Decomposing local: a conjoint analysis of locally produced foods.

(1) [V.sup.i.sub.j]([M.sup.i] - [P.sub.j], [A.sub.j], [S.sup.i.sub.j], [e.sup.i.sub.j]) = [alpha]L + [e.sup.i.sub.j]

where [V.sup.i.sub.j] denotes individual i's indirect utility from choosing product j; [M.sup.i] is respondent i's annual household income; [P.sub.j] is the price of product j; [A.sub.j] denotes a column vector of attributes associated with product j; [S.sup.i.sub.j] denotes a column vector of interaction terms, which may include interactions between product attributes as well as interactions between product j's attributes and household i's characteristics; L = [[[M.sup.i] - [P.sub.j][A.sup.T.sub.j]([S.sup.i.sub.j]).sup.T]].sup.T]is a column vector of regressors; superscript T denotes the transpose operator; a = [[[alpha].sub.M] [[alpha].sub.A] [[alpha].sub.S]] is a row vector of coefficients to be estimated; and [e.sup.i.sub.j] denotes a disturbance term.

When faced with a choice of two products, the individual chooses the one expected to provide the highest utility. Here each individual's choice set contains two products, so we model the choice decision based on the difference in utility. Thus framed, the utility difference between product x and y is

(2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [DELTA](k)=[k.sub.x] - [k.sub.y], [[epsilon].sup.i.sub.xy] = ([e.sup.i.sub.x] - [e.sup.i.sub.y]) and [[epsilon].sup.i.sub.xy] is assumed to be normally distributed. Following Johnson and Desvousges (1997), we include interaction terms between product attributes and households; this allows for measurement of differences in preferences for product attributes across different types of households. When d[V.sup.i.sub.xy] > 0 respondent i chooses product x, and the probability that respondent i chooses product x rather than product y is

(3) prob(d[V.sup.i.sub.xy] > 0) = [PHI]([alpha][DELTA](L))

where [PHI](*) is the normal cumulative distribution function.

We implicitly define the deterministic WTP (compensating variation in our case), C, for a change in attributes from [A.sub.x] to [A.sub.y] for individual i as

[V.sub.x]([M.sup.i] - [P.sub.x], [A.sub.x], [S.sup.i.sub.x]) = [V.sub.y]([M.sup.i] - [P.sub.y] - C, [A.sub.y], [S.sup.i.sub.y])

where [S.sup.i.sub.x] and [S.sup.i.sub.y] are the vectors of interaction terms corresponding to the vectors of product attributes [A.sub.x] and [A.sub.y], respectively. That is, if C was subtracted from the income of an individual evaluating a product y with attributes [A.sub.y] and price [P.sub.y], the individual's expected utility would equal that from product x with attributes [A.sub.x] and price [P.sub.x]. In other words, if the change in attributes from [A.sub.x] to [A.sub.y] were welfare increasing, an individual would be willing to pay C more than [P.sub.y] to bring about the change in the attributes. Alternatively, if the change in attributes were welfare decreasing, an individual would have to be paid C to accept the change in attributes.

Given the functional form in (2), we derive 1 a closed-form solution for C:

(4) C = -[[[alpha].sub.A][DELTA](A) + [[alpha].sub.s][DELTA]([S.sup.i])]/[[alpha].sub.M] + [DELTA](P).

To derive the stochastic representation of compensating variation, c, we must take into account that the deterministic measure, C, ignores unobserved components. That is, not all individuals will choose y over x because the unobservable factors may outweigh the observable (deterministic) drivers of indirect utility (see Lancsar and Savage [2004] for an intuitive discussion of the derivation of stochastic representation of compensating variation). The stochastic representation of compensating variation is

(5) c = [1 - [PHI]([alpha][DELTA](L))]C

where the term in brackets is the probability the consumer chooses product y rather than x. We use the expressions for compensating variation in (4) and (5) to estimate individuals' WTP for the key product attributes. So, for example, we will calculate the amount of money (compensating variation or WTP) that would equate the utility received by a consumer between a base product (x) with no local designation, a corporate producer and no freshness guarantee and an alternative product (y) with the same attributes except that it also includes a local production designation. For simplicity, we will assume during these calculations that the price of the base and alternative products are equal (e.g., [DELTA](P) = 0). We will present the stochastic expression (5) and, for reference, the deterministic representation (4).

Survey and Empirical Methods

The data used in this article are drawn from responses to a survey instrument administered to 530 shoppers at 17 Midwestern locations in face-to-face interviews conducted during the period August 2005 to January 2006. The locations included six farm markets, four farmers' markets, and seven retail grocery stores located in Ohio. (2) Two grocery stores were located in small towns, two were in urban locations in a major city, and three were in surrounding suburban locations. Interviews took place between 10:00 a.m. and 4:00 p.m., Monday through Friday at the urban grocery stores and Saturdays 8:00 a.m. to 4:00 p.m. at the rural stores and farmers' markets. Interviewers randomly selected consumers, asked for their participation, and verified that each participant was at least 18 years of age. (3) After completing a series of eight choice experiments, the customers completed a survey that included attitudinal questions and elicited economic and demographic information. In total, 477 shoppers (90%) provided enough information to include in the regression analysis.

Descriptive statistics for the sample are reported in table 1. Our respondents had higher incomes and more formal education than the average residents of Ohio; respondents were also more likely to be white and female than would a representative sample from this state. In addition to differences between our sample and state averages, there also existed differences between respondents from the two shopping outlets. Grocery store shoppers had significantly higher incomes, greater food expenditures, and larger households than did direct market shoppers; they were also more likely to be female and white. Although our respondents are not representative of all residents of the state and there are differences between two identifiable subsamples of respondents, it is less clear how different the composition of our sample is from the universe of produce shoppers in Ohio and from those who frequent these two types of outlets.

Survey and Question Design

The survey begins with the conjoint instrument. Specifically, the preface to the conjoint question (figure 1) asks the respondent to suppose they were choosing between two baskets of fresh strawberries that were equivalent in all aspects except those attributes subsequently described. Two product profiles, presented side-by-side, show identical pictures of a basket of strawberries and provide information on four attributes: location of production (neighboring farm, within the state, within the United States, or left blank); name of firm producing the strawberries (Fred's Berry Farm or Berries Incorporated); freshness guarantee (yes or no); and purchase price ($2.00, $2.50, $3.00, $3.50, or $4.00). The full listing of attributes and their experimental levels are listed in table 2.

Respondents were then asked to state that they preferred product 1 or product 2 or were indifferent. The survey also elicited key demographic variables including household income, typical food expenditure levels, education, and age. A list of the definitions of variables included in the final model is provided in table 3.

Experimental Design

To generate the product profiles used in the survey, we use a variation of a standard full-factorial design. A standard full-factorial approach (see Hensher, Louviere, and Swait 1999 for an overview) begins by generating a pool of product profiles that includes all possible permutations of attribute levels. If this number is small, a respondent is asked to evaluate all permutations; analysis of the resulting choices allows for inference concerning the main effects of all attributes of the respondent's preferences as well as all possible interactions among attributes (i.e., first-order as well as all higher-order interactions).

As the number of attributes and attribute levels increase, however, the number of profiles grows exponentially and no single respondent can evaluate all permutations. Hence, the researcher randomly assigns subsets of profiles from the full factorial design to each respondent. If the researcher wants to infer individual preference structures, each respondent is typically assigned a large enough subset of profiles such that the main effects of attributes on preferences can be recovered. Such a subset is typically generated by an orthogonal fractional factorial design (Green and Srinivasan 1990). If respondents can effectively evaluate larger numbers of profiles, the design can be augmented such that key first-order interaction terms can also be consistently estimated.

If, as in our case, individual-level preference structures are not obtainable (e.g., if each respondent can only be asked to evaluate a limited number of profiles), then each respondent is randomly assigned several profiles from the full factorial design. Because a common utility function is assumed for all respondents, all levels of interaction terms can be estimated for the common utility function.