4.1 Design of DCE
Discrete DCEs provide a link between observed behaviour and economic theory. They are based on Lancaster's consumer theory which posits that consumer preferences are shaped by the individual characteristics a good or service possesses and not by the good as a whole (Lancaster, 1966). During a DCE, a respondent is asked to choose between hypothetical scenarios that consist of attributes with varying attribute levels. In our study, the alternatives describe different situations of child-raising, with, in line with the Q-Q trade-off theory, specific emphasis on the quantity of children and the quality of child-raising. As the validity of a DCE largely depends on the choice of the attributes (Mangham, Hanson and McPake, 2009), a detailed literature review, and multiple key informant interviews and focus group discussions in Senegal and Uganda were implemented prior to the design of the experiment to identify and select attributes that represent the quality of child-raising. In total we specify four attributes, with the first referring to the quantity aspect of child-raising, and the next three to the quality aspect, covering education, nutrition and health care (Table 2). [Table 2 near here]
The first attribute specifies the number of children and consists of six levels. The range of 1 to 12 children is based on the observed number of children in the study regions, as derived from the quantitative surveys.
The second attribute is defined as the share of children from the household that can complete lower secondary education. The attribute contains three levels: none, half and all of the children. In both countries lower secondary education comprises 4 years (children ages 12 to 15 in Senegal, and 13 to 16 in Uganda), after which a certificate of completion is awarded. In Uganda, we consider private schools that charge high tuition fees, as focus group discussions pointed towards a very low quality of public schooling. In Senegal, we consider public schooling, as private schools are not available in rural areas. While no official tuition fees are charged in Senegalese public schools, costs remain high as children have to commute or stay overnight, books and school supplies are expensive, and informal “maintenance fees” are charged.
The third attribute is defined as the number of days a week a household can eat a complete meal, including carbohydrates, proteins and vegetables, for the main meal of the day. On the other days an incomplete meal is consumed (e.g. only carbohydrates). The attribute consists of three levels: zero, four and seven days a week. In Senegal, a very known local dish “thieboudienne” is taken as an example, which comprises rice, fish and vegetables. In Uganda, a complete meal is defined as containing posho (maize meal) or matoke (green bananas), beans and green leafy vegetables.
The fourth attribute is defined as the quality of health care institute the household can consult when a child has a severe fever. The attribute contains three levels: low-quality, medium-quality and high-quality. A low-quality health care institute is defined as a small health care facility, located in almost every rural community, with only a health worker or nurse present. Basic treatments can be performed using basic equipment (such as disinfecting wounds, applying bandages, and treating common pathologies, such as acute diarrhoea or malaria), but diseases cannot be diagnosed. A medium-quality health care institute is operated by a larger staff of at least one nurse, one midwife and one assistant nurse. Medical equipment is more advanced and basic disease diagnosis is possible. In a high-quality health care facility, at least one doctor is stationed, often complemented by different specialists. Diagnosis and treatment of more complex or uncommon diseases are possible. The three quality attributes are similar in both countries but are adapted to the local context (e.g. in Senegal low-quality health care is a “case de santé”, while in Uganda it is a “health center II facility”).
We use choice sets with three alternatives and visual illustrations to assist illiterate people with making their choice (Figure A1 in appendix). We present 12 choice cards to each respondent and randomize the order to avoid learning bias. Hence, we obtain 36,000 observations in total. As information is missing on one choice card of two respondents, we retain 35,994 observations for the DCE analysis. We use a Bayesian design, which accounts for uncertainties around the true values of the a priori information of the parameters (Kessels et al., 2008). Using the D-efficiency criterion, the determinant of the variance-covariance matrix of the parameter estimators is minimized and the efficiency of the design is increased (Kessels, Goos and Vandebroek, 2006). As we hypothesize that respondents have positive preferences for the quality attributes, we use small positive priors for these levels. We hypothesize a positive but diminishing preference for the number of children, so priors are higher for 4 and 6 children, and lower for 1, 2, 9 and 12 children.
While the inclusion of an opt-out or status quo option is common practice in DCEs as it increases the realism of the choice task (Carson et al., 1994; Louviere, Hensher and Swait, 2000; Vanermen et al., 2021), we did not include an opt-out or status quo option in our choice experiment. This means that respondents are forced to make a choice between the three proposed scenarios. The decision not to include an opt-out option was guided by the fact that an opt-out option reduces the efficiency of the experiment because of a higher number of no-choices (Brazell et al., 2006; Veldwijk et al., 2014), and because the respondents are confronted with these forced choices in daily life, without the possibility to opt-out if characteristics do not match with their preferences. The application of a forced choice structure entails some consequences for the data analysis and interpretation of the results. As research shows that individual willingness to pay is different in forced and unforced choice sets (Penn, Hu and Cox, 2019), we do not calculate welfare estimates based on the estimated coefficients. Moreover, we need to remain cautious when interpreting the results.
The experiment was introduced to both spouses together. The attributes were explained in detail and the hypothetical character of the experiment was emphasized (i.e. that the proposed household should be taken as given, not taking into account possible economic, social or physical limitations, or the actual composition of the household). After the introduction, the spouses were interviewed separately by an enumerator of the same gender. Each experiment started with a test card, to check whether the respondent understood the rationale of the study[10].
4.2 Analysis of DCE
Discrete choice modelling is embedded in the random utility theory framework and assumes that respondents choose the alternative that yields the highest utility level from each choice set (Louviere, Hensher and Swait, 2000). Following this framework, we separate the utility respondent i derives from alternative j ( ) into an observable deterministic component ( ) – linearly depending on the attributes of the alternative ( ) and individual-specific socioeconomic characteristics ( ) – and a stochastic component ( ) capturing unobserved heterogeneity across alternatives and individuals (equation 1) (Hensher, J. M. Rose and Greene, 2005).
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As utility is a latent variable, we cannot directly observe the utility the respondent derives from a specific alternative. Therefore, we use the probability that respondent i chooses alternative j as an approximation, expressed in terms of a logistic distribution (Louviere, Hensher and Swait, 2000; Hensher, J. M. Rose and Greene, 2005). We use a mixed logit model (MXL), which is most common and allows for preferences to be heterogeneous across respondents, and maximum likelihood estimation (Train, 2003). We estimate different specifications of the MXL, treating all attributes as random and using 1500 Halton draws, to analyse respondents’ fertility preferences as well as the Q-Q trade-off. A first model specification is a basic MXL, including only main effects (1). In a second specification, we add a quadratic term of the quantity attribute to control for non-linear preferences (2). In models three to six, we test whether respectively gender, education level, poverty status and country are correlated with fertility preferences by adding interaction terms with four binary variables in separate models: female respondent (3), owner of a lower secondary education diploma (4), household poverty status (5) and country (6). In a fourth model specification, we assess the Q-Q trade-off by adding interaction terms between the quantity attribute and the three quality attributes (7). In models (8) to (11), we test whether gender, education level, poverty status and country are correlated with the Q-Q trade-off by adding double- and triple-interaction terms with these four variables.
4.3 Limiting Potential Bias
A DCE is a stated preference method and is inherently subject to hypothetical and social desirability bias (Menapace and Raffaelli, 2020). On the one hand, we expect these biases to be low in our DCE. The choices that the respondents are forced to make are similar to the decisions they face in daily life (i.e. do we invest in sending more children to school, or do we invest in more nutritious food). In addition, enumerators were carefully selected such that they share the same gender and ethnicity as the people they interview, with the survey taking place in the private setting of the own household with husband and wife interviewed separately.
On the other hand, DCEs are typically used to infer preferences on consumer goods or in an environmental valuation setting. These choices can be considered to be more trivial or independent from the choices you previously made in life, and are less likely influenced by hypothetical or social desirability bias. For example, the hypothetical character of choosing between a conventional or an organic apple might be less influenced by the fact that you actually bought conventional apples a week ago, than that the choice between a hypothetical household of two or eight children might be influenced by the fact that you actually have seven children. Moreover, buying apples in the supermarket is likely to be less of a taboo topic when compared to a household’s fertility. Enumerators were trained to emphasize the hypothetical character of the experiment, such that respondents focus on the characteristics of the household presented on the choice cards, and to not take into account characteristics of their actual living conditions, or possible social, monetary or physical limitations.
Even though we tried to reduce the hypothetical bias to a maximum, complete mitigation is impossible. The remaining hypothetical bias could inflate the preference for the number of children in cases where the respondents’ actual number of children is bigger than the number of children they would have preferred. On the other hand, the hypothetical bias could deflate the preference for the number of children, in cases where the respondents’ actual number of children is lower than the number of children they would have preferred.
We find other studies that use a DCE to infer preferences on more difficult, unconventional or “once in a lifetime” choices, or taboo topics. Dieci et al. (2021) use a DCE to understand the mechanisms that lead providers to avoid giving modern and long-acting family planning methods to adolescent girls. Baert et al. (2020) and Vlaeminck et al. (2016) infer resettlement preferences of smallholder farmers away from landslide prone areas in respectively Cameroon and Uganda. Carlson (2015) uses a DCE to report on the link between Ugandan voters’ ethnicity and their voting preferences in presidential elections. Malhotra et al. (2015) infer the willingness to pay of palliative cancer patients and their caretakers to extend the patients’ life with one year. Sculpher et al. (2004) infer preferences of cancer patients on the trade-off between life expectancy and troublesome side effects such as limitations in physical energy. Boyden et al. (2021) explore how parents rate and prioritize different domains regarding their child’s palliative and hospice care in the home setting. Tsuge, Kishimoto and Takeuchi (2005) even use a DCE to quantify the monetary value of a person’s life-year.
We control for attribute non-attendance, as previous studies show that ignoring one or more attributes could lead to biased estimates (Hensher, J. Rose and Greene, 2005; Hensher and Greene, 2010; Hole, Kolstad and Gyrd-Hansen, 2013), by using the information on respondents’ attribute non-attendance statements. We test for scale heterogeneity, using the generalized multinomial logit model developed by Fiebig, Keane, Louviere, and Wasi (2010). We cluster standard errors at the respondent level. The results of the stated attribute non-attendance and scale heterogeneity checks are presented in Table A1 in the appendix. The estimates of both the stated attribute non-attendance and the scale heterogeneity models are similar in magnitude, sign and significance level compared to estimates of the basic MXL model estimates. We therefore conclude that the MXL model estimations are not sensitive to attribute non-attendance and scale heterogeneity, and base our results and interpretation on these estimates.
[10] The test card contained three scenarios of which one scenario dominated the other two. If the respondent did not choose the dominant scenario, every aspect of the experiment was explained again.