Data
This paper used secondary data from the 2014 Zambia Household Health Expenditure and Utilisation Survey (ZHHEUS). The Central Statistical office with the support from the Ministry of Health and the University of Zambia conducted the survey to inform the National Health Accounts estimation and the development of the healthcare financing strategy. Using a two stage stratified sampling approach, it covered a total of 12000 households, including some 59 500 individuals, in all provinces and districts of the country (Ministry of Health, 2015).
Eliciting Willingness To Pay
Within the questionnaire, the bidding game version of contingent valuation was used to estimate willingness to pay for household head and other members of the family. Nine iterations were used in the bidding game and the starting bid was K3 000 per month, followed by the bids K2 000, K1 000, K500, K300, K100, K50, K20 and then K10. The final bid question is a binary response question that indicates if the respondent is willing to pay less than K10 per month or not. This study mainly distinguished respondents who were willing to pay for the scheme from those that were not willing to pay at all.
Outcome Variable
Outcome variable
The health outcome studied was willingness to pay, a binary variable. The English translation of the relevant survey question was: “Are you willing to pay for national social health insurance scheme?”
Socioeconomic Rank
Per capita expenditure was used as the measure of socioeconomic status. Ekman (2007) explains that in situations with reliable income statistics and a large section of the population in salaried work, socioeconomic status would be measured by the reported income from labour and capital. But in settings, such as those of most low-income countries, expenditure is taken as that measure. The use of per capita expenditure as a choice of socioeconomic status is necessitated by the relatively large sections of the population in unsalaried labour and the significant seasonal variations in household income (Ekman, 2007).
Factors
The following factors were used in the decomposition analysis.
Table 1
Description of the factors
Variable | Definition | Description |
Age | Age of household head at last birthday | Continuous |
Female | Indicate gender of household head, Encoded as Female = 1, Male = 0 | Dichotomous |
Marital status | Indicate the marital status of household head: Never Married = 1, married = 2, | Categorical |
| cohabiting = 3, Separated = 4, Divorced = 5, Widowed = 6. | |
Education | Highest attained level of formal education by household head: 0 = None; 1 = Low; | Categorical |
| 2 = Middle and 3 = High | |
Employment status | Indicates employment type of the household head: unemployed = 1, informal employment = 2 and formal employment = 3 | Categorical |
Religion | Denomination of household head: 1 = Catholic, | Categorical |
| 2 = Protestant, 3 = Jehovah’s witness, 4 = Muslim, 5 = Traditionalist, 6 = Atheist and 7 = Others | |
Household size | Number of people in a household | Continuous |
Children | Number of children below the age of 5 years in a household | Continuous |
Elderly | Number of persons above the age of 65 years in the household | Continuous |
Urban | Location of household: 0 = Rural and 1 = Urban | Dichotomous |
Visits | Total outpatient visits by household members in the last four weeks | Continuous |
Days | Total number of inpatient days by household members | Continuous |
Illnesses | Indicate whether any household member suffers from a chronic illness: | Dichotomous |
| 0 = No, 1 = Yes | |
Insurance | Health Insurance coverage of a household: 1 = Insured, 0 = Uninsured | Dichotomous |
Per capita expenditure | Total per capita monthly household expenditure in Kwacha | Continuous |
Note: All individual-level characteristics refer to the characteristics of the respondent that answered the questions on household willingness to pay, namely the household head.
Concentration Curve And Concentration Index
Analyses on the extent of households’ socioeconomic inequalities in willingness to pay were done in two stages. The first stage was to use a concentration curve (CC) to examine socioeconomic inequalities in willingness to pay for National Social Health Insurance. In the second stage, a Concentration Index (CI) was used. The standard concentration index is defined below:
$$CI=\frac{2}{\mu }Cov\left(h,r\right)$$
2
Where\(h\) is the willingness to pay for the scheme, \(r\) is the fractional rank of a household in the expenditure score distribution, \(Cov\) is covariance and µ represents the mean of the willingness to pay values. Since the outcome variable is binary, Erreyger’s corrected concentration index was used. The index is desirable as it satisfies properties required for bounded variables (Erreygers, 2006). The equation for the Erreyger index is as follows:
$$CCI=\frac{4\mu }{b-a}\times C \left(3\right)$$
where CCI is the corrected concentration index, µ is the mean of the willingness to pay, \(a \text{a}\text{n}\text{d} b\) are minimum and maximum values of willingness to pay, respectively, and C the standardised concentration index defined in Eq. (2). This study makes use of the coindex functionality in STATA to calculate concentration index and concentration curve (O’Donnell et al., 2016).
The concentration index can either be positive or negative. The sign of the concentration index explains the relationship that exists between willingness to pay and position in the wealth score distribution. If the concentration index is zero, it means that there is no inequality in the distribution of willingness to pay by wealth and hence the concentration curves will coincide with the line of equality. A negative value of the concentration index is obtained if willingness to pay is disproportionately concentrated among the poorest households while a positive value of concentration index suggests willingness to pay is concentrated among the richest households. The value of the concentration index ranges between − 1 and + 1 and the concentration index provides information about the strength of the relationship (O'Donnell et al., 2008). The closer the absolute values of the concentration index to one, the greater the level of inequality.
Decomposition Analysis
After estimating concentration index, the causes of the socioeconomic inequalities were determined. Decomposing socioeconomic inequalities helps to uncover specific factors that are potentially modifiable by policy decision makers. This was done using the Wagstaff et al. decomposition method proposed by Wagstaff, et al. (2003).
Wagstaff Et Al. Decomposition
Wagstaff, et al. (2003) proposed an approach that identifies factors that explain the socioeconomic inequalities in the willingness to pay for the National Social Health Insurance Scheme. Following Wagstaff, et al. (2003), Eq. (4) below depicts the linear relationship between willingness to pay and its determinants:
$${y}_{i}=\alpha +{\sum }_{k=1}^{K}{\beta }_{k}{x}_{ik}+{\epsilon }_{i}$$
4
where \(y\) is the binary outcome variable for willingness to pay,\(\alpha\) is a constant,\(\beta\) measures the relationship between each explanatory factor\(\left(x\right)\)and the willingness to pay variable, and ε the error term. Like the concentration indices, the decomposition technique used for the standard concentration index (CI) was modified to suit the corrected concentration index (CCI) as follows:
$$CCI\left(y\right)=4\left[{\sum }_{k=1}^{K}{\beta }_{k}{\stackrel{-}{x}}_{k}CI\left({x}_{k}\right)+{GC}_{\epsilon }\right] \left(5\right)$$
Where\({ \beta }_{k}{\stackrel{-}{x}}_{k}\) denotes the elasticity of willingness to pay to marginal changes in the \({k}^{th}\) factor. \(CI\left({x}_{k}\right)\) denotes the concentration index of the \({k}^{th}\) contribution factor, while \({GC}_{\epsilon }\) denotes the generalized concentration index of the error term. The first term in equation \(\left[{\beta }_{k}{\stackrel{-}{x}}_{k}CI\left({x}_{k}\right)\right]\) represents the contribution of factor \(k\) to socioeconomic inequality in willingness to pay. It constitutes the deterministic component of the willingness to pay concentration index. The second term \(\left({GC}_{\epsilon }\right)\) captures the unexplained component or the residual (O'Donnell et al., 2008).
The Generalised Linear Model (GLM) with binomial family and logit link was used to decompose the binary outcome variable. The use of GLM with binomial distributed outcome variable and specifying the identity link function is suitable choice in the decomposition analysis of the binary outcome, because it considers the structure of the distribution while preserving the link between the regressors and dependent variables (Vasoontara et al., 2010).
The contribution made by each factor is dependent on the sign and size of the calculated elasticity and concentration index for each factor. All things being equal, an increase (decrease) in inequality in \({\stackrel{-}{x}}_{k}\)(i.e \(CI\left({x}_{k}\right)\)will increase (reduce) the degree of inequality in willingness to pay (Wagstaff et al., 2003). This study also computed bootstrapped standard errors using 500 replications to determine whether the contribution of each factor to socioeconomic inequality in willingness to pay is statistically significant. This study used the variables in Table 1 as contributing factors in the decomposition. All categorical variables were converted to dummies in the Wagstaff et al. decompositions. Data analyses were conducted in STATA software version 16.