Modeling Consumer Bidding Behavior on Food Items

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Modeling Consumer Bidding Behavior on Food Items: Application of a Two-Stage Sequential BDM Field Experiment Miguel Henry-Osorio

1,*

Vicki McCracken

2,†

Levan Elbakidze

3,Ŧ

1

Dept. of Economics, University of Oklahoma, Norman, OK, USA School of Economic Sciences, Washington State University, Pullman, WA, USA 3 Dept. of Agricultural Economics and Rural Sociology, University of Idaho, Moscow, ID, USA 2

Received XXXX, revised version received XXXX, accepted XXXX

Abstract A two-stage sequential experiment was conducted in a retail grocery setting to elicit willingness to pay for four food products. In this article, we examine how bidding behavior over choices for food items, using the demand-revealing BDM experimental auction mechanism, is influenced by bidding on a single item vs. bidding for multiple items simultaneously. In the first bidding round participants bid on one of the four products, while in the second round participants bid simultaneously for the other three products. Econometric analyses are performed using single-equation regression models (Powell's SCLS, OLS, Tobit I and Tobit III) and the SUR system approach. Results suggest that bids are sensitive to the context of bidding. Compensation has little impact on individual's bidding decision. However, there is some evidence that the uncertainty about which product will be binding in the second round, or the round order, can have an effect on participants’ bidding decisions.

Keywords: Choices, experimental auction, valuation

* Corresponding author, T: +1-(405)325-2643, F: +1-(405)325-5842, [email protected] T: +1-(509)335-4728, F: +1-(509)335-1173, [email protected] Ŧ T: +1-(208)885-7382, F: +1- (208)885-5759, [email protected]

Miguel Henry-Osorio, Vicki McCracken and Levan Elbakidze,

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1 Introduction

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An increasing number of economic experiments have been conducted in a field context

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rather than in a laboratory setting in the last decade to address a wide range of different

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economic research questions (e.g. see List and Lucking-Reiley, 2000; Lusk and Fox, 2003;

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List 2004; Ding, Grewal and Liechty, 2005; Landry et al., 2006; Marette, Roosen and

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Blanchemanche, 2008). Harrison and List (2004) classify field experiments into three

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categories: artefactual, framed, and natural field experiments. This study falls within the

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category of framed field experiments, which unlike the other two experiment types

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incorporates important elements of the naturally-occurring environment and let the subjects

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know that they are participants in the experiment.1 When research questions pertain to

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measuring consumer willingness to pay (WTP2) for food products, an appealing field

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experiment setting is in-store valuation where grocery store visitors are recruited to take

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part in the experiment. As Lusk et al. (2001) note, “in-store valuation has demonstrable and

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potential advantages for the experimenter compared to a lab setting.” Therefore, we

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collected data for this study from grocery store visitors during their shopping trips.

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Research related to preference elicitation in the context of food experimental economics

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has been carried out using incentive compatible/non-hypothetical3 auction mechanisms

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such as the first and Vickrey second price auction, the random nth price auction, and the

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For a comprehensive review of artefactual, framed, and natural field experiments in economics see Levitt and List (2009). 2 In this article, WTP is defined as the maximum amount a person is willing to pay to obtain a product. 3 Incentive compatibility is referred to the property that participants in the experiment admit a unique dominant strategy as the truthful revelation of private values, while non-hypothetical implies experimental settings involving a transaction of actual goods and/or actual cash as opposed to hypothetical state preference based survey technique.

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Miguel Henry-Osorio, Vicki McCracken and Levan Elbakidze

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Becker-DeGroot-Marschak (1964; hereafter, BDM) auction (Lusk and Shogren, 2007).

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This article employs the BDM mechanism to elicit adult shoppers' WTP values for four

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perishable food items (a functional4 bread, organic milk, organic apples, and conventional

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milk). The BDM method, while theoretically equivalent to the second price auction,

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random nth price auction, and English auctions (Lusk, Feldkamp and Schroeder, 2004;

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Lusk and Rousu, 2007) is not without critics (see Karni and Safra, 1987; Noussair, Robin

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and Ruffiex, 2004; Horowitz, 2006; and Buckley et al., 2012 for formal discussions about

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the strengths and weaknesses of the BDM method). Nevertheless, its rules are simple

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compared to other incentive compatible auction mechanisms, and it avoids many of the

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concerns associated with hypothetical stated preference-based valuation procedures,

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including overestimation of the true WTP due to the hypothetical contexts (see e.g.

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ɺɺ , 1995; Fox et al., 1998; List and Shogren, 1998; Lusk Cummings, Harrison and Rutstrom

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ɺɺ (1998)’s experimental results, and Schroeder, 2004). In addition, based on Rutstrom

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Noussair, Robin and Ruffiex (2004) note that the bias towards high bidding is less severe

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in the BDM than in the Vickrey second price auction format.

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In this article, we examine how bidding for food items, using the demand-revealing

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BDM experimental auction mechanism, is influenced by bidding for a single item vs.

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bidding for multiple items simultaneously. In pursuit of this objective, we formally test

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whether the round in which a product was auctioned affects the bid amount. We also

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examine potential effects of compensation on participants' bidding behavior across the two

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rounds. All participants in this study were compensated prior to engaging in bidding with a

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In this article, we define “functional food” as food with some added functionality like vitamins, minerals, herbs, etc. We refer to “conventional food” as food not being organic and not enhanced with any dietary supplements (e.g. vitamins, minerals, herbs and other botanicals, amino acids, enzymes, etc.).

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$10 store gift certificate. Concretely, we examine whether the expenditures by the winners

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in the first round influence their bids in the second round. Even though the participants

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were not restricted to spending only and no more than the allocated $10, we hypothesize

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and examine the possibility that the participants may still behave as if they were

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constrained by the allocated funds. Brosig and Reiβ (2007) found that bidding behavior is

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significantly affected by the opportunity cost of early bid submission under sequential

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auctions games, while Phillips, Battalio and Kogut (1991) show that the more bidding

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opportunities a participant has, the more likely sunk costs5 will be ignored by the decision

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makers. Experimental evidence from Arkes and Blumer (1985) show that once an

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investment in money, effort, or time has been made the commitment to an endeavor is

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manifested with more vigor. For the previous examinations, we employ different

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econometric methodologies (ordinary least square (OLS) approach, Tobit I and Tobit III

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models, the Powell's semiparametric symmetrically censored least squares (SCLS)

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estimator, and the Seemingly Unrelated Regression (SUR) model) that account for the

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bidding contexts across rounds and products. We use different estimators in order to

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compare results across techniques and verify robustness of the results. In addition, given

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our relatively small sample size, the actual effect of the theoretical large sample properties

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(particularly consistency) of the OLS and fully parametric Tobit models on the results is not

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known.

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Our research contributes to the literature in two ways. First, and similar in spirit to the

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sequential-move framework of the experiments used by Rozan, Stenger, and Willinger

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Payment made or committed as a result of an earlier decision, e.g., the opportunity cost associated with the money spent in the first round.

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(2004), Corrigan and Rousu (2008) and Rousu and Corrigan (2008), in the current article

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participants moved sequentially through two separate bidding rounds. The vast majority of

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BDM studies rely on single-round auctions (see e.g. Lusk et al., 2001; Lusk, Feldkamp and

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Schroeder, 2004; Silva et al., 2007; Froelich, Carlberg and Ward, 2009; Carlberg and

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Froehlich, 2011) or multiple repeated rounds (see e.g. Ariely, Loewenstein, and Prelec,

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2003; Urbancic, 2011). Unlike Rozan, Stenger, and Willinger (2004), Corrigan and Rousu

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(2008) and Rousu and Corrigan (2008), our experimental design introduces a single-item

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shopping scenario (item for first round selected randomly from the four items) in the first

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round, and multiple food items of different types (not necessarily competing products) in

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the second bidding round. Using the random nth-price auction mechanism, List (2002)

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finds evidence for decision preferences to be typically unstable, not well defined, and

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significantly different when goods are seen in isolation vs. juxtaposed. To the best of our

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knowledge, no BDM based study has compared and examined WTP estimates obtained

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from single vs. multiple item bidding schemes. Furthermore, our study uses relatively more

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common items for experimentation than baseball cards used by List (2002).

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Second, to our knowledge, no other studies have used and compared the SCLS and the

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SUR system estimation procedures with commonly used standard regression techniques

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(e.g. the Tobit or OLS models) using data from economic experiments. Although Tobit

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models allow us to control for censoring and model WTP with zero bids, they rely on

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tenuous assumptions that can lead to biased and inconsistent estimates and distort our

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statistical inferences. The SCLS estimator overcomes model misspecification issues that

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arise when relying on tenuous assumptions, even when the error term is non-normal and/or

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exhibits non-sphericity (heteroskedasticity). In our SUR system specification, bids for each 5


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product are analysed using corresponding individual equations, which are estimated jointly

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as a system. Ignoring the potential cross equation error correlations can lead to less precise

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and inefficient parameter estimates (Zellner, 1962). As a result, statistical inferences based

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on the calculated t-statistics for testing parameter significance can be distorted.

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The remainder of this article is organized as follows. In the next section we describe

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and characterize the experiment. Section three presents the auction data collected in the

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experiment. Section four discusses our modeling strategy and describes the variables. In

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section five we report and discuss the results. Concluding remarks as well as some

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limitations of this article and suggestions for future research are detailed in the final

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section.

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2 The Experiment

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The experiment was conducted in two separate and sequential BDM rounds (experimental

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treatments), followed by participants completing a questionnaire.6 The experimental

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auctions were conducted in a retail grocery setting in October, 2009 in the Pacific

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Northwest, United States. Prior to the actual experiment, a pilot study was conducted to

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finetune the details of the experiment.

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The experiment proceeded as follows:

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In Step 1, shoppers were recruited for participation in the experiment near the entrance (or

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inside) of the selected store. Potential participants were informed that university researchers

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The questionnaire was taken at the end of the experiment. The interested reader can find the complete questionnaire in the supplementary appendix online.

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were conducting an “in store consumer study.” After agreeing to participate in the

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experiment, each participant was assigned an identification number to preserve the

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participant’s anonymity. Each participant worked through a “practice round” with the

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researcher after going over the instructions and an introduction to the mechanics of BDM

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auction (The interested reader can find the experimental instructions in a supplementary

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appendix online).

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In Step 2, researchers provided participants with detailed oral and written instructions about

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the BDM mechanism. They were told that they would be bidding for four different food

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items (flax seed bread, conventional milk, organic milk, and Fuji organic apples)7 in two

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separate bidding rounds. The identity of the products was not revealed to the participants at

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this point of the experiment.

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In Step 3, each participant bid separately for only one of the four products. The food

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product was randomly assigned to the participant and displayed as the participant was

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asked to submit his/her bid.

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In Step 4, a binding price for the food product being auctioned (the previous step) was

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determined at random by drawing a number from a bowl containing prices ranging from

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$0.10 to $6.00 in $0.10 increments.

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In Step 5, the participant received the food product being auctioned and paid for it if the

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binding price was lower than or equal to the participant’s bid. Each winner was obligated to

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buy the product at the lower drawn price. If the binding price was higher that the

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These products were selected because they provided variation in attributes and were of economic importance to the region. None of them were major brands, and the organic and conventional milk products were selected based on similar colored labels with 2% of fat. The loaf of bread was selected to be a functional food and it was labeled as such (i.e. high fiber with omega-3 fatty acids). The apples were identified by variety (i.e. organic Fuji apples) and presented in groups of three (approximately one pound).

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participant’s bid, then they would not get to purchase the product (see flow chart in the

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appendix).

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In Step 6, researchers placed each of the other three products on display to show the

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participant exactly what he/she would be bidding on in the next step (separate second

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round).

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In Step 7, researchers informed the participant that the same BDM bidding mechanism

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would be used, but that now bids on these three food products would be submitted

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simultaneously. Each participant was informed that only one product (randomly selected

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and identified after bidding) would be binding.

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In Step 8, the participant’s bid for the randomly selected binding product was compared to a

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randomly drawn binding price for this product to determine if the participant won or did not

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win in the second round.

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In Step 9, the participant received the binding product being auctioned and paid for it

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following the same mechanism as described in step 5.

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In Step 10, participants were asked to complete the questionnaire specific to the binding

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product that was randomly selected in the second round.

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In Step 11, the experiment ended and the participant signed a form that he/she received the

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compensation. The participant was also asked not to discuss the experiment with others in

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the store.

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The two rounds and the auction elicitation mechanism used in this article are explained

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more fully in the supplementary appendix online. The experiment was designed to be

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balanced in terms of the total number of cross-sections per food item, and as completely

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randomized design having one-treatment structure with repeated measures (four food 8


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items). The products being auctioned in the first vs. second rounds were randomized across

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individuals. Participants were asked to bid in a common context (reflecting on product

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value at that specific point of time) and all participated in both rounds (within-participant

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experimental design). They did not bid against one another, but one at a time as is

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customary for the BDM mechanism. Each participant recorded the bids on a paper clip pad

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that was collected by the monitors. Participants not winning in either of the two rounds

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received the $10 gift certificate, while those winning in one or both rounds had the

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“binding” price(s) deducted from the $10 gift certificate and were given the food products

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they won during the experiment. Lastly, participants were not informed about the prices

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that the auctioned food products were being sold in the store.

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3 Data Description

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The experiment described in the previous section involved 136 cross-sectional

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observations. Table 1 summarizes the demographics and other characteristics of the

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participants included in our experiment. Nearly 59 percent of the participants are females.

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The vast majority of the participants are middle age and older (> 45 years old), white non-

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Hispanic (94 percent), primary food shoppers (74 percent), received at least an associate

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degree, and have an annual income less than or equal to $60,000 (64 percent).

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Approximately 73 percent of the participants have never been employed in agricultural

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occupations and the average household size ranges between 2 to 3 people.

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Table 1. Features of Participants (n = 136)

208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251

Characteristic Descriptive Statistics Age 18-24 17.65 25-34 11.76 35-44 8.09 45-54 17.65 55-64 20.59 > 65 24.26 Gender Female 58.82 Male 41.18 Education Less than 12th grade 2.21 High school graduate 18.38 Some college 34.56 Associate degree 3.68 Bachelor degree 23.53 Graduate or professional degree 17.65 Race/ethnicity American Indian or Alaska Native 0.74 Asian-American, Native Hawaiian or Pacific Islander 0.74 Black or African American 1.47 Hispanic or Latino 0.74 White (non-Hispanic) 94.12 International 0.00 Other 2.21 Household income < $20,000 22.06 $20,001 - $40,000 22.79 $40,001 - $60,000 19.12 $60,001 - $80,000 12.50 $80,001 - $100,000 11.76 > $100,000 9.56 Missing 2.21 Primary food shopper? Yes 73.53 No 26.47 Currently or previously employed in an agricultural occupation? Yes 27.21 No 72.79 Household size (SD) 2.34 (1.22) Notes: Results are shown as percentages, except for household size which is the mean. SD denotes standard deviation. 10


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Table 2 shows summary statistics of bids per food item over the two rounds. In general,

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the bids are slightly right-skewed despite the mean response for organic milk being smaller

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than the median. The skewness and kurtosis tests based on Snedecor and Cochrane (1989)

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and the coefficients of skewness and kurtosis reported in table 2 suggest that the bid

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distributions for each food product are not symmetric and possess non-normal kurtosis

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characteristics.

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Note: SD is the standard deviation,

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of kurtosis as defined in Pearson and Harley (1970), where mr =

Table 2. Summary Statistics of Bids over the Two Rounds Food Item

Mean Median

SD

Min

Max

Bread Milk O. milk O. apples

2.20 1.21 1.38 1.38

0.99 0.74 0.86 0.79

0 0 0 0

5 4 4 5

2.00 1.16 1.50 1.25

0.27 0.62 0.26 1.23

b2 2.95 4.12 3.09 6.03

b1 = m3 / m23/ 2 is a measure of skewness, and b2 = m4 / m22 is a coefficient n

∑ i =1

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b1

( xi − x )r n

n

,x =

xi

∑ n , r ≥ 2, and m is the r

i =1

rth moment of the observations. The Mean, Median, SD, Min and Max statistics are in U.S. dollars.

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Some extreme8 values were identified for milk, organic apples, and organic milk. These

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identified extreme bid values were compared with participants’ self-reported “field prices”

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for the same products. In more than 50 percent of the cases, the extreme values and the self-

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reported field prices for conventional milk and organic apples coincide in terms of

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magnitude, and in 60 percent of the identified extreme bid values the primary food shopper

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intended to buy the product. Corrigan and Rousu (2008) argue that this is consistent with

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theory in the sense that the field auction is demand-revealing. For those cases in which the

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The term “extreme” is not formally defined in the statistical literature, but we refer to extreme observations as observations that deviate from the rest of the sample and are not necessarily outliers. As noted in Hawkins (1980) “the intuitive definition of an outlier would be ‘an observation that deviates so much from other observations as to arouse suspicions that it was generated by a different mechanism’.”

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extreme bid values were not close to the self-reported field prices, participants did not

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intend to purchase the food items. One possible explanation for this behavior would be that

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participants were not familiar with the “market” price of the product. Note that most of the

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auction bids are concentrated between $0 and $2. Out of the 544 bids, 41 of them (i.e. 7.54

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percent) are equal to zero - 4 correspond to bread, 14 to milk, 5 to organic apples, and 18 to

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organic milk. The larger number of zeros for the organic milk product might indicate that

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participants did not intend to purchase these food products at that particular moment.

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Figure 1 shows the average bid for each food product across the two bidding rounds.

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Bids tend to increase across the two rounds, but the difference between the bids in round 1

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and bids in round 2 is not statistically significant, except for organic apples, according to

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the nonparametric Wilcoxon-Mann-Whitney two-sample test (p-value bread = 0.4154; p-

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value milk = 0.7910; p-value organic apples = 0.0184; p-value organic milk = 0.3757). 2.50 Auction Bid (US $)

288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304

2.00 1.50 1.00 0.50 0.00

Bread

Milk

O.Apples

O.Milk

Round 1

2.10

1.18

1.12

1.26

Round 2

2.23

1.22

1.45

1.43

Food Product

Figure 1. BDM Average Bids across the Two Bidding Rounds for each of the Four Food Products

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Auction bid price distributions by food product are shown in figure 2 for the first

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and second rounds. Horizontal axes go by increments of $0.5. The number of observations

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in round 1 was about 1/3 of those in the second round due to the experimental design. The

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distributions in round 1, where participants bid for one food item in isolation, tend to be

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more uniform for bread and organic milk and illustrate that bid prices for the flax-seed

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bread are higher relative to the other food items ($4 being the maximum). In round 2,

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where participants bid in a multi-good auction setting, bid prices increased to $5 for both

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flax-seed bread and organic apples. Participants were willing to pay a minimum of $1 for

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bread in the first round. However, when this functional food was juxtaposed with other two

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food items in the second round some participants placed a zero bid on it. This suggests that

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WTP estimates obtained from BDM auctions in isolation can differ from corresponding

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estimates when the auction is implemented in a multiproduct context. This finding is

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similar to List (2002) who used random nth price auctions.

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328 Bread 0

4

5

0

1

2

3

4

5

3

4

5

3

4

5

4

5

20 0

ROUND 1

Organic apples

Organic milk

20

30

334

ROUND 1

40

Percent

10

331

333

Milk 3

30

330

332

2

40

329

1

10

335

0

336

0

1

2

3

4

5

ROUND 1

337

0

1

2

1

2

ROUND 1

Bids (US dollars) Graphs by food

338 Bread

339

1

2

Milk 3

4

5

0

30

0

20

340

10

341

0

Organic apples

Organic milk

10

345

ROUND 2

30

344

ROUND 2

20

343

Percent

342

0

346 347 348 349 350

0

1

2

3

4

5

ROUND 2

0

1

2

3

ROUND 2

Bids (US dollars) Graphs by food

Figure 2. Bid Price Distributions per Round and Type of Food

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4 Modelling Strategy and Variables

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The previous section presented the bid data, emphasizing that the variable of interest is

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observed only on some interval of its support. Similar to Lusk and Fox (2003), possible

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reasons that lead participants to have a zero WTP include budgetary considerations,

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disengaged behavior in the experiment itself, or dislike of the goods under study. In the

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econometric literature, zeros are also treated as corner solutions where the issue is not data

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observability but instead the distribution of the response variable given covariates such as

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income. This is likely not the situation in this study as participants were not income

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constrained and some of them may have held negative values for some food items or for

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their attributes in the experiment (e.g. organic).

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Our data structure suggests that our sample is left fixed-censored9 at zero. Chay and

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Powell (2001) indicate that when censoring occurs, it is expected that the variation of the

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variable to be explained will lead to an understatement of the effect of the explanatory

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variables on the “true” dependent variable. Censoring renders OLS coefficient estimates

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biased and inconsistent (Greene, 1981), yielding misleading statistical results.

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Given the left-censored nature of the dependent variable and that our data are

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realizations of a discrete and continuous process, a Tobit maximum likelihood estimator

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(MLE) might seem most appropriate. However, this commonly used fully parametric

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estimation technique for fixed censoring suffers from several shortcomings. First, this

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nonlinear method, also known as Gaussian censored-regression model or Tobit I, is

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restrictive as it does not allow for different covariates in the two parts (continuous and

9

The distinction between censoring and truncation is usually loose among practitioners. In statistical parlance, the term “censoring” is a property of the sample itself, whereas “truncation” is a property of the distribution. As Maddala (1983) points out a censored distribution is rarely used.

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discrete) of the model. As Haines, Guilkey and Popkin (1988) state “ignoring the two-step

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nature of the decision process may hamper understanding of true behavioral patterns, lead

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to erroneous conclusions, and generate incorrect policy recommendations.” Second, the

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Tobit I model and all its generalizations (e.g. Heckman’s two-step procedure) become

377

inconsistent under heteroskedasticity and non-normality (see Amemiya (1984) among

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others). Third, these models require a full specification of a parametric distribution of the

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disturbances. Unfortunately, researchers usually have insufficient information regarding the

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actual distribution of the errors, and theory provides very little guidance for a reasonable

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structural specification of the heteroskedasticity. Powell (1986) points out that this is a

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serious concern, since the adoption of an incorrect parametric functional form can lead to

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spurious statistical inferences due to biased and inconsistent estimates.

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Following Cameron and Trivedi (2009), we formally tested for homoskedasticity and

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normality using conditional moment tests, which are based on generalized residuals for

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censored regression. The test results (Normality test: p-value = 1.00e-14; homoskedasticity

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test: p-value = 2.78e-19) reveal departures from the Tobit model assumptions, rendering

388

inconsistent ML-Tobit coefficient estimates. Next, we tested for the Tobit specification

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against a somewhat more general model (e.g. the two-part (hurdle) model) using the

390

likelihood

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2 LR = 44.261 > χ 0.05,17 = 27.587 ,

392

(H o : Tobit model is correct) . That is, the Heckman two-part model is preferred to the

10

ratio

(LR)

test

proposed

by

we

Ruud

reject

(1984).10 the

Given null

that

the

hypothesis

LR= -2 ⋅  LLH Tobit Model - ( LLH Probit Model + LLH Truncated Regression Model )  ~ χ n2−1 , where LLH is the log-likelihood

value and n is the sample size. A number of alternative tests are also available in the econometric literature such as Nelson (1981) and Lin and Schmidt (1984).

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393

Tobit model. For these model diagnostics, we pooled the data over food items and included

394

the variables specified in table 1 as well as intercept shifters for all food items among other

395

variables.

396

Although OLS and the ML frameworks are inconsistent, the extent of the consequences

397

is not clear given the sample size in this article. Therefore, results based on OLS, Tobit I,

398

and Heckman two-step (Tobit III) estimators in a product-by-product context are all

399

presented in section 5. We also present an alternative single equation approach to the fully

400

parametric techniques known as the Powell's (1986) SCLS estimator, which provides

401

consistent coefficients for censored data, even when the noise term is non-normal and/or

402

exhibits non-sphericity. This estimation procedure is semiparametric11 in nature, have

403

certain robustness properties, and is relatively well-established in the statistics and

404

economics literature (see e.g. Kwak, Lee and Russell, 1997; Chay and Powell, 2001; Yoo,

405

Kim and Lee, 2001; Wilhelm, 2008). Despite these features, this method trims the sample

406

(discussed in the next section) and thus might result in a loss of valuable information about

407

individuals' decisions.

408

Lastly, we provide an empirical application of the SUR model, developed by Zellner

409

(1962), in a system context that does not impose cross-equation parameter restrictions and

410

does not control for censoring, but it accounts for the cross equation correlation of the

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stochastic disturbance terms (across the four WTP equations). The intra-respondent bids

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exhibit some degree of positive correlation across the four food products with bids for milk

413

and conventional milk being most correlated (correlation coefficient = 0.7). This outcome is

11

Semiparametric estimation typically involves a parametric and a nonparametric specification. The former refers to an underlying regression function assumed to be linear in the covariates, while the second part involves not imposing specific parametric family of distributions on the unobservable idiosyncratic error term.

17


414

not surprising considering that conventional milk and organic milk are highly substitutable

415

in the diet. The existing correlation across responses might be explained due to common

416

unobservables for a given respondent, whose interaction with some regressors might lead to

417

heteroskedastic errors. The set of regressors were not the same for each of the four

418

equations. Due to our small sample size, the SUR system estimation is conducted using the

419

iterated feasible generalized least-squares (IFGLS) estimator rather than using the GLS,

420

two-step FGLS or ML approach.

421 422

Since the single equation SCLS approach for Tobit models is novel to the experimental and food economics literature, we will briefly review this method next.

423 424

4.1 Symmetrically Censored Least Squares Estimator

425

We start by introducing notation. Let yi be the bid for participant i for a specific product

426

(e.g. conventional milk) and xi be a 1 × K matrix of observed explanatory variables that

427

may influence the participant's bid, and K is the number of unknown parameters (including

428

the intercept). Then, assuming that censoring from below at zero is present and the

429

parametric distribution of the disturbance term in the model is unknown, a common

430

statistical approach for the functional relationship between yi and xi is the censored

431

regression model:

{

}

{

}

432

yi = max 0, x'i β + σ 0ε i = max 0, yi*

433

i = 1,..., n (the number of total participants in the experiment)

(1)

434

where yi is non-negative, asymmetrically distributed due to left-censoring, β is a vector of

435

unknown parameters, σ 0 ∈ ( 0, ∞ ) is an unknown scale parameter, ε i - the unobservable 18


436

disturbance term – is assumed to be independent of xi , and yi* is the latent not fully

437

observed dependent variable. Notice that when ε i is assumed to be independent and

438

identically distributed model (1) becomes Tobit I.

439

Considering that the error distribution family remains unknown, the moment-based

440

approach appears to be appealing for solving this problem. However, since model (1) is

441

(left) censored, then ε i ≥ − xi' β so that the orthogonality condition is violated. Assuming

442

that the conditional error distribution function of ε | x , fε|x , is symmetric and unimodal

443

around zero (i.e., homoskedasticity is not necessary), Powell (1986) suggests the SCLS

444

estimator, which does not require knowledge of σ 0 and allows to restore the orthogonality

445

condition by "trimming" the error density.

446

To “trim” equation (1), extreme values of yi are replaced with a maximum value

447

( 2x β )

448

distributed around x'i β . By doing so, we are able to restore symmetry of yi . That is to say,

449

we censor the upper tail of fε|x in the opposite direction to allow us to estimate least

450

squares coefficients consistently. As Santos Silva (1998) describes, under the symmetry

451

restriction, the SCLS estimator results in the following model:

452

yi* = x'i β + ε i* , 1 x'i β > 0 , ∀i, i = 1,..., n

' i

such that the resulting distribution of the censored sample is symmetrically

(

)

(2)

453

where 1( ⋅) is an indicator function equal to 1 if the condition is satisfied and

454

− x'i β   yi* = 0      ε i* =  ε i  if 0 < yi* < 2x'i β  . To solve for this inverse problem the moment-based  x' β   y * = 2 x' β  i  i   i  19


455

approach is invoked so that a set of theoretical (population) moment conditions are

456

specified by E 1 x'i β > 0 yi* − x'i β ⋅ x i  = 0 and its corresponding sample estimating

457

equation-moment is given by:

(

)(

n

)

)(

(

{

}

)

n −1 ∑ 1 x'i β > 0 ⋅ min yi , 2x'i β − x'i β ⋅ xi = 0, ∀i, i = 1,..., n

458

i =1

(3)

459

Since equation (3) is discontinuous we can expect more than one solution to this

460

moment condition. However, under the generalized method of moments framework we can

461

choose β for which equation (3) is as close to the zero vector as possible. In pursuit of this

462

task, the SCLS estimator is an implicit solution to the following minimization problem with

463

respect to β : βˆSCLS = n

(

{

argmin (1 / n ) ∑ yi − max 0.5 yi , xi' β

464

β

i =1

})

2

(4)12

+

2 2 (1 / n ) ∑ 1( yi > 2 xi' β ) ⋅ ( 0.5 yi ) − ( max {0, xi' β } )  n

i =1





465

4.2 Variables

466

Dummy variables for gender and primary food shopper (pfs), as well as dichotomous

467

indicators for bachelor's and graduate or professional degrees (see table 1) as Bachelor and

468

Graduate/Professional, respectively, were included in the specifications of the models. The

469

first four education levels denoted in table 1 were incorporated as a reference category

470

subsumed into the intercept term, since they were identified as being collinear with other

471

included variables. Dummy variables were constructed to capture income variation,

12

In this article, equation (4) was implemented using Aptech Systems’ GAUSS 11 and numerically solved using an iterative optimization routine.

20


472

omitting the lowest income group (i.e. less than $20,000) and the missing observations

473

from the model for estimation purposes. The variable age was created using the midpoint of

474

the age categories represented in table 1, and included in its logarithmic form. The variables

475

race, current agricultural occupation (ao), and household size (HHsize) were initially

476

considered, but excluded from the models reported here because they were shown to be

477

insignificant across the models or were collinear with other included variables.

478

The questionnaires employed in the experiments also included six Likert scale13

479

questions on participants' perceptions about the quality attributes of the organic apples

480

(nutrition, taste, appearance, safety, and environmentally sound practices) relative to

481

conventional ones and seven binary questions about participants' shopping habits for

482

organic apples (the store under study, other supermarkets and grocery stores, natural foods

483

markets, food Co-ops, warehouse retailers (e.g. Costco), farmers markets, and other type of

484

stores different than the previous ones). To reduce the number of variables representing this

485

information, the forward stepwise model selection approach was used, with a significance

486

level for adding and deleting a variable equal to 0.05 and 0.01, respectively. As a result,

487

four variables from the two sets (tb: taste better, mn: more nutritious, wr: warehouse

488

retailers, and ots: other type of stores) were retained in the models.

489

In addition to the variables discussed above, three binary indicators were included into

490

the corresponding models for the specific product. These variables are equal to 1 if the

491

participant usually purchased the corresponding product category at the store under study

492

and zero otherwise. Thus, the variable breads (indicating whether or not the participant

493

usually purchased flax-seed bread) was included in the bread regression equation, dairy

13

5 “strongly agree”, 4 “agree”, 3 “not sure”, 2 “disagree” and 1 “strongly disagree”.

21


494

was included in the conventional milk regression equation, and onf (organic or natural

495

foods) was included in both the organic apple and organic milk regression equations.

496

Two variables were constructed to address the main objective of the study: a dummy

497

variable dp1 (= 1 if product m=1,2,3,4 was auctioned in the first round for the participant; 0

498

otherwise) and a numerical variable gain1 indicating the amount of money on the gift

499

certificate available when the product appeared in the auction. The variable gain1 was

500

equal to $10 for all first round products (dp1=1). In the second round it was equal to $10

501

minus the dollar amount a participant spent in the first round. To examine bid sensitivity

502

across the two rounds and compensation effects we tested the following hypotheses:

503

H o : β dp1 = 0 vs. H1 : β dp1 ≠ 0

(5)

504

H o : β gain1 = 0 vs. H1 : β gain1 ≠ 0

(6)

505

where β dp1 and β gain1 are the associated unknown parameter estimates for dp1 and gain1,

506

respectively. To test theses hypotheses, we conducted the traditional parametric t-test for

507

each product estimate, separately, with each participant represented once in each food

508

product equation. For the SUR system, the product datasets were stacked, resulting in a

509

balanced multiple-equation system with each product having their own set of coefficients.

510 511

5 Estimation Results and Discussion

512

Tables A1-A4 in the appendix report parameter estimates and standard errors for all the

513

variables included in the equation-by-equation models (i.e. OLS, Tobit I, Tobit III, and

514

SCLS) for each of the four products under study. Table A5 displays the SUR system

515

results. Due to the limited variation in several independent variables in the sample and 22


516

limited amount of censoring for the dependent variable for bread and organic apples, the

517

Tobit III model (i.e., the Heckman two-step model) results are not presented for these two

518

products.

519

Consistent with prior expectations, the contribution of the explanatory variables to the

520

explanation of the participant’s WTP and the magnitude of these effects vary significantly

521

depending on the choice of the food product and the estimation method. Based on our

522

results (see tables A1 through A5), the SUR system model losses less efficiency among all

523

estimation procedures so that their point estimates appear to be more precise than those

524

obtained by using the single equation estimation procedures. This occurs even when using

525

the robust semiparametric SCLS estimator with which a 16.3% of the sample is trimmed

526

(two observations from bread, five from milk, nine from organic milk, and five from

527

organic apples).

528

Table 3 summarizes point estimates for the variables of interest (dp1 and gain1) in this

529

study, across food products and estimation procedures. Recall that dp1 is the dummy

530

variable for whether the product was in the first round, and gain1 indicates the amount of

531

the gift card compensation that was available to the participant when the product was being

532

bid on. As shown in this table, the five set of estimates across single equation estimation

533

procedures tell in general a consistent story for dp1: the round in which the product that

534

was auctioned is organic apples has a negative and statistically significant effect on

535

participant’s bidding behavior. Therefore, we reject the null hypothesis in favour of the

536

alternative hypothesis, implying that rounds can matter in this case. The negative sign

537

indicates that participants are willing to pay less if the product is auctioned in the first

538

round than if it is auctioned in the second round, which might be explained by a learning 23


539

effect of the auction mechanism or by the uncertainty associated with the food products that

540

would be bid in the second round. Participants might realize they have lost an opportunity

541

to purchase the product at a lower price. Parametric t-tests for the single product models for

542

bread, milk and organic milk indicate that we cannot reject the null hypothesis at any

543

significance level. For the system approach we cannot reject the null hypothesis for milk

544

and organic milk, but reject it for bread and organic apples. Overall, the results suggest that

545

non-hypothetical bids are sensitive to the context of bidding, participants' preferences for

546

particular food items and to the approach to estimation of the model.

547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570

Table 3. Summarized results for selected variables across food products and estimation procedures ESTIMATION PROCEDURE OLS1

OLS2

Tobit I

Tobit III

SCLS

SUR System

FOOD PRODUCT Bread Milk Organic Apples Organic Milk

βˆdp1

-.2221 -.0066 -.3354**

-.1584

βˆgain1

.0017 -.0239 -.1231

-.1473

βˆdp1

-.3361 -.1509 -.3449**

.0263

βˆgain1

.0933 .0768 -.1402

-.0460

βˆdp1

-.2063 .0214 -.3529**

-.1767

βˆgain1

-.0092 -.0465 -.1220

-.1686

βˆdp1

-.0518

.0438

βˆgain1

-.0169

-.0324

βˆdp1

-.2625 .0262 -.3542**

-.1646

βˆgain1

.0121 .0165 -.0830

-.1564

βˆdp1

-.3689**-.0989 -.3333***

-.1603

βˆgain1

.1432

.2232**.0318

.1343

OLS1: ordinary least square using the full sample; OLS2: ordinary least square using the uncensored sample; Standard errors and the way they were computed are denoted in tables A1-A5. ***Statistically significant at 99% confidence level;**statistically significant at 95% confidence level

24


571 572

Focusing on the Tobit III model for milk and organic milk, the inverse mills ratio (IMR)

573

variable was found to be insignificant for both products at the 0.05 level. However, the

574

IMR is "close" to being significant at the 0.10 level for conventional milk. The apparent

575

insignificance of the IMR variable for organic milk could be due to the multicollinearity, a

576

typical problem in this type of datasets.

577

For the variable gain1, the partial effect in general is clearly positive and not

578

statistically significant on participant’s bidding behavior, except for conventional milk

579

whose point estimate contribute to the explanation of the dependent variable at the 0.05

580

level of type I error. Thus, we cannot reject the null hypothesis of no compensation effect

581

(see [6]) when using individual and system estimation methods. This overall outcome

582

suggests that compensation effects have little impact on individual's bidding decision. We

583

argue that this might be explained due to the uncertainty associated with the lack of

584

information about the products that would be bid in the second round and due to the fact

585

that participants were not actually income constrained during the experiment. However,

586

there is some evidence that the uncertainty about which product will be binding in the

587

second round, or the round order, can have an effect on participants’ bidding decisions.

588

It seems that participants perceived the amount they spent for the food items as an

589

opportunity cost. Thirty out of 136 participants (i.e., 22 percent) won the single good-

590

auction in the first round, being the conventionally produced milk the least frequently

591

purchased product and the average cost (from the gift certificate) across all products

592

purchased was near $1. The average earning for the entire sample at this stage of the

593

decision process was $9.8. Even though every participant could potentially win the auction 25


594

and the opportunity of learning was allowed in the current setting, the resulting decision

595

behavior might be explained by the uncertainty associated with the binding product in the

596

second round. This result provides evidence that compensation effects in the context of our

597

experiment have mostly no impact on individual's bidding decision.

598 599

5. Conclusion

600

This paper reports a field experiment in which participants are asked to value goods in a

601

homegrown value elicitation context with no pre-assigned induced value. Individual

602

bidding behavior in multi round BDM auctions with uncertainty about the binding product

603

in one of the rounds has not been analyzed in economic literature.

604

Participants proceed sequentially through two rounds where they bid on one food

605

product in the first stage (round) and then bid simultaneously for other three different

606

products in the second round. The estimation results show different effects of participant

607

demographics and participants' perceptions about the quality attributes of the organic apples

608

(nutrition and taste) relative to conventional ones and participants' shopping habits for

609

organic apples (warehouse retailers and other type of stores). For instance, the variable

610

“age”, which is most consistently highly significant across all the estimation procedures

611

considered in this study, is negatively associated to participants’ WTP for both organic food

612

items (i.e., organic apples and organic milk).

613

We find that bids are sensitive to the context of bidding and participants' preferences for

614

particular foods. The results also differ across estimation procedures. Compensation mainly

615

did not impact individual's bidding decision, implying that since the participants were not

616

constrained in terms of how much money they could spend during the experiment, 26


617

outcomes of the first round and associated spending in the first round did not have an effect

618

on the behavior in the second round. This means that participants rational decisions are not

619

affected by a potential “latent” constraint that may be argued to be present when the

620

participants are compensated with a certain amount of money as long as the rules of the

621

experiment do not explicitly restrict the participants spending amounts.

622

There are two limitations that need to be pointed out with regard to this research;

623

however, none of them have significant implications to successfully complete the research

624

objectives of this study. First, it is true that this first attempt at modeling consumer’s

625

bidding behavior using the IFGLS-SUR system model allows us to account for the error

626

correlation across equations and, therefore, take advantage of the fact that four WTP values

627

for four different food products come from the same participant. However, this approach

628

does not control for the censoring, and as such, an avenue of future research would be to

629

implement a system approach that is able to account simultaneously for both the error

630

correlation across equations and the censoring without imposing parametric assumptions

631

that can lead to biased and inconsistent estimates and distort our statistical inferences.

632

Another limitation of this study is associated with the order in which the bidding rounds

633

were implemented in the experiment. In our study, the order of the bidding rounds was the

634

same for all participants. The first round was always for a single product auction, and the

635

second round was always for the multi-product auction. An important consideration in

636

future research with a greater number of participants would be to allow for randomization

637

of the bidding sequence. This will allow to separate the effects of uncertainty and round

638

order on participant behavior.

27


639

Also important, and especially when having limited data as in our case, is to recognize

640

that we as researchers do not have enough information about the underlying data sampling

641

process to make strong assumptions for the appropriate functional specifications.

642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676

Acknowledgements This research was funded by the Washington State University-Agricultural Research Center. We thank Nathan Skuza and Joan Ellis for their assistance in conducting the field experiments. We also gratefully acknowledge helpful comments and suggestions by Gregory J. Colson and seminar attendees at the 6th Annual Conference of the American Association of Wine Economists and Food Economists' AAWE-AFE in Princeton, NJ.

28


677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721

Appendices Experimental Instructions General Instructions: My name is__________ and I am part of team researchers from Washington State University. We are conducting a market study, which consists of two parts: an experiment and a short questionnaire. If you participate, we will compensate you for your time with a gift certificate worth $10. This will take 15-20 minutes and you will receive your gift certificate upon completion of the experiment and questionnaire. Would you be willing to participate? Specific Instructions: You will have the opportunity to buy some products without spending any more money on the purchases than you want to. How this will work?

o We will show you a variety of products, and give you the opportunity to bid individually on each of the products like you would in an auction. o We do not have anyone for you to bid against, so the opposing bid will be determined by drawing a price from this (bowl) of random prices. o Just like in an auction, if your bid is greater than or equal to the price we draw, you win the auction and the right to buy the product. Different from an auction, if you win the auction, the price that you pay for the product is the lower drawn price o Just like in an auction, if your bid is lower than the drawn price, you don’t win the auction and you don’t get to buy the product. o You only get to bid once, and if you win we expect you to buy the product. Example: • Suppose for example that we showed you a bottle of wine and you submit a bid of $10. • If the price that we drew was $5, then your bid is higher and you win the auction and get to buy the bottle of wine for $5. • Suppose that you submit a bid of $10 for the bottle of wine, and we draw a price of $12. • Your bid is lower than the drawn price, so you don’t win the auction and don’t get to buy the bottle of wine. o If you value the product and would like to buy it today, it is in your best interest to bid your true value for the product. If you bid more than you value the product you might end up paying more than you wanted for the product. If your bid is lower than your true value, you may miss the opportunity to buy the product for a low price.

29


722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750

The experiment will consist of two rounds of bidding using the auction procedure that I just explained. Round 1: • You have a chance to buy this product (e.g. one pound of organic apples). • Your price offer for the product should be the highest amount you would be willing to pay to have the product right now. • After you submit your bid, you will draw a price from this bowl that contains prices ranging from $0.10 to $6.00 in $0.10 increments. • If your price offer is higher than the price you draw, you will be obligated to buy the product (from us) at the drawn price. If your price offer is lower than the price you draw, you will not be able to buy the product. • Inform the participant(s) of the results, and discuss if necessary. Round 2: • You have the opportunity to bid on each of these products individually. • The auction will work the same as in round 1, but this time you will bid on three products simultaneously. • You will not have to buy all three products. One of the three products has been randomly predetermined to be the binding product. After you submit your three bids, we will reveal the binding product and randomly draw a price for the product. • Inform the participant(s) of the results. Thank you for your participation in the experiment. We would now like to complete a questionnaire. Take as much time as you need and feel free to ask (person at the other table) for clarification of any question. You will receive your compensation and products from (person at the other table) upon completion of the questionnaire.

Price Offer Random Determination of Buying Price Price Offer >= Random Drawn Price Buying Obligation

751 752 753 754 755

Price Offer 0  min ε , x β SCLS   ***Statistically significant at 99% confidence level;**statistically significant at 95% confidence level; *statistically significant at 90% confidence level.

t0.01 = −2.62393, t0.05 = −1.98304, t0.1 = −1.65964

32


866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920

Table A3. Estimation Results for Organic Apples dp1 gain1 onf ln(age) gender income_d2 income_d3 income_d4 income_d5 income_d6 pfs educ_d5 educ_d6 osgs wr oa_n oa_tb intercept

OLS1 -0.3354** (0.1572) -0.1231 (0.1358) -0.1710 (0.1556) -0.4733*** (0.1625) 0.0366 (0.1440) -0.2515 (0.1893) -0.1568 (0.2601) -0.1409 (0.2601) -0.0951 (0.2343) -0.5173* (0.2832) -0.1442 (0.1527) 0.2121 (0.1711) 0.1845 (0.2077) 0.2226* (0.1333) -0.2899** (0.1450) -0.1052 (0.0849) 0.2309** (0.0944) 4.2025** (1.6134)

OLS2 -0.3449** (0.1571) -0.1402 (0.1335) -0.2507* (0.1512) -0.3440** (0.1614) 0.1385 (0.1421) -0.3850** (0.1875) -0.2639 (0.2062) -0.3291 (0.2560) -0.1667 (0.2321) -0.6197** (0.2748) -0.1451 (0.1509) 0.2360 (0.1683) 0.1602 (0.2006) 0.1574 (0.1313) -0.2865** (0.1416) -0.1276 (0.0824) 0.2022** (0.0920) 4.1768*** (1.5860)

Tobit I -0.3529** [0.1521] -0.1220 [0.1312] -0.1547 [0.1508] -0.5027*** [0.1569] 0.0075 [0.1669] -0.2273 [0.1819] -0.1538 [0.1987] -0.1077 [0.2484] -0.0718 [0.2227] -0.4990* [0.2746] -0.1330 [0.1484] 0.2078 [0.1648] 0.1894 [0.1989] 0.2352* [0.1284] -0.3025** [0.1396] -0.0963 [0.0822] 0.2425*** [0.0913] 4.2166*** [1.5617]

Tobit III

SCLS -0.3542** {0.1418} -0.0830 {0.1236} -0.1455 {0.1246} -0.4903*** {0.1475} 0.0784 {0.1306} -0.2134 {0.2021} -0.1488 {0.2569} -0.0947 {0.2856} -0.0359 {0.2522} -0.4562* {0.2723} -0.1361 {0.1530} 0.1928 {0.1864} 0.2071 {0.1821} 0.2376* {0.1419} -0.2697** {0.1169} -0.0950 {0.0945} 0.2275** {0.0985} 3.7547** {1.4896}

OLS1: ordinary least square using the full sample (N=136); OLS2: ordinary least square using the uncensored sample (N=131); Standard errors for OLS are in parenthesis and were computed by deriving the adjusted sampling variance of the residuals. Standard errors in square brackets were calculated based on the inverse of the negative Hessian, while standard errors in curly brackets were estimated with the covariance matrix

{

}

−1

{

(

))

(

2

}

{

}

−1

' ˆ 2 ' ˆ ' ' '    '   'ˆ  xx  E 1  ε < x βˆSCLS  xx  .  E 1  ε < x β SCLS  xx  E 1  x β SCLS > 0  min ε , x β SCLS   ***Statistically significant at 99% confidence level;**statistically significant at 95% confidence level; *statistically significant at 90% confidence level.

t0.01 = −2.62393, t0.05 = −1.98304, t0.1 = −1.65964

33


921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975

Table A4. Estimation Results for Organic Milk dp1 gain1 onf ln(age) gender income_d2 income_d3 income_d4 income_d5 income_d6 pfs educ_d5 educ_d6 osgs wr oa_n oa_tb intercept

OLS1 -0.1584 (0.1736) -0.1473 (0.1483) -0.1507 (0.1704) -0.5658*** (0.1779) 0.0435 (0.1562) 0.0101 (0.2059) -0.0449 (0.2289) 0.2961 (0.2847) -0.0031 (0.2554) 0.0375 (0.3090) -0.2451 (0.1673) -0.3084* (0.1863) -0.1494 (0.2297) 0.2588* (0.1477) -0.2580 (0.1620) 0.2113** (0.0917) -0.0598 (0.1038) 4.7316*** (1.7224)

OLS2 0.0263 (0.1571) -0.0460 (0.1251) -0.1786 (0.1534) -0.4786*** (0.1589) 0.0786 (0.1395) -0.1311 (0.1814) -0.1351 (0.2089) 0.2606 (0.2575) -0.1615 (0.2232) -0.4052 (0.2662) -0.3407** (0.1488) -0.1359 (0.1678) 0.0320 (0.2018) 0.1415 (0.1317) -0.2221 (0.1438) 0.1762** (0.0805) 0.0099 (0.0959) 3.5956** (1.4712)

Tobit I -0.1767 [0.1842] -0.1686 [0.1573] -0.1380 [0.1812] -0.6193*** [0.1895] 0.0351 [0.1590] 0.0443 [0.2148] -0.0258 [0.2307] 0.3599 [0.3032] 0.0482 [0.2759] 0.1642 [0.3276] -0.2329 [0.1774] -0.3717* [0.1996] -0.1984 [0.2443] 0.2984* [0.1575] -0.2977* [0.1727] 0.2347** [0.0973] -0.0645 [0.1107] 5.0025*** [1.8295]

Tobit III 0.0438 (0.1782) -0.0324 (0.1423) -0.1790 (0.1542) -0.4544** (0.1988) 0.0795 (0.1403) -0.1564 (0.2202) -0.1460 (0.2165) 0.2288 (0.3019) -0.1887 (0.2607) -0.4896 (0.4917) -0.3466** (0.1523) -0.1006 (0.2413) 0.0688 (0.2709) 0.1263 (0.1517) -0.2073 (0.1616) 0.1650*** (0.0976) 0.0161 (0.1011) 3.4329** (1.6788) -0.1585 (0.7747)

IMR

SCLS -0.1646 {0.1809} -0.1564 {0.1556} -0.2783** {0.1329} -0.5746*** {0.1784} 0.1406 {0.1729} -0.0777 {0.1691} -0.1915 {0.2444} 0.3658 {0.2852} -0.0322 {0.2861} 0.1849 {0.3274} -0.2880* {0.1524} -0.3678 {0.2360} -0.4014* {0.2436} 0.4014** {0.1629} -0.2088 {0.1624} 0.2365*** {0.0877} -0.0195 {0.1073} 4.5741** {1.9098}

OLS1: ordinary least square using the full sample (N=136); OLS2: ordinary least square using the uncensored sample (N=118); Standard errors for OLS are in parenthesis and were computed by deriving the adjusted sampling variance of the residuals. Standard errors in square brackets were calculated based on the inverse of the negative Hessian, while standard errors in curly brackets were estimated with the covariance matrix

{

}

−1

{

(

))

(

2

}

{

}

−1

' ˆ 2 ' ˆ ' ' '    '   'ˆ  xx  E 1  ε < x βˆSCLS  xx  .  E 1  ε < x β SCLS  xx  E 1  x β SCLS > 0  min ε , x β SCLS   ***Statistically significant at 99% confidence level;**statistically significant at 95% confidence level; *statistically significant at 90% confidence level.

t0.01 = −2.62393, t0.05 = −1.98304, t0.1 = −1.65964

34


976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032

Table A5. IFGLS-SUR System Estimation Results dp1 gain1 breads

BREAD -0.3689** (0.1671) 0.1432 (0.2110) 0.1784 (0.1472)

dairy

MILK -0.0989 (0.1120) 0.2232** (0.1063)

gender income_d2 income_d3 income_d4 income_d5 income_d6 pfs educ_d5 educ_d6 osgs wr oa_n oa_tb intercept

ORGANIC MILK -0.1603 (0.1194) 0.1343 (0.1196)

-0.1699 (0.1284) -0.4453*** (0.1517) 0.0527 (0.1341) -0.2604 (0.1763) -0.1559 (0.1940) -0.1306 (0.2426) -0.0868 (0.2193) -0.5385** (0.2649) -0.1593 (0.1427) 0.2188 (0.1602) 0.1926 (0.1944) 0.2286* (0.1247) -0.2912** (0.1357) -0.0917 (0.0793) 0.2264** (0.0881) 2.5438* (1.3773)

-0.0442 (0.1196) -0.5300*** (0.1673) 0.0342 (0.1467) 0.0207 (0.1936) -0.0276 (0.2155) 0.3628 (0.2674) 0.0282 (0.2420) 0.0223 (0.2921) -0.2948** (0.1580) -0.3182** (0.1765) -0.2007 (0.2162) 0.2640* (0.1386) -0.2702* (0.1516) 0.2215** (0.0869) -0.0625 (0.0972) 1.8197 (1.4410)

0.0853 (0.1049)

onf ln(age)

ORGANIC APPLES -0.3333*** (0.1247) 0.0318 (0.1130)

-0.2984 (0.2027) 0.2022 (0.1770) 0.1928 (0.2367) -0.1540 (0.2622) 0.6369** (0.3211) 0.4952*** (0.2966) -0.3433 (0.3548) -0.2379 (0.1923) -0.1714 (0.2144) -0.1577 (0.2616) 0.2466 (0.1721) -0.1920 (0.1811) 0.0486 (0.1080) 0.0319 (0.1168) 1.5614 (2.2540)

-0.3247** (0.1536) -0.0079 (0.1350) -0.1371 (0.1775) -0.0506 (0.1978) 0.2264 (0.2450) -0.1227 (0.2241) -0.3305 (0.2697) -0.2083 (0.1464) -0.2491 (0.1634) -0.2731 (0.1987) 0.1291 (0.1276) -0.2588* (0.1385) 0.1012 (0.0814) -0.0747 (0.0899) 0.4602 (1.2851)

Standard errors are in parenthesis. ***Statistically significant at 99% confidence level;**statistically significant at 95% confidence level; *statistically significant at 90% confidence level.

t0.01 = −2.62393, t0.05 = −1.98304, t0.1 = −1.65964

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