Anchoring effects and the role of information

Anchoring in stated-preference methodology

The notion of anchoring as a decision-making heuristic was first introduced in the psychological literature by Slovic (Reference Slovic1967) who studied patterns of preference reversals among bets of varying risk, but the anchoring-and-adjustment heuristic developed in the seminal work of Tversky and Kahneman (Reference Tversky and Kahneman1974) has been the workhorse theory for much of the related literature. They propose that anchoring is caused by “insufficient adjustment” away from an initially presented value, i.e. the anchor, and thus starting pieces of information disproportionately influence the choices of decision makers. This assumes that decision makers are influenced primarily by an initial anchor and slowly adjust back to some starting value and has alternatively been termed “starting-point” effects in the resulting literature. Using this theory of anchoring, many studies have illustrated the prevalence of anchoring in decisions regarding both general knowledge (Epley and Gilovich Reference Epley and Gilovich2001; McElroy and Dowd Reference McElroy and Dowd2007; Mussweiler and Strack Reference Mussweiler and Strack1999; Strack and Mussweiler Reference Strack and Mussweiler1997) and probability estimates (Chapman and Johnson Reference Chapman and Johnson1999; Plous Reference Plous1989).

An alternative view of the anchoring model is that of selective accessibility, based on the psychological theory of confirmation bias. Here, a decision maker is thought to selectively access information consistent with an anchor, and thus attempt to confirm the hypothesis that some anchor represents the “correct” choice. Compared to the anchoring-and-adjustment heuristic, this suggests that decision makers are primarily influenced not by an initial anchor, but rather by values presented later in the choice process. In this alternative view, the prevalence of anchoring can be expected to increase over the choice process. Chapman and Johnson (Reference Chapman and Johnson1999) and Strack and Mussweiler (Reference Strack and Mussweiler1997) provide empirical evidence that selective accessibility is a plausible mechanism for anchoring.

Each of these explanations for anchoring directly contradicts the assumptions of utility maximization, in which individuals’ choices are assumed to reflect their underlying preferences for the product. In the context of a choice experiment, varying the scale and/or range of the price vector should not change individuals’ responses as they are expected to possess exogenously determining valuations for the product that are unaffected by preference elicitation framing. From this perspective, welfare estimates derived from the choice experiment should not be influenced by the set of presented prices.

The prices attached to alternatives in CEs are displayed simultaneously in each choice set. If these prices act as an anchor under which choices are made, then one would expect that, across individuals, the distribution of choices between alternatives in each choice set to differ based on the presented set of prices, holding all other attributes constant. For instance, if the presented prices are high enough relative to a decision maker’s income, then it is possible they find that the price is high enough to make a difference in their choices. Though, if this type of anchoring is present, it is not a priori clear whether the respondent anchors on the highest, lowest, or average prices presented in the choice set, or some other combination of prices and attributes altogether. Within the CE framework, studies examining anchoring have focused on two potential effects: (1) price vector effects; and (2) starting point effects, and results have been mixed.

With regards to price vector effects, individuals are thought to anchor their preferences on the vector of prices used for the price attribute. Within the context of water quality improvements, Hanley et al. (Reference Hanley, Adamowicz and Wright2005) and Frykblom and Shogren (Reference Frykblom and Shogren2000) each use an experimental split-sample approach to study price vector effects and find no significant impact of changing the price vector on estimates of preferences or willingness to pay. Further, Ohler et al. (Reference Ohler, Le, Louviere and Swait2000) investigate attribute range effects in binary response conjoint analysis tasks in the context of public bus choices and find that varying attribute range impacts preferences to a small degree. On the other hand, using split sample approaches, Carlsson and Martinsson (Reference Carlsson and Martinsson2007) and Ryan and Wordsworth (Reference Ryan and Wordsworth2000) find that marginal willingness to pay estimates are sensitive to price vector scale in the context of power outages and cervical screening programs, respectively. Most recently, Su et al. (Reference Su, Adam, Lusk and Arthur2017) use a choice experiment to determine WTP for improvements in rice insect control and storage and again find that WTP estimates are sensitive to the price vector presented in the CE.

On the other hand, starting point effects are thought to influence respondent perceptions of prices in subsequent choice sets through the prices used in the first choice. To the author’s knowledge, only two studies examine starting point effects in the CE framework. Carlsson and Martinsson (Reference Carlsson and Martinsson2007) used a split sample design in which one split was presented with an additional choice set with low prices and large attribute improvements at the beginning of the choice experiment found no presence of starting point bias. Conversely, Ladenburg and Olsen (Reference Ladenburg and Olsen2008), using a split sample design in which they fix the prices used in an Instruction Choice Set (ICS) at different levels, find the presence of starting point bias, though the effect is significant only for females.

This study focuses on the effects of varying the price vector on consumer preferences. Following the related literature, we hypothesize that an increase (decrease) in the mean of the price vector would increase (decrease) willingness to pay estimates by decreasing the estimated coefficient on the price variable, in other words, by decreasing price sensitivity. That is, holding all else equal, an increase in the price vector of a choice experiment will decrease the mean marginal disutility of price. Here, we would expect that $|{\beta _{p;j,k|LP}}| \gt \left| {{\beta _{p;j,k|HP}}} \right|$ , or the absolute value of the marginal utility on price (p) for attribute j of product k conditional upon receiving the low price vector (LP) will be greater than the absolute value of the marginal utility on price (p) for the same attribute j of the same product k conditional now upon receiving the high price vector (HP). That is, an increase in the price vector of the choice experiment will induce an income and substitution effect, which, within the random utility discrete-choice framework used in this study, has second-order effects on welfare estimates (McFadden Reference McFadden1973). In terms of generating marginal welfare estimates (i.e. ${\rm{WTP}})$ , we follow McFadden (Reference McFadden1974) who shows that for an individual i is calculated as the negative of the marginal rate of substitution between the attribute (j) and price (p) for a given product (k), or

(1) $$WT{P_{i,j,k}} = {{{{\delta {U_i}} \over {\delta {j_k}}}} \over {{{\delta {U_i}} \over {\delta {p_k}}}}} = - {{{\beta _{j,k}}} \over {{\beta _{p,k}}}}$$

Given (1) and the assumption of an income effect induced by increasing the mean price vector, we can expect that individuals presented with the high price vector will have a higher marginal WTP than individuals presented with the low price vector for the same attribute/product combination. This “anchoring” hypothesis can be expressed according to the null hypothesis $H_0^A:WT{P_{i,j,k|LP}} \gt = WT{P_{i,j,k|HP}}$ . Rejection of the null of equal marginal WTP estimates by attribute across price vectors would suggest that an anchoring effect exists.

Experimental design and data summary

A survey and choice experiment were designed to elicit consumer preferences for local and organic produce in Northern New England and included three sections: “Introduction” section familiarized the consumer with the products being valued and gathered information on attribute preferences for the target population; “Anchoring Effects and the Role of Information” section presented the choice experiment and a set of related follow-up questions; and “Experimental Design and Data Summary” section gathered a set of socio-economic indicators from each of the survey respondents. For the empirical experiment concerned with testing for anchoring bias and the effectiveness of information scripts on mitigating such bias in a discrete choice framework, the responses to a study collecting individuals’ preferences for local and organic agriculture in Northern New England were analyzed. Here, an online survey is used to compare a treatment group, i.e. anchoring information (INFO) with a neutral control group, i.e. no anchoring information (NoINFO). Formally, the test was carried out by using a split-sample design, in which the full sample was split along two dimensions: price vector (Low/High) and anchoring information exposure (NoINFO/INFO). The price-vector dimension split the sample according to the level of the price attribute presented for each choice set, where respondents exposed to the high price split were presented with prices double that of those faced with the low price split, as shown in Table 1.

Table 1. Attributes and attribute levels in choice experiment survey

Respondents exposed to survey versions with the anchoring information (INFO) were presented with an identical set of survey questions, but the choice experiment portion of the survey was prefaced with a short script describing the issue of anchoring bias in stated preference valuation techniques. The information script presented to the respondents was as follows:

Based on qualitative information gathered from focus groups of consumers and producers in the region, tomatoes are presented in the choice experiment as being composed of five product attributes, summarized in Table 1 below. The first two attributes are indicators of whether the produce were grown locally or through certified organic practices.Footnote ⁴ Another indicator describing the method of purchase (i.e. directly from farmers or indirectly from other markets) was included as an attribute and is expected to capture preferences around purchasing convenience, as well as social capital considerations.Footnote ⁵ Further, Bond et al. (Reference Bond, Thilmany and Keeling-Bond2008) and Brown and Miller (Reference Brown and Miller2008) suggest that freshness and quality are the most important attributes for consumers who purchase produce. Thus, to capture the fact that consumers are often forced to make quality judgments based on appearance alone, an attribute indicating if the produce has visual blemishes was included in the experimental design. Finally, price is included to obtain the willingness to pay estimates for each of the non-price attributes.

Among the five attributes detailed in Table 1, four attributes have two levels (Yes/No) and the price attribute takes on four levels. As shown in Figure 1, consumers are asked to make a choice over three bundles of produce, two of which are hypothetical bundles proposed in the choice set, and the third representing their current purchasing habits. An orthogonal main effects design was conducted using the JMP software suite to ensure no interactions between the attributes, as each level of one factor occurs with each level of another factor with equal or at least proportional frequencies. Results from this design technique reduced 2⁴ x 4 = 64 possible combinations into eight combinations of attributes, which are then split into four versions of the survey with two combinations in each version. Therefore, information is gathered on two choice sets over varying tomatoes for each respondent.

Figure 1. Example of choice experiment survey bundle.

The four versions of the survey are divided into four subsamples: (1) LP/NoINFO; (2) HP/NoINFO; (3)LP/INFO; and (4) HP/INFO, for a total of 16 versions of the survey. The survey questionnaires were created and distributed via the Qualtrics Survey Research Suite, through which a quota-based approach was used to sample from an online panel, where respondents were screened and filtered according to three criteria: (1) at least 18 years old; (2) the households primary food shopper; and (3) a resident of New Hampshire, Maine, or Vermont. Additionally, respondents who failed a “focus test” were also removed from the analysis. ^{Footnote 6} Details on the development of the survey instrument and the policy background can be found in Pyburn et al. (Reference Pyburn, Puzacke, Halstead and Huang2016). Data collection was handled in 2017 by the Marketing Systems GroupFootnote ⁷ , who controls an online panel consisting of members of the general United States public. Respondents were invited via email and due to the sampling scheme, it is not possible to calculate a standard response rate as a quota-based sampling frame was employed. After clearing incomplete responses and non-compliers, 523 respondents remain in the final sample, consisting of 197 respondents from New Hampshire, 202 from Maine, and 124 from Vermont. The proportions of respondents chosen from each state were based on share of population across the three states.

Table 2 presents demographic summary statistics of survey respondents and their associated populations for comparison, by state. Across the full sample, 71.3% of respondents are female, though this percentage is somewhat lower in Vermont (62.9%) and represents a larger proportion of females than their population average of about 50%. The mean age across the sample is about 50 years old, with a standard deviation of 16.3, indicating that the sample has a broad coverage of age groups used in estimation and is roughly consistent with population averages, though the sample in New Hampshire and Vermont are about 7 years older than their population average. The median annual household income across the sample is $65,033, where this average is higher in VT ($70,887) and lower in ME ($58,069), and most likely found in NH ($68,5489). In terms of educational attainment, 79.6% of respondents have at least some college education and is slightly higher than each of the three states averages.

Table 2. Summary statistics of respondent characteristics by state

Modeling framework and specification

To test for the presence of anchoring effects and whether anchoring information treatments were an effective anchoring mitigation technique, a set of discrete choice models are used to analyze and compare the preference structures and WTP estimates across each of the treatment and control groups for the product. The discrete-choice random utility (RUM) framework (McFadden Reference McFadden1973) is used to analyze respondents’ choices among different bundle alternatives.

Equation 2 below represents the utility function of decision maker i over choice alternative j. It is assumed to contain both a deterministic and random component. The deterministic component ( $\beta \prime{x_{ij}})$ is usually assumed to be a linear function of the choice attributes, the price of the choice, and individual characteristics, which are included through their interactions with an alternative-specific constant and $\beta $ is a vector of coefficients assumed constant across individuals and choice alternatives.Footnote ⁸ The random component ( ${\varepsilon _{ij}})$ is included as an error term and is assumed to be randomly distributed.

(2) $${U_{ij}} = \beta ^{\prime}{x_{ij}} + {\varepsilon _{ij}}$$

A rational decision maker chooses the alternative that yields the highest utility, such that the probability of decision maker i choosing alternative j over other alternatives k is

(3) $${\pi _{ij}} = {\rm{Pr}}(\beta ^{\prime}{x_{ij\;}} + {\varepsilon _{ij}} \gt \beta ^{\prime}{x_{ik\;}} + {\varepsilon _{ik}})\;\;\forall j \ne k$$

Assumptions about the distribution of the error term in Eq. 3 lead to different types of discrete choice models. For example, if we assume the error term follows an i.i.d. Type I extreme value distribution, the conditional logit model arises. This type of model is widely used in the choice-modeling literature. The benefits of using the conditional logit model are in its operational simplicity, whereas the costs are in: (1) its inability to account for preference heterogeneity across decision-makers; and (2) its restrictive IIA assumption.

Within this model, the conditional probability that decision maker i chooses alternative j can be expressed as

(4) $${\pi _{ij}} = \;{{{\rm{exp}}\left( {\beta ^{\prime} {x_{ij}}} \right)} \over {\sum\nolimits_{j = 1}^J {{\rm{exp}}} \left( {\beta ^{\prime} {x_{ij}}} \right)}}$$

where J is the maximum number of choice alternatives faced by decision maker i. The log-likelihood function of the choice responses made by n decision-makers can be expressed as

(5) $$L = \;\mathop \sum \nolimits_{i = 1}^n [{y_{i1}}\log \left( {{\pi _{i1}}} \right) + {y_{i2}}\log \left( {{\pi _{i2}}} \right) + \ldots + {y_{iJ}}\log \left( {{\pi _{iJ}}} \right)]\;$$

where $n$ is the total number of decision makers, and ${y_{i1}} = 1$ if decision-maker i chooses alternative j, and ${y_{i1}} = 0$ otherwise.

For this analysis, the mixed logit modeling approach is used. (Train Reference Train2003) This class of models allows for individual preference heterogeneity and relaxes the restrictive IIA assumption by allowing one or more of the parameters in the model to be randomly distributed (Revelt and Train Reference Revelt and Train1998). Here, if we assume $\beta $ to be randomly distributed with density $f\left( {{\beta _i}{\rm{|}}\theta } \right)$ where $\theta $ represents the true parameters of the distribution, the unconditional probability of decision-maker i choosing alternative j is the conditional probability of (6) integrated over the distribution of $\beta $ , or

(6) $${\pi _{ij}^*} = \;{{{\rm{exp}}\left( {\beta ^{\prime}_i{x_{ij}}} \right)} \over {\mathop \sum \nolimits_{j = 1}^J {\rm{exp}}\left( {\beta ^{\prime}_i{x_{ij}}} \right)}}\;f\left( {{\beta _i}{\rm{|}}\theta } \right)\;d{\beta _i}\;\;$$

Since the integral in (6) cannot be evaluated analytically, exact maximum likelihood estimation is not possible. Instead, the probability is approximated through simulation. The simulated log likelihood is given by

(7) $$SLL\left( \theta \right) = \;\sum\limits_{n = 1}^N {{\rm{ln}}} [{1 \over R}\sum\nolimits_{r = 1}^R {\pi _{ij}^*} \left( {{\beta ^r}} \right)]$$

where R is the number of replications and ${\beta ^r}$ is the r-th draw from $f\left( {{\beta _i}{\rm{|}}\theta } \right)$ .

Within this framework, welfare measures, i.e. marginal willingness to pay (WTP), are calculated according to Eq. 1, in which the non-monetary coefficients of interest (i.e. local, organic, etc…) are divided by the price coefficient and is carried out using the wtp command in Stata 13.1, the details of which can be found in Hole (Reference Hole2007a).

To test for anchoring effects, we run the following specification separately for each price split group who were not exposed to anchoring information (NoINFO), specifically,

(8) $${U_{ij|LP,NoINFO}} = f({P_{ij}},{D_{ij}},\;S{Q_i},{Y_i}*S{Q_i},{e_{ij}}|\beta )$$

and

(9) $${U_{ij|HP,NoINFO}} = f({P_{ij}},{D_{ij}},\;S{Q_i},{Y_i}*S{Q_i},{e_{ij}}|\alpha )$$

where P _ij indicates the price of alternative j presented to individual i, D _ij is a series of indicator variables identifying all of the choice alternative attributes, SQ _ij represents the status quo, or current purchasing behavior of individual i, and (Y _i *SQ _i ) which represents a set of interactions between the status quo alternative and other individual characteristics, including sex, income, and education, state-level dummy indicators, and a measure of purchasing experience ^{Footnote 10} , and finally $\beta $ and $\alpha $ represent the set of parameters that define each group. The test for anchoring effects is carried out by testing the equivalence of $\beta $ and $\alpha $ across the two models via a likelihood ratio test developed in Swait and Louviere (1993), where the null hypothesis is $H_0^{Anch1}:$ $\beta $ = $\alpha $ , or that parameter estimates are equivalent across the two groups. Within this specification, the binary attributes of interest (i.e. local, organic, indirect, and non-blemish) are assumed random and uncorrelated, each following a normal distribution.Footnote ¹¹ Once preference estimates are obtained and if $H_0^{Anch1}$ is rejected, we also test for anchoring effects by differences in attribute-level marginal willingness-to-pay estimates across the two groups. The null hypothesis here is $H_0^{Anch2}\;:WTP_j^{LP|NoINFO} = WTP_j^{HP|NoINFO}$ , where j represents the attribute of interest. Failure to reject $H_0^{Anch1}$ or $H_0^{Anch2}$ would suggest that price anchoring effects are not present in this choice experiment.

Lastly, to test the effectiveness of anchoring information (INFO) in mitigating anchoring effects relative to the neutral no information control (NoINFO), we take a similar approach as outlined above, but only estimate for those exposed to the information prompts. Specifically, we estimate

(10) $${U_{ij|LP,INFO}} = f({P_{ij}},{D_{ij}},\;S{Q_i},{Y_i}*S{Q_i},{e_{ij}}|\gamma )$$

and

(11) $${U_{ij|HP,INFO}} = f({P_{ij}},{D_{ij}},\;S{Q_i},{Y_i}*S{Q_i},{e_{ij}}|\tau )$$

and carry out similar likelihood ratio tests for data pooling, where the null hypotheses now can be represented by $H_0^{INFO1}:$ $\gamma $ = $\tau $ and $H_2^{INFO2}\;:WTP_j^{LP|INFO} = WTP_j^{HP|INFO}$ . Here, failure to reject either $H_0^{INFO1}$ or $H_0^{INFO2}$ would suggest that the information intervention completely eliminated any anchoring effects. On the other hand, if $H_0^{INFO1}$ or $H_0^{INFO2}$ are rejected, then we test for mitigating effects of information by developing a measure of the difference in anchoring both before and after exposure to anchoring information, represented by

(12) $$DIFF = \left( {WTP_{j,k}^{INFO|HP} - \;WTP_{j,k}^{INFO|LP}} \right) - \left( {WTP_{j,k}^{NoINFO|HP} - \;WTP_{j,k}^{NoINFO|LP}} \right).$$

Here, the null hypothesis is $H_0^{INFO3}\;:\;DIFF = 0$ , or that anchoring effects before and after the information exposure are the same. If $H_0^{INFO3}$ is rejected and $DIFF \lt 0$ , this would indicate that information treatment instead had a mitigating effect on price anchoring. Finally, if $H_0^{INFO3}$ is rejected and $DIFF \gt 0$ , the anchoring intervention had a perverse effect on anchoring behavior.

If anchoring information did indeed have an effect on the level of anchoring, we can expect one of two things to happen. First, for those exposed to the low price sample, information treatment would reduce the price sensitivity of those consumers and for those exposed to the high price sample, we can expect just the opposite, in that price sensitivity for these individuals increases. That is to say, anchoring information can have an effect on price sensitivity for either group, but as the prices presented to the low price sample more closely align with actual market prices, we would expect greater effects of information in the high price sample.

All models based upon the above procedure are estimated in Stata (StataCorp 2013), using the mixlogit (Hole Reference Hole2007b) command, which is simulated through Halton draws using 1000 replications.