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Economic Model

The hedonic price regression can be traced back to at least Court (Reference Court1938). Unlike the traditional theory of consumer demand in which goods are the direct objects of utility, the theory of hedonic pricing is based on the notion that utility is, in fact, derived, not from goods per se but from their hedonic attributes. Rosen (Reference Rosen1974) derives a model of product differentiation in a competitive market and provides an interpretation of the estimated hedonic (implicit) prices. Assume a market of differentiated products that are characterized by n attributes, z ₁, …, z_n. It is assumed that consumers have the same perception of the quantity of attributes in each product. Each product has an observed market price such that p(z) = p(z ₁, …, z_n). Rosen then derives consumption and production decisions and shows that in equilibrium, the implicit price function p(z) represents a joint envelope of a buyer's value function and seller's offer function.

Later, Ladd and Suvannunt (Reference Ladd and Suvannunt1976) derive the consumer goods characteristics model based on assumptions that specifically define the behavior of individual consumers. In this model, a product's observed market price is a weighted linear combination of the product's attributes, where each weight is the marginal implicit price of an attribute. Suppose Z _0j is the total quantity of attribute j provided by all products consumed, Z_ij is the quantity of attribute j provided by one unit of product i, Z _0m+i is the quantity of unique attribute m provided by product i, q_i is the quantity consumed of product i, and I is income. Therefore,

(1)$$Z_{0j} = f_i\lpar {q_1\comma \;\ldots \comma \;q_n\semicolon \;\;Z_{1j}\comma \;\ldots \comma \;\;Z_{nj}} \rpar \;\hbox{and}\;Z_{0m + i} = f_{m + i}\lpar {q_i\semicolon \;\;Z_{im + i}} \rpar $$

The consumer maximizes

(2)$$U = U\lpar {Z_{01}\comma \;\;\ldots \comma \;Z_{0m}\semicolon \;\;Z_{0m + 1}\comma \;\ldots \comma \;Z_{0m + n}} \rpar $$

subject to

(3)$$\mathop \sum \limits_i p_iq_i \le I$$

Hence,

(4)$$p_i = \mathop \sum \limits_j \lpar {\partial Z_{0j}/\partial q_i} \rpar [ {\lpar {\partial U/\partial Z_{0j}} \rpar /\lpar {\partial U/\partial I} \rpar } ] + \lpar {\partial Z_{0m + i}/\partial q_i} \rpar [ {\lpar {\partial U/\partial Z_{0m + i}} \rpar /\lpar {\partial U/\partial I} \rpar } ] $$

The term in the first square brackets is the marginal rate of substitution between income (or expenditure according to equation 3) and attribute j. It is the marginal (implicit) price of attribute j. Notice that

(5)$$\displaystyle{{\lpar {\partial U/\partial Z_{0j}} \rpar } \over {\lpar {\partial U/\partial I} \rpar }} = \displaystyle{{\partial I} \over {\partial Z_{0j}}} = \displaystyle{{\partial E} \over {\partial Z_{0j}}}$$

where E is the total expenditure on all products and (δZ _0j/δq_i) is the marginal yield of attribute j by product i. Thus, equation 4 implies that the observed market price of a product is equal to the sum of the marginal values of the attributes, where each attribute's marginal value is the quantity of the attribute per marginal unit of the product (i.e., yield) multiplied by the attribute's hedonic price. Equation 4 is the implicit (hedonic) price equation and can be rewritten as follows:

(6)$$p_i = \mathop \sum \limits_{\,j = 1}^m p_{ij}Z_{ij} + u$$

where the coefficients p_ij are the hedonic or implicit marginal prices of attributes, which can be interpreted as the marginal WTP for a change in the attributes since they encapsulate consumers’ preferences (Nerlove Reference Nerlove1995; Costanigro, McCluskey, and Mittelhammer Reference Costanigro, McCluskey and Mittelhammer2007), and u is the random error term. If an additive intercept is added to equation 6, the coefficients can be interpreted as premiums or discounts over a base price defined by the intercept.

To analyze market sorting, we apply latent class (LC) analysis to equation 5. LC analysis is a set of techniques used to model situations in which the observed data are comprised of a finite number of distinct classes (subgroups), but class membership is not directly observed (Canette Reference Canette2018). LC models permit disaggregation of a sample into existing latent classes using one or more observed dependent variables, which may be categorical or continuous.Footnote ² In this study, we apply a finite mixture linear regression model,Footnote ³ a type of LC maximum-likelihood-based model derived from a mixture of underlying distributions, and use one dependent variable (Greene Reference Greene2008, p. 558; Costanigro, Mittelhammer, and McCluskey Reference Costanigro, Mittelhammer and McCluskey2009; Canette Reference Canette2018).

Following Greene (Reference Greene2008, p. 559), if a population consists of a mixture of two underlying normal distributions,Footnote ⁴ the contribution to the likelihood function for individuals or products in classes 1 and 2 is, respectively,

(7)$$f\lpar {y_i{\rm \vert clas}\hbox{s}_i = 1} \rpar = N[ {{\rm \mu }_1\comma \;{\rm \sigma }_1^2 } ] $$

(8)$$f\lpar {y_i{\rm \vert clas}\hbox{s}_i = 2} \rpar = N[ {{\rm \mu }_2\comma \;{\rm \sigma }_2^2 } ] $$

where y_i is the outcome variable for individual or product i. Assuming that the proportion of individuals or products in class 1 is Prob(class_i = 1) and those in class 2 is (1 − Prob(class_i = 1)), and z_i is the vector of variables (attributes) that might explain class probabilities, then the conditional density for product i is

(9)$$f\lpar {y_i{\rm \vert }z_i} \rpar = \displaystyle{{\hbox{Prob}\lpar {\hbox{class} = 1{\rm \vert }z_i} \rpar \hbox{exp}[ {-\lpar 1/2\rpar {\lpar {y_i-{\rm \mu }_1} \rpar }^2/{\rm \sigma }_1^2 } ] } \over {{\rm \sigma }_1\sqrt {2{\rm \pi }} }} + \displaystyle{{[ {1-\hbox{Prob}\lpar {\hbox{class} = 1{\rm \vert }z_i} \rpar } ] \exp [ {-\lpar 1/2\rpar {\lpar {y_i-{\rm \mu }_2} \rpar }^2/{\rm \sigma }_2^2 } ] } \over {\sigma _2\sqrt {2{\rm \pi }} }}$$

The usual logit model can be used to parameterize the probabilities. The log-likelihood, in this case, features two random variables; the outcome variable y _i and class_i. For the more general case of K classes, the finite mixture model for variable y _i can be specified as

(10)$$f\lpar {y_i{\rm \vert clas}\hbox{s}_i = k\comma \;\;z_i} \rpar = h_k\lpar {y_i\comma \;z_i\comma \;{\rm \gamma }_k} \rpar $$

where h_k is the density conditioned on class k, z_i is a vector of covariates, and γ_k is the kth parameter vector. However, even if it is impossible to conjecture the classes present in the sample, as is the case in this study, the model remains amenable to estimation as illustrated by Canette (Reference Canette2018).

Estimated hedonic prices can be used to calculate the change in CS due to a nonmarginal improvement in attributes. As in Unnevehr (Reference Unnevehr1986), we use a partial equilibrium model to this end. Improvement in a quality attribute causes a rightward shift in demand, and the gain, G, in CS per unit of the product consumed by a given class of consumers can be calculated as follows:

(11)$$G = \mathop \sum \limits_{\,j = 1}^m \lpar {Z_{ij}^\ast -Z_{ij}} \rpar p_{ij}$$

where $Z_{ij}^\ast$ is the new value of attribute j per unit of the product and p_ij is the estimated hedonic price for a given class of consumers. At the aggregate level, assuming the infinitely elastic supply of the improved product and constant production costs, the level of demand for the product after quality improvement, $q_i^\ast$, is

(12)$$q_i^\ast = q_i\lpar {1 + {\rm \varepsilon }_{ij}^q } \rpar $$

where

(13)$${\rm \varepsilon }_{ij}^q = -\displaystyle{{\,p_{ij}Z_{ij}} \over {\,p_i}}{\rm \varepsilon }^\ast $$

is the elasticity of quantity consumed of the product with respect to the quantity of attribute j, and ɛ* is the own-price elasticity of demand for product i. These assumptions do not permit gain in producer surplus. The total gain in CS is

(14)$$\hbox{CS} = q_iG + \displaystyle{1 \over 2}\lpar {q_i^\ast -q_i} \rpar G$$

Unlike in Unnevehr (Reference Unnevehr1986), our study requires an estimate of ɛ* for each class of consumers. However, we do not have the necessary data to empirically obtain estimates of it, and turning to the literature, we find a paucity of empirical studies that have estimated ɛ* for rice in Benin. For all we know, the recent study by Codjo (Reference Codjo2019) has been the only attempt to estimate the parameter; he estimates ɛ* for three income groups (low, middle, and high) and three levels of rice quality and finds it to range between −0.91 and −2.69. Therefore, we use the average of Codjo's (Reference Codjo2019) estimates, and we conduct a sensitivity analysis for the relevant consumer classes in order to ascertain the robustness of our model's results.

Data and Estimation

In a study like this that aims to generate aggregate demand and CS based on sample data, ensuring that the sample is representative of the population is imperative. At the time of this study, a list of all rice retailers in the country and the types or brands of rice they sell was unavailable. Moreover, the cost of obtaining it and collecting samples from retailers who are dispersed throughout the country would have been prohibitive. Nonetheless, we were able to obtain rice samples representative of the rice consumed in the country's four official geopolitical and cultural regions, namely Northeast, Northwest, Central, and South. For each region, a list of all food markets was obtained, from which a random sample of markets was drawn. The number of markets randomly selected from each region was proportional to the region's share of markets in the country. Thus, a total of 33 markets were randomly selected: South (20), Central (4), Northwest (6), and Northeast (3). In each market, rice retailers and the type(s) of rice they sell were identified, and rice samples randomly collected. Only one sample per rice type or brand was obtained from each selected retailer. A total of 316 rice samples, which is adequate for our finite mixture model (Van Horn et al. Reference Van Horn, Jaki, Masyn, Howe, Feaster, Lamont, George and Kim2015), was obtained: South (176), Central (35), Northwest (64), and Northeast (41).

The distance of each market (in km) from the Cotonou port was recorded. The Northeast and Northwest of Benin are about 800–1,000 km from Cotonou port, and the populations there have a history of rice cultivation. The Northeast is the most important rice-producing region in Benin and harbors one of the country's rice sector development hubsFootnote ⁵—Malanville. The Central region is about 300–500 km from Cotonou port and harbors the other rice hub, Glazoue. Unlike Malanville, which is irrigated, the Glazoue hub is rainfed. The South is close (<300 km) to Cotonou port and is home to Cotonou city, the largest city in Benin, and to Porto-Novo, the country's political capital. Most of the inhabitants of this region do not have a rice cultivation history.

A detailed description of the grain quality analysis that produced data on the attributes used in the hedonic pricing model is available from the authors on request, and summary statistics of the physical (extrinsic) and chemical (cooking) attributes used in the model are presented in Table 1. Extrinsic attributes include moisture content, head rice (proportion of intact grains), length–width ratio (grain shape), chalkiness (white belly/opaque portion of a rice grain), lightness/whiteness, distance (km) of a market from Cotonou port, market type (1 = rural, 0 = urban), rice type (1 = parboiled, 0 = nonparboiled), and origin (1 = imported, 0 = local). A high moisture content of above 14 percent is undesirable as it leads to a deterioration of grain during storage (Tang et al. Reference Tang, Ndindeng, Bigoga, Traore, Silue and Futakuchi2019). The distance of a market from the port, type of market, and origin of rice are informational cues that may influence consumers’ perception of the quality of rice. For instance, the type of market may account for ease of access to market and quality information about the product, while the origin of a product may influence consumers’ perception of its quality (Elliott and Cameron Reference Elliott and Cameron1994), in addition to capturing consumers’ ethnocentric attitudes.

Table 1. Summary Statistics of Variables Used in the Analysis (n = 316)

Chemical attributes include amylose content, setback viscosity, and alkali spreading value (ASV). Amylose content determines the texture of cooked rice, whereby the greater the amylose content, the drier, the less sticky, and less tender the rice is. Setback viscosity, an indicator of the pasting quality of rice, determines the firmness of cooked rice, with higher values indicating greater firmness after cooling. The ASV is used to measure gelatinization temperature and, hence, cooking time. The higher the ASV, the lower the gelatinization temperature and, hence, the shorter the cooking time.

Summary and Conclusions

This study uses a hedonic price model to examine market sorting in the Beninese rice market and examines the effect of grain quality improvement on CS. It applies data obtained from laboratory tests of grain quality traits. Controlling for, among other things, two attributes, namely the origin and type of rice that are commonly used to characterize the country's consumer categories, the study has established that there are at least three classes of consumers in the Beninese rice market, manifesting in proportions of 5, 56, and 39 percent. Of the three classes, the smallest class pays the highest price, significantly discounts parboiled rice, and prefers imported to local rice. The second class also discounts parboiled rice but does not place a significant value on the origin of rice, whereas the third category values neither the origin nor the type of rice. Similarly, preferences for other quality attributes vary from one class to another.

Hedonic prices obtained for head rice and chalkiness are applied to a partial equilibrium model to determine the welfare implications of quality improvement for categories 2 and 3. The first important outcome from this exercise is the computed elasticities of demand for rice with respect to the quantities of the two attributes. This is especially informative because these elasticities enable breeders and private seed companies to quickly understand how consumers will respond to grain quality improvement. We then find that an increase in head rice and a reduction in chalkiness autonomously lead to modest gains in consumer welfare.

These results have two important implications for upgrading rice value chains in Benin and other African countries. First and foremost, any upgrading strategy ought to begin by recognizing potential heterogeneity in consumer preferences for rice quality attributes and that existing product categories may not fully capture the heterogeneity. As demonstrated in this study, each class of consumers has a unique hedonic price function and almost all quality attributes—head rice, grain shape, chalkiness, lightness, cooking time, and amylose content—can be targeted for product upgrading. Therefore, upgrading rice value chains requires information on the nature of demand or hedonic price function of the different categories of consumers.

Second, knowledge of the impacts of quality improvement on consumer welfare is informative for setting priorities for spending on research and development. For instance, although our estimates are generally small on economic impact, we see that an improvement in head rice leads to far greater benefits for consumers than an improvement in chalkiness. Our analysis, therefore, demonstrates a straightforward application of hedonic pricing and partial equilibrium methods to evaluating priorities for crop improvement and value chain upgrading. Currently, there are ongoing efforts by the CGIAR Consortium to develop product profiles of mega rice varieties in Africa in order to achieve certain development outcomes. The analysis used in this study can be integrated in the proposed three-stage approach to product profiling. Of course, it would be even more enlightening to consider net welfare changes by accounting for impacts on producers.