To investigate this further, we converted numeric income data to categorical according to the categorisations shown in Table25. Pool- ing these with income data that originally had been reported as categorical and again restricting our population to those house- holds for which income data was reported, we considered a cumu- lative logit model171
of income on the same variables as considered 171
Cumulative logit models are a form of regression model for ordinal data.
in previous models. Here, however, due to the estimation routine used in fitting a cumulative logit model, it was necessary to re- move variables corresponding to the monthly cost of water and monthly cost of electricity172
to produce a model where the algo- 172
Neither of these were statistically significant in previous models, so this should not be cause for significant concern.
rithm would converge and produce valid parameter estimates and standard errors. Additionally, in this model we included a variable that indicates whether the income data was originally reported as categorical or numeric. This variable would be critical in explaining the relationship between incomes that were reported as categorical and those reported as numeric.
Table27presents parameter estimates and standard errors, and some of the key results are presented in Box4. The results in regard
f ac t o r s i n f l u e n c i n g i n c o m e a n d t h e w i l l i n g n e s s t o r e v e a l i t 79
to the relationship between income and occupation of the head of households and household use of electricity are as would be expected, but the real focus here is on the variable providing a comparison between incomes reported as categorical and incomes reported as numeric. The statistically significant positive coefficient for this variable indicates that households reporting income as categorical tend to report higher incomes than those reporting income as numeric. This seems to confirm previous speculation that households opting to report income data as numeric actually tend to have lower household income. Thus, analyses based on numeric income data might be expected to be more conservative than those based on categorical income data.
Estimate Std. Error z-value Pr(>|z|) Income reported as categorical 0.5940 0.2035 2.92 0.0035∗∗∗
Female respondent -0.4166 0.2207 -1.89 0.0590∗
Age of respondent 0.0093 0.0099 0.94 0.3471
Town/City: (Reference: Nampula)
Liúpo -0.6755 0.4395 -1.54 0.1243
Ribáuè -0.8619 0.2862 -3.01 0.0026∗∗∗
Education level of head of household: (Reference: None)
Primary of1stdegree -0.8577 0.6266 -1.37 0.1711 Primary of2nddegree 0.5804 0.6302 0.92 0.3570 Secondary of1stdegree 0.4469 0.6042 0.74 0.4596 Secondary of2nddegree 0.8178 0.6030 1.36 0.1750 Higher level 1.3112 0.8583 1.53 0.1266 Do not know 1.3160 0.7998 1.65 0.0999∗
Occupation of head of household: (Reference: Managers)
Professionals 0.0378 0.5786 0.07 0.9479
Technicians -0.4631 0.5549 -0.84 0.4040
Clerical support 0.6830 1.1968 0.57 0.5683
Services, sales -0.4003 0.5873 -0.68 0.4955
Agriculture, forestry, fisheries -1.7610 0.5821 -3.03 0.0025∗∗∗
Craft and related trade -1.3151 0.5688 -2.31 0.0208∗∗
Plant/machine operators 0.7548 0.9894 0.76 0.4455 Elementary occupations -1.6117 0.6096 -2.64 0.0082∗∗∗ Armed forces -1.3921 1.0364 -1.34 0.1792 Unemployed -2.2076 0.7176 -3.08 0.0021∗∗∗ Student -1.7516 1.3467 -1.30 0.1934 Homemaker -2.5058 0.7098 -3.53 0.0004∗∗∗ Benefits/pension -2.0300 1.0200 -1.99 0.0466∗∗ Other -0.5550 0.8515 -0.65 0.5146
Primary water point: (Reference: Household connection)
Yard tap -0.0218 0.7580 -0.03 0.9771
Standpipe 0.2218 0.8182 0.27 0.7863
Borehole 0.2125 0.7967 0.27 0.7897
Unprotected well 0.1110 0.7936 0.14 0.8887
Protected spring -3.3245 1.6978 -1.96 0.0502∗
River, stream, lake -0.0150 1.0317 -0.02 0.9884
Neighbour’s tap -0.2340 0.7973 -0.29 0.7692
Household pays for water -0.1480 0.2956 -0.50 0.6167
Household has electricity 1.1035 0.2746 4.02 0.0001∗∗∗
Household treats water 0.1892 0.1979 0.96 0.3391 Note: ∗p<0.1;∗∗p<0.05;∗∗∗p<0.01
Table27: Cumulative logit model of income (as categorical) on relevant variables, including town/city, age and sex of the respondent, household primary water point, and a number of proxies for income. This model also includes an indicator of whether income was originally reported as categorical.
Income reported as categorical: • There is a significant difference between those households for which the respondent report income data as numeric and those for which the respondent reports income as cat- egorical. In particular, households for which income data is reported as categorical report incomes falling into higher income categories on average than households reporting in- come as numeric. In other words, it would seem that those reporting income as numeric tend to correspond to lower income households on average than those households that report income as categorical.
Town/City: • Households in Ribáuè report significantly lower incomes than those in Nampula.
Sex of respondent: • Women are more likely to report lower incomes than men. Occupation of head of household: • Those households where the head of household works
in occupations higher up the occupation ladder are more likely to report higher incomes.
Household has electricity: • Households that have a connection to the electrical grid report higher incomes than those that do not.
Box4: Key relationships between income (as categorical) and variables considered in Table27, which include
demographic characteristics and proxies for income. It also includes an indicator of whether income was originally reported as categorical.
Validating Proxies for Income
Considering that lack of income data results in a reduction in the set of usable observations for analyses, finding a robust set of prox- ies for income can be vital in ensuring that models represent a greater proportion of the population of interest. We already pre- sented a set of potential proxies in Table23and previous models. To try to validate these proxies, we considered a linear regression of log-transformed income on town/city, age and sex of the respon- dent, household primary water point, and a number of proxies for income considered previously, including education and occupa- tion of the head of household, whether a household treats water, whether a household pays for water and how much, and whether a household pays for electricity and how much.
Results for this model fit are presented in Table28, and we note the key results presented in Box5. These results are in line with what we would expect if these were in fact reliable proxies for in- come173
, and, consequently, in considering models for WTP, we will 173
Note thatR2=0.471for this model. consider separate regression models that incorporate numeric val-
ues for income and that include proxies for income as explanatory variables. This will give us greater flexibility, as models based on proxies have fewer missing values and, consequently, may be able to more accurately represent not only those of high SES but also those of lower SES.
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Estimate Std. Error z-value Pr(>|z|) (Intercept) 8.0398 0.7383 10.89 0.0000
Sex of respondent -1.1534 0.2910 -3.96 0.0001∗∗∗
Age of respondent 0.0041 0.0061 0.67 0.5063
Town/City: (Reference: Nampula)
Liúpo -0.5600 0.2877 -1.95 0.0526∗
Ribáuè -0.4037 0.2137 -1.89 0.0599∗
Education level of head of household: (Reference: None)
Primary of1stdegree -0.2199 0.3953 -0.56 0.5784 Primary of2nddegree 0.3143 0.4159 0.76 0.4505 Secondary of1stdegree -0.0486 0.4141 -0.12 0.9066 Secondary of2nddegree 0.3486 0.4233 0.82 0.4110 Higher level 0.7958 0.5455 1.46 0.1458 Do not know 0.5654 0.5953 0.95 0.3431
Occupation of head of household: (Reference: Managers)
Professionals -0.4635 0.3540 -1.31 0.1915
Technicians -0.5989 0.3288 -1.82 0.0696∗
Clerical support -0.3853 1.1990 -0.32 0.7482
Services, sales -0.4932 0.3728 -1.32 0.1869
Agriculture, forestry, fisheries -0.9237 0.3399 -2.72 0.0070∗∗∗
Craft and related trade -0.6364 0.3692 -1.72 0.0859∗
Plant/machine operators -0.0033 0.6382 -0.01 0.9959 Elementary occupations -0.6405 0.4415 -1.45 0.1480 Armed forces -0.7841 0.7208 -1.09 0.2776 Unemployed -1.2823 0.3618 -3.54 0.0005∗∗∗ Student -0.3737 0.4896 -0.76 0.4460 Homemaker 0.2367 0.4926 0.48 0.6313 Benefits/pension -1.6876 0.6884 -2.45 0.0149∗∗ Other -0.6262 0.6481 -0.97 0.3347
Primary water point: (Reference: Household connection)
Household size -0.0310 0.0356 -0.87 0.3845 Yard tap 0.2781 0.4636 0.60 0.5491 Standpipe -0.1689 0.5054 -0.33 0.7385 Borehole 0.0991 0.5119 0.19 0.8466 Unprotected well -0.0612 0.5330 -0.11 0.9086 Protected Spring -1.3971 1.2905 -1.08 0.2799
River, stream, lake 0.7654 0.6926 1.11 0.2701
Neighbour’s tap 0.3854 0.5509 0.70 0.4847
Household treats water 0.3701 0.1493 2.48 0.0138∗∗
Household pays for water 0.1438 0.1935 0.74 0.4580
Household has electricity 0.5451 0.1928 2.83 0.0050∗∗∗
Monthly cost of electricity 0.0002 0.0001 1.58 0.1143
Note: ∗p<0.1;∗∗p<0.05;∗∗∗p<0.01
Table28: Linear regression of log- transformed income on relevant variables, including town/city, age and sex of the respondent, household primary water point, and a number of proxies for income.
Town/city: • Households in Ribáuè and Liúpo report significantly lower incomes than those in Nampula.
Sex of respondent: • Women are more likely to report lower incomes than men. Occupation of head of household: • Those households where the head of household works
in occupations higher up the occupation ladder are more likely to report higher incomes.
Household has electricity: • Households that have a connection to the electrical grid report higher incomes than those that do not.
Household treated water: • Households that treat their water report higher incomes than those that do not.
Box5: Key results for linear model of numeric income on proxies for income. This model is used to validate proxies.