma or GED� 9–12 years, no high school diploma or GED

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� High school diploma or GED� Some college, no degree yet obtained� Associate’s degree� Bachelor’s degree� Master’s degree� Doctorate or professional degree

4. What is your household’s annual income? (Please check only one category.)� Less than or equal to $25,000 per year.� $25,001–$50,000 per year� $50,001–$75,000 per year� $75,001–$100,000 per year� $100,001–$150,000 per year� Greater than $150,000 per year

5. What is your marital status? (Please check only one category.)� Single� Living as domestic partners� Married� Divorced� Widowed

6. How many people currently live in your household (including children)? _____

7. Of the people currently living in your household, how many are over the age of 18? _____

8. How do you define your ethnicity? (Please check only one category.)� Caucasian/White� Hispanic� Pacific Islander� Native American� African American� Other

This completes the survey. Again, thank you for your participation. If you would like toenter our drawing for the $100 Lowe’s gift card, please enter your personal access code providedon the survey information page that brought you to this website (located on the bottom left ofthe paper). On November 7th, 2011, the randomly drawn winning code will be posted at thisweb address (http://usereuseableandwin.blogspot.com) with further instructions on how toclaim your prize.

Appendix B: Recruitment Postcard

Want to further science and have a chance at winning a $100 gift card to Lowe’s? Please fill out oursurvey regarding plastic and reusable bag use in Logan, Utah. Respondents should be over 18 yearsof age and be responsible/co-responsible for your household’s grocery shopping decisions. Thesurvey data will be used for a Utah State University graduate student’s research thesis. Please take10–15 minutes to complete a web survey at this site: www.surveygizmo.com/xxx/

Thank you!

Appendix C: The spike model

To see how the spike model differs from the standard interval regression model, we return to Equa-tion (2) and denote the probability that respondent j does not accept bid ti as

Pj ¼ Pr½accept WTPj ¼ 0� ¼ Pr½tj � WTPj� ¼ Pr½ej � tj � X jb� ¼ Yðtj � X jbÞ: ð4Þ

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Following Kristr€om (1997), Yð�Þ has the following general form:

Yðtj � X jbÞ ¼0 if tj < 0

p if tj ¼ 0

cðtj � X jbÞ if tj > 0

8<: ð5Þ

where p 2 ð0; 1Þ and cðtj � X jbÞ is a continuous and increasing function such that cð�X jbÞ ¼ pand limti!1cðtj � X jbÞ ¼ 1. Thus, as Kristr€om (1997) points out, there is a jump-discontinuity,i.e. a spike, at tj ¼ 0. In our case, WTPj is assumed to be a distributed logistic for tj > 0, implyinga specific functional form for Equation (5), which we present and discuss further in Section 4.

Derivation of the spike-model’s associated loglikelihood function requires an assessment of twovaluation thresholds. The first threshold is the same as in the standard interval regression, i.e.accept_WTPj ¼ 1 implies WTPj > tj, which, for expository purposes, we now denote as Tj ¼ 1 ifWTPj > tj (0 otherwise). This threshold assesses whether the individual is willing to pay the non-zero tax. The second threshold is defined as Sj ¼ 1 if WTPj > 0 (0 otherwise), i.e. the individual isasked whether willing to pay anything at all to continue using plastic bags. Given these two thresh-olds, the loglikelihood function (3) is conveniently rewritten as

Log L ¼XNj¼1

�SjTjln

�1� cðtj � X jbÞ

�þ Sjð1� TjÞln�cðtj � X jbÞ � cð�X jbÞ

�

þ ð1� SjÞln�cð�X jbÞ

��:

With respect to our spike-model estimates of WTP1, WTP2, and WTP3 in the text, recall that WTPj

is assumed to be a distributed logistic for tj > 0. As a result, the specific functional form used forEquation (5) is

Yðtj � X jbÞ ¼0 if tj < 0

½1þ ea��1if tj ¼ 0

½1þ eða�btiÞ��1if tj > 0

8<: ð5’Þ

where (1) tj ¼ taxbidj, (2) b is the coefficient estimate on taxbidj in the first threshold equation of thespike-model regression, where taxbidj is regressed on Tj, i.e. b is an estimate of the marginal utilityof income, and (3) a is the constant in the second threshold equation, where a is regressed on Sj, i.e.a is interpreted as the marginal utility associated with using no plastic bags (Kristr€om 1997;Azevedo 2009). In our case, rbfreej ¼ 0 proxies for Sj ¼ 1, since if individual j will not switch toreusable bags even if they are free (i.e. rbfreej ¼ 0), then the individual’s WTP for plastic bags cansafely be assumed to be greater than zero (i.e. Sj ¼ 1). Azevedo (2009) shows that the mean WTP isthen derived as ln [1 þ ea]/b.

Note that in Equation (5’) for WTA, tj represents subbidj, b is the coefficient estimate on subbidjin the first threshold equation of the spike-model regression, where subbidj is regressed on Tj, Tj ¼ 1if WTAj > tj (0 otherwise), and a is the constant in the second threshold equation, where a isregressed on Sj, Sj ¼ 1 ifWTAj > 0 (0 otherwise) (Kristr€om 1997; Azevedo 2009).

The ‘Spike’ command in Stata was used to obtain these estimates. The estimated a and b coeffi-cients from these regression models are available upon request from the authors. For these models,we followed Azevedo (2009) by regressing only tj and Sj on Tj. To be directly comparable withmean WTP estimates obtained from the interval regression model represented by Equations (2) and(3), we also ran a ‘reduced’ interval regression model with only tj and Sj regressed on Tj to see if themean WTP estimate obtained from this model (using the Krinsky and Robb (1986) method) differedfrom the Krinsky and Robb (1986) mean WTP estimate obtained from a ‘full’ interval regressionmodel using the same set of explanatory variables as listed in Table 2. The mean WTP estimatesacross these two interval regression models were both quantitatively and qualitatively similar.Thus, our spike-model estimates of the mean WTP are comparable with the estimates we otherwisewould have obtained from the full interval regression model. The Krinsky and Robb (1986) WTPestimate was obtained in Stata using the ‘wtpcikr’ command.

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Appendix D: Ordered-probit-regression results for WTP and WTA models.

Table D1. Ordered-probit results for WTP model.

Explanatory variable Coefficient valuea

Taxbid �1.192 (1.351)Rbfree �0.845�� (0.371)Pbrecy �0.649� (0.359)Young 0.450 (0.566)Middle 0.664 (0.579)Sex 0.437 (0.390)Totnhh 0.057 (0.128)Lowinc �1.411�� (0.555)Midinc �0.668 (0.482)Cut Point 1c �0.833 (0.800)Cut Point 2c 0.253 (0.764)

Summary statistic Valueb

N 76Loglikelihood �48.871X2(9) 26.03���

Pseudo R2 0.210

a,bStandard errors are in parentheses.cEstimated cut points on latent WTP used to differentiate accept_WTP ¼ 0 fromaccept_WTP ¼ 1 (Cut Point 1) and accept_WTP ¼ 1 from accept_WTP¼ 2 (Cut Point 2)when the values of the remaining explanatory variables are evaluated at zero.���Significant at the 1% level.��Significant at the 5% level.�Significant at the 10% level.

Table D2. Ordered-probit results for WTA model.

Explanatory variable Coefficient valuea

Subbid 2.616� (1.484)Rbfree 0.731�� (0.337)Pbrecy 0.410 (0.318)Young �0.358 (0.516)Middle �0.648 (0.517)Sex �0.590� (0.304)Totnhh 0.145 (0.096)Lowinc 0.486 (0.382)Midinc 0.731� (0.412)

Summary statistic Valueb

N 100Loglikelihood �62.424X2(9) 21.27��

Pseudo R2 0.146Cut Point 1c 0.391 (0.681)Cut Point 2c 0.839 (0.684)

a,bStandard errors are in parentheses.cEstimated cut points on latent WTA used to differentiate accept_WTA ¼ 0 from accept_WTA ¼ 1 (Cut Point 1) and accept_WTA ¼ 1 from accept_WTA ¼ 2 (Cut Point 2) whenthe values of the remaining explanatory variables are evaluated at zero.���Significant at the 1% level.��Significant at the 5% level.�Significant at the 10% level.

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