Statistical estimation of WTP for malaria
The mean WTP for malaria was estimated statistically using interval regression since the data were gathered using payment cards. The regression model below was estimated to give coefficients which were used in estimating mean WTP. In the proceeding section, the determinants of WTP are analysed. A parametric function was used to estimate the mean WTP for grouped data following [
17]. According to this approach, the mean of the untransformed dependent variable (i.e. WTP) is estimated using
where,
and
are the expected values (or means) of the significant predictors of WTP (see results below) while the β'
s are their respective coefficients. σ
2 is the variance of the model. The mean WTP equation above calculates the average WTP presented below, which was influenced by at least five explanatory variables identified as reported in the regression results in Table
2 in the index. The mean WTP was multiplied by the population of Zambia in order to derive the aggregate economic value of malaria treatment. This estimate can be interpreted as the economic value of, or a measure of demand for, an ideal malaria treatment programme.
Table 2
Household WTP estimates
Mean WTP | 46.67 (ZAM K233,380.02) |
Median | 35.92 (ZAM K179,624.92) |
Aggregate WTPa | 77,076,666.30 |
Aggregate WTPb | 56,794,956.07 |
Per capitaa | 7.08 |
Per capita
b
|
5.22
|
% GDPa | 1.8 |
Both the mean WTP and median WTP are presented as recommended in the literature [
18]. As can be seen the median is much lower than the mean due to the sensitivity of the mean to skewness in income. However, in further analysis mean WTP is used on the grounds that from a CBA point of view the mean is the theoretically correct statistic to use. The mean, when multiplied by the population size, gives the total or aggregate benefits which have been reported in table
2 for Zambia [
18].
The magnitude of WTP for malaria treatment relative to Zambia's gross domestic product per capita suggests that malaria treatment has significant economic value. Despite the common threat of over-valuation in many WTP surveys, these results do appear to be in line with findings from studies in similar socio-economic contexts. A similar study found a WTP of about US$2.00 per capita for
an increase in households' access to more and better treatment and diagnostic services for malaria in Nepal [
19].
The unpublished national health accounts estimates indicate that total health expenditure in Zambia was about K917 billion or approximately US$230 million in 2002 United States dollars. This implies that the desired treatment programme for malaria represents 34% of current total health expenditure. However, this ratio would conceivably be substantially less than 34% of desired total health expenditure.
Socio-economic and demographic determinants of WTP
A regression model was formulated and estimated to capture the determinants of WTP for malaria treatment. Initially, the model included nine explanatory variables and their expected signs (Table
3). To capture income, the survey relied upon self-reported income. Three dummy variables were used to depict the impact of health status on WTP. First, HS1 elicited an overall assessment of the household health status over the preceding six months. The variable HS1 was defined to carry a one if the respondent had poor self-assessed family health status, and zero otherwise. Similarly, the second (HS2) was one if there had been an occurrence of acute short-term illness (a maximum of 21 days of full recovery) in last six months and zero otherwise.
Table 3
Determinants of willingness to pay and expected signs
Income | + |
Education of household head | + |
Education of spouse | + |
Location (rural or urban) | +/- |
Poor Health status | + |
Sex of respondent | ? |
Sex of household head | ? |
Household size | +/- |
Age | +/- |
The last dummy (HS3) carried a value of one if the respondent or any member of the family suffers from a chronic illness and zero otherwise. HS3 captured existence of chronic illness which was operationalized as an illness which requires lengthy treatment or regular visitations to a health facility of say once or twice a month continually for at least six months. This typically captured ill-health associated with long term conditions such as diabetes, tuberculosis, stroke, and so on. Of course it can be difficult to distinguish consistently chronic from acute ill-health. The survey relied upon the respondents' own self-assessment of what is chronic and what is not. Local terminologies such as "on and off" were useful during the survey in characterising chronic illness.
The variable Education was assigned a value of one if the head of the household had attained at least grade nine, and zero otherwise. In Zambia attainment of grade nine is conventionally considered to be the benchmark for basic education and functional literacy. Other variables include age of household head, location and sex of household head. Age was a continuous variable while the variables sex of respondent or household head were assigned a value of one for males and zero for females. Location was assigned a value of one if respondent lived in an urban area and zero otherwise.
After taking account of diagnostic problems, particularly multicolinearity, normality and specific errors, the model below was specified. In particular, income and WTP variables were transformed to natural logarithms in order to minimize normality problems and also to avoid heteroscedasticity. The variables location, age of spouse and education of spouse were dropped on account of their correlation with income, age of household head and education of household head, respectively. Further, the robust regression option, which uses the maximum likelihood (ML) estimation procedure, was adopted in order to derive heteroscedasticity-corrected standard errors as well as parameter estimates.
logWTPMAL = β0 + β1 logINCOM
i
+ β2EduHead
i
+ β3HS 1
i
+ β4HS 2
i
+ β5HS 3
i
+ β6SEX
i
+ β7HHSiz
i
+ β8AGESQ
i
+ ε
i
The regression results are presented in Table
4. As can be seen the coefficient on the variable income is positive and significant at the 1% level.
Table 4
Regression results of determinants of stated WTP
Log Income | 0.2914 | 0.04940*** |
Log AGESQ | -0.0001 | 0.00008 |
HS1 | 0.2908 | 0.13867** |
HS2 | 0.3184 | 0.2446** |
HS3 | 0.1600 | 0.12098 |
Education head | 0.2047 | 0.12384* |
Household Size | 0.0349 | 0.02763 |
Sex Respondent | -0.0434 | 0.11194 |
Constant | 4.7380 | 0.73705** |
Sigma | 0.7815 | 0.0331*** |
Log-likelihood | 476.775 | |
McFadden's R-squared | 0.07 | |
Wald Chi-sq stat | 98.88*** | |
No. of Observations | 274 | |
The estimation results presented in Table
4 generally indicate that the empirical model performed quite well. In particular, measures of overall model significance, namely the F and log likelihood statistics were highly significant, indicating that the specified model would be better than a constant only model. Regrettably, the recorded explanatory power of the model, as given by the McFadden R-squared, was quite low at 7%. This result suggests that the variables included in the empirical model do not explain variations observed in the dependent variable. However, such levels of explanatory power are comparable with those from similar studies [
20‐
24]. Multicollieanity is usually one of the factors blamed for low explanatory power in many survey-based studies.
In terms of the individual explanatory variables, estimation results show that virtually all coefficients generally exhibit expected signs and, in several cases, statistical significance as well: four out of eight coefficients are significant within 0.000 <
p ≤ 0.10 levels of significance. The estimated coefficient on the income variable was positive and highly significant indicating a high income-effect. Everything else being equal, high-income earners are willing to pay substantially more than low income earners. This result suggests that the malaria treatment commodity is a normal good [
25]. Given the specification of the WTP model, the coefficients on the income variables can be interpreted as the income-elasticity of demand. The measure of income elasticity of 0.29 reported in this paper suggests that a 10 % increase in household income increases the demand for the malaria treatment by about 3 %. The magnitude of the income effect is reasonably close to those reported in other similar studies [
25].
Two of the three health status indicators, HS1 and HS2, were found to be positive and significant at the 5% level. This result suggests that households who reported a generally poor self-assessed health status overall (HS1) were willing to pay more than households who had a good self-reported health status. Then, households who reported an experience of short term ill-health (HS2) within the six months prior to the survey were willing to pay more than those who did not report any such specific illness. This result is rather surprising given that economic theory would suggest that an increasing marginal disutility of illness associated with chronic ill-health should generate a positive and highly significant effect on the WTP. In other words, all else being constant, a household's health status should be negatively related with the marginal utility of seeking insurance. But there are plausible reasons to explain this. One of the reasons for this finding could be that problems of disclosure prevented respondents stating their health status. Another explanation could be that some might not have been aware that their illnesses were chronic at that stage. There was no significant correlation among the three indicators of ill-health.
Sometimes it is suggested that WTP may have a curvilinear relationship age [
23]. The rationale is that, everything else being equal, WTP is expected to increase with age up to a point (e.g. during the first fifteen years of life when demand for health care is relatively low), decline through a certain age range (say between 15 and 40), and then increase in the later years as people grow older (of course in Zambia with a life expectancy at barely 40, this may not be the case). So both age and AGESQ (the square of Age) were tested. When both variables, AGE and AGESQ were included, there was noticeable multicollinearity in the estimated model while individually only AGESQ proved to be significant. The variable AGE was dropped in favour of lnAGESQ, which is the logarithm of AGESQ. The sign of the coefficient on the variable AGESQ was as expected positive to signal that age had a generally positive impact on WTP.
In terms of education, the coefficient was also correctly signed and significant. In quantitative terms, the magnitude of the effect of education is illustrated as follows. An interpretation of coefficients on dichotomous variables is provided by [
26] which indicates the effect of a variable on the dependent variable by the quantity (exp(
)-1). Thus, households headed by individuals with more than nine years of education (beyond 9 years is often considered as functional illiteracy) were willing to pay 23 % more for the malaria programme than those headed by less educated individuals. This is a key result established in both the theoretical and empirical illustrations of Grossman-based models that better educated individuals (assumed to possess a higher level of human capital) are more likely to have a higher demand for health insurance programmes.
The sex of the respondent does not appear to have any significant effects on WTP, although it carried a positive sign. It is necessary to point out that the dummy variable for education was assigned a value of one for male and zero for female heads of household respectively. This means that a positive coefficient estimate implies that men are willing to pay more than women. Overall, empirical results in this study display a picture that is in satisfactory conformity with both theoretical predictions and empirical findings in the literature. This gives credence to the valuation technique and results obtained in terms of validity and reliability. Indeed, it would be difficult to imagine that such regularity, in both the WTP estimates and multivariate analysis findings, could be accomplished with a bogus instrument. Therefore, all the acknowledged weaknesses notwithstanding [
27‐
29], these findings can be considered to be reasonably valid and reliable estimates of public demand for these programmes.