Data collection
The study used primary data collected from consumers who were mainly traders trading in various categories of commodities (e.g. agricultural produce commodities sellers, vendors, consumables, electrical installation materials, plumbing materials, small scale mobile phone accessories and small scale shoes sellers) as well as commercial drivers in the Kumasi metropolis using a structured questionnaire. Traders and commercial drivers were used because of the tedious work they do and because yoghurt is some kind of a readily available drink which is easily reached by these traders and drivers which is also able to boost their energy levels as soon as it is consumed. It employed the formula advanced by Yamane (
1967) in the determination of the sample size. The formula is given as:
$$ n=\frac{N}{1+N{e}^2} $$
(1)
where
n = desired sample size,
N = the finite size of the population,
e = maximum acceptable margin of error as determined by the researcher and 1 = a theoretical or statistical constant. According to the 2010 Population and Housing Census, the population of Kumasi metropolis is 2,035,064 (GSS
2012). That is, assuming everybody in the metropolis is a potential consumer. Therefore, with a 5% margin of error, the sample size for the study was calculated as:
$$ n=\frac{\mathrm{2,035,064}\ }{1+\mathrm{2,035,064}\ {(0.05)}^2}=400 $$
The Multi-stage sampling technique was employed in the study. In stage one, five (5) communities were systematically selected from a list of communities in the Kumasi metropolis obtained from the Kumasi Metropolitan Assembly. This was done by selecting a community from the list at random as the starting point and then selecting every kth community in the list or frame. “k” was calculated by dividing the total number of communities in Kumasi Metropolis by the sample size (5). The selected communities were Asokwa, Atonsu, Manhyia, Subin and Bantama. In the second stage, 80 consumers who were either traders or commercial drivers were randomly selected from each of the five (5) communities with 10 consumers selected from each of agricultural produce commodities sellers, vendors, consumables dealers, electrical installation materials dealers, plumbing materials dealers, small scale mobile phone accessories dealers, small scale shoes sellers as well as commercial drivers. With 400 questionnaires that were sent out during the data collection, only 315 returned and therefore the researchers had no option than to use it as the sample size for the study.
The questionnaire was divided into four parts. Part one was designed to gather information on socio demographic information of the respondents such as age, sex, educational background of respondents, marital status, religious affiliation, ethnic affiliation of respondent, occupation of respondent, household size, average monthly income of respondent, and average monthly income of household. The second part elicited information on respondents’ knowledge and awareness of tiger nut products and yoghurt. Information included in this section included frequency of purchase, quantity purchase and amount spent on tiger nut and yoghurt within a given time. Another aspect of part two talked about rating of attributes of yoghurt such as colour, taste, sweetness, thickness, consistency, price, general appearance, nutritional level and other attributes. The third part of the questionnaire was dedicated to consumers’ perception about tiger nut and yoghurt. The last part of the questionnaires collected data on consumers’ willingness to pay for tiger nut yoghurt.
Methods of data analysis
Descriptive statistics such as frequencies, percentages, mean and standard deviation were used to summarize the socioeconomic characteristics of the respondents. The important product attributes consumers considered in purchasing yoghurt were also ranked using Kendall’s Coefficient of Concordance (
W). Kendall’s Coefficient of Concordance (
W) measures the agreement on the scale of zero to one (0–1), with a value close to one (1) indicating greater agreement in rankings and a value close to zero (0) representing lower ranking agreement. The main hypothesis tested here is as follows:
Respondents ranked the attributes of yoghurt based on their experiences and decisions. These rankings were used to obtain the
W between the respondents, given as:
$$ W=\frac{12\sum {T}^2j-3{k}^2N\ {\left(N+1\right)}^2\ }{k^2N\ \left({N}^2-1\right)} $$
(2)
Where:
Tj is column totals,
N is number of attributes ranked,
k is number of respondents doing the ranking. Since
k is greater than 7, the following quantity is approximately normally distributed as a chi-squared on
N − 1 degrees of freedom:
$$ {X}_{\left(N-1\right)}^2=K\left(N-1\right)W $$
(3)
Chi-Squared (
X2) estimation and asymptotic significance level were used to determine the level of agreement in the ranking of the attributes. The attributes were categorised into two main perception statements, viz. nutritional/health and purchasing statements. A three (3)-point Likert Scale was also used to analyse consumers’ perception about tiger nut yoghurt. The mean score
\( \widehat{X} \) of a perception statement on the Likert Scale was computed as:
$$ \widehat{X}=\frac{\sum {f}_{ij}{x}_{ij}}{n} $$
(4)
Where
x is the ranked value of a perception statement
i on the three (3)-point Likert Scale and
f is the total number of respondents assigning value
x to a perception statement
i on the three (3)-point scale. The three (3)-point Likert Scale takes a ranked value of 1 if respondent
j agreed to a perception statement
i, 0 if respondent is undecided (neutral) and − 1 if disagreed. The parameter
n is equal to the total number of respondents. The overall perception index (
PI), which reflects the general agreement of all respondents on all the perception statements on the Likert Scale was computed as:
$$ PI=\frac{\sum \frac{\sum {f}_{ij}{x}_{ij}}{n}}{Number\ of\ Perception\ Statements} $$
(5)
All variables have their usual meaning.
Conceptually, using an indirect utility framework, the economic valuation construct can be represented as:
$$ {V}_0\left({Y}_0,{E}_0,{P}_0\right)={V}_0\left({Y}_0- WTP,{E}_1,{P}_0\right) $$
(6)
where, for a given consumer,
V0 is a base level of utility,
P0 represents existing prices,
Y0 is current income,
E1 and
E0 represent the cases of buying the product and not buying the product, respectively. Average consumer WTP is the amount of income a consumer would give up in order to gain a high level of tiger nut yoghurt,
E1,while maintaining a constant level of utility. Among contingent valuation method (CVM) practitioners, there is no consensus on the optimal bid format. Some researchers prefer one of a number of dichotomous choice elicitation variants, which are thought to simplify the cognitive task faced by respondents while at the same time providing incentives for the truthful revelation of preferences (Hanemann
1989; Cameron and James
1987). Others prefer open-ended formats as an increasing number of empirical studies have revealed that values obtained from dichotomous choice elicitation are significantly and substantially larger than those resulting from comparable open-ended questions (Desvousges et al.
1992; McFadden
1994; Banka et al.
2018). In a comparison of question formats, Reaves et al. (
1999) showed that the payment card format exhibited desirable properties pertaining to item non-response and protest bids relative to dichotomous choice and open-ended questions.
The current study employed the double bound contingent valuation model, proposed by Mäler and Vincent (
2003) and consisted of asking a second bid (follow-up question) to the respondent after asking the first question. If respondent
i answers yes to the first bid,
b1i, the second bid
b2i is higher and lower if otherwise. According to the standard procedure, Carson and Hanemann (
2005) assumed that respondents’ WTPs are independent of the bids and deals with the second response in the same manner as the first discrete choice question. Thus, the double bound model assumes that the same random utility mode generates both responses to the first and the second bids. As each individual is offered two separate bid opportunities, the simplest empirical strategy considers the combination of answers. Defining the potential outcomes as
Yi = (0, 1) = (
no,
yes) yields
Yi = (
Yi1,
Yi2), the observed outcomes for each individual. Assuming rationality, an individual does not agree to pay more than they are willing. Mathematically, the observed responses yield a set of intervals for estimating WTP which comprises:
$$ {Y}_i=\left(1,1\right)=\left( yes, yes\right) $$
(7)
$$ {Y}_i=\left(1,0\right)=\left( yes, no\right) $$
(8)
$$ {Y}_i=\left(0,1\right)=\left( no, yes\right) $$
(9)
$$ {Y}_i=\left(0,0\right)=\left( no, no\right) $$
(10)
For Donaldson et al. (
1998), the appropriate technique for econometric analysis of willingness to pay (WTP) data depends firstly on the type of question asked. For example, closed-ended questions and dichotomous choice with follow-up valuation only generate qualitative responses for WTP. This is why it is advised to use discrete choice models such as binary logit and probit for regression analysis (Greene
2005). For data elicited by using a payment scale, the most appropriate econometric methodology is grouped data regression, also called interval regression or ordered logit/probit (Greene
2005; Yasunaga et al.
2006; Bärnighausen et al.
2007). When using an open-ended question or a bidding process, the WTP values obtained are quantitative and several modeling methods have been proposed in the literature. For responses obtained through the bidding process, the first regression analysis mostly estimated standard linear models by ordinary least squares (OLS) (O’Brien and Viramontes
1994; Miedzybrodzka et al.
1995). However, the observed data for WTP responses are generally censored. When analyzing the distribution of WTP, we generally observe that the WTP variable does not take values below zero and has positive density at zero. The large proportion of zeros calls into question the continuity of the dependent variable and consequently the use of the classical multiple regression model. In the presence of data censoring, OLS estimation yields biased and inconsistent estimates as a result of its failure to account for the qualitative difference between the limit (zero) observations and non-limit (continuous) observations. Consequently, all conclusions on the determinants of WTP are potentially erroneous (Kurth et al.
2004). Therefore, OLS is one of the least preferred methods to use when it comes to estimating WTP since it cannot capture the full effect of the qualitative data expressed as quantitative data.
The study also posed an open-ended question and the responses for this question were employed in the econometric analysis. Because some variables are censored around zero WTP, Tobit model is an appropriate approach to follow. That is, the Tobit model is the correct alternative frequently proposed for censored data in contingent valuation literature in economics (Kurth et al.
2004). Tobit model is preferred for estimating willingness to pay because it is designed in such a way that it captures the full effect of the variable. Hence the coefficients that are inconsistent and biased in OLS are consistent in Tobit regression. The underlying assumption in the Tobit model is that the same specification is used both for the continuous and the zero decision processes. This implies that the Tobit specification is relevant when all zero realizations represent an economic decision, i.e. a real zero preference for the product under evaluation.
The Tobit model identifies characteristics of consumers that determine WTP for the tiger nut yoghurt. Following Greene (
2005), the Tobit model can be generally expressed as:
$$ {\displaystyle \begin{array}{ll}{WTP}_i={X}_i\beta +{u}_i& {X}_i\beta +{u}_i>0\\ {}{WTP}_i=0& {X}_i\beta +{u}_i\le 0\end{array}} $$
(11)
where for the
ith consumer,
WTPi is individual consumer willingness to pay amount,
Xi is a
kx1 vector of known explanatory variables,
β is a
kx1 vector of unknown parameters common to all consumers and
ui is a random disturbance term which is independently and normally distributed with zero mean and variance. Then, by using the maximum likelihood estimation, the
βs are estimated on the basis of
N observations on
WTPi and
Xi. This is basically an estimation with censored normal regression model. The log likelihood of the Tobit model is specified as:
$$ \ln L=\sum \limits_{y_i>0}-\frac{1}{2}\left[\log \left(2\pi \right)+\ln {\sigma}^2+\frac{{\left({y}_i-{X}_i^{\hbox{'}}\beta \right)}^2}{\sigma^2}\right]+\sum \limits_{y_i=0}\ln \left[\frac{1-\phi \left({X}_i^{\hbox{'}}\beta \right)}{\sigma}\right] $$
(12)
That is, maximizing this likelihood function with respect to
β and
σ gives the maximum likelihood estimates of these parameters. Empirically, Table
1 presents a description of the variables employed in the model. Assuming the random error is independent and normally distributed across respondents, the expected WTP for an observation drawn at random is:
$$ E(WTP)=\Phi \left(\frac{X\beta}{\sigma}\right) X\beta +\sigma \phi \left(\frac{X\beta}{\upsigma}\right) $$
(13)
where Φ represents the normal distribution function,
ϕ represents the normal density function, and
σ represents the standard deviation. Furthermore, the expected value of WTP for observations above zero, here called
E(
WTP∗), is simply
Xβ plus the expected value of the truncated normal error terms (Greene
2005). Then, the expected WTP can be expressed as:
$$ E(WTP)=\Phi \left(\frac{X\beta}{\sigma}\right)E\left({WTP}^{\ast}\right) $$
(14)
Table 1
Variables employed in the study and their a priori expectations
Willingness to Pay (WTP) | Amount consumers are willing to pay for 500 ml of tiger nut yoghurt (Gh¢) | | |
Age | Age of consumer, measured in years | – | Loureiro and McCluskey ( 2000), Bee and Selamat ( 2010), Yahaya et al. ( 2015) and Dolgopolova and Teuber ( 2016). |
Sex | Gender of consumer, measured as a dummy, 1 for male and 0 otherwise | +/− | Yahaya et al. ( 2015), Bee and Selamat ( 2010) |
Education | Educational level of consumer, measured in both levels of education and years of schooling | + | Noor et al. ( 2010), Bee and Selamat ( 2010) and Balogh et al. ( 2016) |
Household size | Number of individuals living with respondent | – | |
Monthly Income | Consumer’s monthly income (Gh¢) | + | Loureiro and McCluskey ( 2000), Basarir et al. ( 2009), Bee and Selamat ( 2010), Meng et al. ( 2014), Fang 2015; Yahaya et al. ( 2015), Balogh et al. ( 2016), Dolgopolova and Teuber ( 2016) |
Price of yoghurt | Price consideration in purchasing yoghurt, measured as a dummy, 1 if consumer considers price when purchasing yoghurt and 0 otherwise | – | |
General Appearance | Appearance consideration in purchasing yoghurt, measured as a dummy, 1 if consumer considers the appearance of the yoghurt when purchasing it and 0 otherwise | + | Straub and Thomassin ( 2006) |
Awareness | Awareness of yoghurt being produced from tiger nut, measured as a dummy, 1 if consumers are aware of producing yoghurt from tiger nut and 0 otherwise | + | |
It should be noted that unlike linear models, the marginal effect or partial derivative for a given explanatory variable is nonlinear and thus not equal to
βi. The decomposition of this marginal effect that is obtained by considering the effect of a change in the
ith variable of
X on WTP is expressed as:
$$ \frac{\partial E(WTP)}{\partial {X}_i}=\Phi \left(\frac{X\beta}{\sigma}\right)\left(\frac{\partial E\left({WTP}^{\ast}\right)}{\partial {X}_i}\right)+\left({WTP}^{\ast}\right)\left(\frac{\mathrm{\partial \Phi}\left(\frac{X\beta}{\sigma}\right)}{\partial {X}_i}\right) $$
(15)
Intuitively, the total change in WTP can be disaggregated into two parts: (1) the change in WTP of the above zero bids, weighted by the probability of being above the zero bid; and (2) the change in the probability of being above the zero bid, weighted by the expected value of WTP if above the zero bid. Equation (
14) can be evaluated at the mean of the
Xs,
\( \overline{X} \) with estimates of
β and
σ. The fraction of the total marginal effect due to the effect above the zero bid is
$$ \frac{\partial E\left({WTP}^{\ast}\right)}{\partial {X}_i}=1-\frac{X\beta \phi \left(\frac{X\beta}{\sigma}\right)}{\Phi \left(\frac{X\beta}{\sigma}\right)}-\frac{\phi {\left(\frac{X\beta}{\sigma}\right)}^2}{\Phi {\left(\frac{X\beta}{\sigma}\right)}^2} $$
(16)
We estimated total marginal effect,
\( \frac{\partial E(WTP)}{\partial {X}_i} \), using Eq. (
14) and the fraction of the total marginal effect above the zero bid,
\( \frac{\partial E\left({WTP}^{\ast}\right)}{\partial {X}_i} \), using Eq. (
15).
We assume in this paper that the discrete decision of willingness to pay for tiger nut yoghurt and the continuous decision of the amount consumers are willing to pay are made simultaneously and that the same factors had the same effects on the two decisions. The Tobit model is able to combine the probit and truncated models of Cragg’s Double Hurdle Model to obtain the joint coefficient,
α, in case the two aforementioned decisions are jointly made, which explains both the discrete decision of willingness to pay for tiger nut yoghurts and the continuous decision of the amount consumers are willing to pay. To confirm the appropriateness of the Tobit model, the Tobit model was tested against Cragg’s model by estimating a probit, a truncated regression, and a Tobit model with the same variables (
Xi) and computing the following likelihood ratio statistic (Katchova and Miranda
2004; Greene
2005; Wiredu et al.
2015; Asante et al.
2018):
$$ \lambda =2\left(\ln {L}_{probit}+\ln {L}_{truncated\ regression}-\ln {L}_{Tobit}\right) $$
(17)
where
λ is distributed as chi-square with
R degrees of freedom (
R is the number of independent variables including a constant). The Tobit model will be rejected in favor of Cragg’s model if
λ exceeds the appropriate chi-square critical value.