## 1. INTRODUCTION

Price is a key factor for consumers to make a choice between products or brands. In most models of consumer choice, a price variable is included as an important explanatory variable. The usual assumption is that consumers are able to correctly interpret and compare prices across choice options. In this paper we challenge this assumption by analyzing experimental choice data, where we manipulated the choice options such that the choice task is difficult, and we examine whether individuals are able to correctly compare price differences, if there are any. The task complexity is created by allowing products to effectively have the same price, but the wording is confounded by introducing price discounts. For example, we make individuals compare prices like 135 euros and 150 euros with 10% discount, while these are of course the same.

Choice experiments provide a useful framework to collect data when real-life data are not available or are more costly. Such situations may occur when one would like to estimate or test hypotheses about the distribution of consumer preferences for a given product. For such problems, experiments offer the advantage that the prices of the products are exogenous. Estimation of consumer preferences using revealed preference data in most cases cannot assume price exogeneity and therefore it requires expensive datasets containing a large number of observations (Berry *et al.*, 1995). The recent literature has witnessed a growing interest in such choice experiments especially in marketing (where the literature is huge; we only mention a pioneering work by Louviere and Woodworth, 1983) but also in various other demand studies, for example, on environmental issues (e.g., Adamowicz *et al.*, 1997; Layton and Brown, 2000), on transportation problems (e.g., Brownstone and Train, 1999; Small *et al.*, 2005), on health care issues (e.g., Scott, 2001; San-Miguel *et al.*, 2002), and on other demand problems (Revelt and Train, 1998; van Ophem *et al.*, 1999).

Most of this literature assumes that consumers are rational utility maximizers. One reason for this assumption is that it allows for the application of reasonably easy-to-analyze models for observed consumer choice. In contrast, there is also substantial literature on consumer decision making which allows for the possibility that consumers do not always behave perfectly rationally, even when they intend to do so (see Bettman *et al.*, 1993). This phenomenon is often coined bounded rationality (e.g., Rubinstein, 1998). The drivers of this bounded rationality are found in the effort that consumers have to make to arrive at a choice. This effort depends on potentially difficult factors of the choice task like the number of effective tasks per respondent, the number of alternatives, the way the choice alternatives are specified, the number of product characteristics involved, and possibly other factors (see, for example, Tyebjee, 1979; Johnson and Payne, 1985). In the sequel, we refer to these as choice complexity variables.

A number of papers analyzing choice experiments made important steps towards measuring how the different choice complexity variables influence consumer choice (e.g., Mazzotta and Opaluch, 1995; Dellaert *et al.*, 1999; Swait and Adamowicz, 2001). The basic methodology for such an analysis is to relate the choice complexity variables to the consistency (with rational behavior) of choice, which is typically measured by the effect of the choice complexity variables on the variance of the error term in the utility. Along these lines, by employing a heteroskedastic logit model, DeShazo and Fermo (2002) find empirical evidence that most of the choice complexity variables listed in the previous paragraph affect the consistency of choice negatively. These authors expressed the way the choice alternatives are specified in a choice set by three variables, namely, the number of characteristics whose levels differ across alternatives and the mean and standard deviation of the dispersion of the characteristics within alternatives. They show that omitting these variables may yield over- or underestimation of welfare by up to 30%

In this paper, by employing a heteroskedastic random coefficient logit model (McFadden and Train, 2000), we examine whether it can happen that choice complexity leads to making mistakes about prices of products. For example, and as we will consider below, we seek to answer the question whether consumers can understand that 135 euros is the same price as 150 euros with a 10% discount, in case the product also has a variety of other characteristics.

We collect experimental data and estimate preferences for mobile phones, with a special focus on measuring the effect of specifying the price. We do so in a way similar to measuring the effect of the choice complexity variables on the variance of the error term in the utility. We specify some prices with discount and the others without discount and investigate whether the prices specified with discount cause difficulties in making choices. For consistency of our parameter estimates it is crucial that we also include variables that measure the consistency of choice. Because of this, besides the price specification variable we include the mean dispersion of the characteristics within alternatives as defined by DeShazo and Fermo (2002) and a variable that measures how similar the alternatives are in terms of utility. This variable is related to the number of characteristics with levels that differ across alternatives (i.e., the first of DeShazo and Fermo's variables; for details see Section 2). We find evidence in our data that this latter variable as well as the price specification variable significantly compromise the consistency of choice.

The main contribution of our paper for consumer research is that we demonstrate that the usual assumption that consumers are able to correctly interpret and compare prices across choice options does not always hold. The estimation results of our model, however, imply two other findings of potential interest. The first is the empirical result that we find the choice complexity variable that measures how similar the alternatives are in terms of utility to be statistically significant. The other finding of potential interest is the implication of this result for the design of statistically efficient experiments. Several authors have advocated the selection of choice alternatives whose utility is similar as a tool for constructing statistically efficient experimental designs (e.g., Huber and Zwerina, 1996; Arora and Huber, 2001; Toubia *et al.*, 2004). However, our empirical results suggest that such experimental designs cause choices to be inconsistent, which leads eventually to inconsistent estimation of consumer preferences. We provide guidelines on how one can still use the ideas from these papers to construct statistically efficient designs in such circumstances.

The paper is organized as follows. We provide details about the model and the choice complexity variables in Section 2 and we formulate the main hypotheses of the paper. In Section 3 we give details regarding the estimation of the model by maximum likelihood. In Section 4 we discuss some issues regarding the collection of the data and present the estimation results on mobile phone preferences. In Section 5 we discuss the implication for the design of experiments mentioned in the previous paragraph. We conclude the paper with a section containing a summary and possible topics for further research.