‘Fair’ welfare comparisons with heterogeneous tastes: subjective versus revealed preferences

Abstract

Multidimensional welfare analysis has recently been revived by money-metric measures based on explicit fairness principles and the respect of individual preferences. To operationalize this approach, preference heterogeneity can be inferred from the observation of individual choices (revealed preferences) or from self-declared satisfaction following these choices (subjective well-being). We question whether using one or the other method makes a difference for welfare analysis based on income-leisure preferences. We estimate ordinal preferences that are either consistent with actual labor supply decisions or with income-leisure satisfaction. For ethical priors based on the compensation principle, we compare the welfare rankings obtained with both methods. The correlation in welfare ranks is high in general and reranking is insignificant for 77% of the individuals. The remaining discrepancies possibly pertain to a variety of factors including constraints (health issues, labor market rationing), irrational behavior and alternative life choices to the pursuit of well-being. We discuss the implications of using one or the other preference elicitation method for welfare analysis.

Appendices

A Appendix

1.1 A.1 Models specification

Specification of the utility functions Both experienced and decision utilities are specified according to the box-cox form:

$$\begin{aligned} u_{it}^{m}\left( y_{it},l_{it}\right) =\beta _{y}^{m} \left( \frac{y_{it}^{\lambda _{y}^{m}}-1}{\lambda _{y}^{m}}\right) +\beta _{l}^{m}(x_{it},\phi _{i})\left( \frac{l_{it}^{\lambda _{l}^{m}}-1}{\lambda _{l}^{m}}\right) , \qquad m=D,E \end{aligned}$$

Used in recent welfare analyses (Decoster and Haan 2015; Bargain et al. 2013), box-cox utility allows easily checking that preferences are well-behaved, which facilitates the derivation of ordinal preferences (i.e., indifference curves) and the calculation of welfare metrics. Monotonicity and concavity conditions on consumption and leisure are satisfied if, respectively, $\beta$’s are positive and $\lambda$’s are in a range between 0 and 1. We check ex post that both conditions are fulfilled empirically for all our observations. More flexible forms could be used but tangency conditions are necessary for calculating welfare metrics.³¹

Preference heterogeneity across individuals is introduced as follows. Parameters on leisure vary linearly with taste shifters $x_{it}$ and a normally distributed random term $\phi _{i}$:

$$\begin{aligned} \beta _{l}^{m}(x_{it},\phi _{i})=\beta _{l0}^{m}+\beta _{l1}^{m\prime } x_{it}+\beta _{l2}^{m}\phi _{i},\qquad m=D,E \end{aligned}$$

Vector $x_{it}$ includes the following binary characteristics: male, age above 40, higher education, presence of children aged 0 to 2, living in London, non-white ethnic origin, migrant, above-average conscientiousness and above-average neuroticism. Unobserved preferences $\phi _{i}$ are dealt with using simulated maximum likelihood.

Budget constraints In both approaches, disposable income is computed according to the budget constraint $y_{it}=\psi _{t}(w_{it}h_{it},\mu _{it},\zeta _{it})$. Function $\psi _{t}$ aggregates gross earnings $w_{it}h_{it}$ and unearned income $\mu _{it}$ into net income $y_{it}$, adding taxes and withdrawing benefits that depend on these income levels (benefit means-tested, tax brackets, etc.) and on individual characteristics $\zeta _{it}$ (tax credits or benefits being a function of family composition, for instance). It is approximated by numerical simulations using the tax-benefit rules of each period $t=1,\ldots ,T$. In the same way, we also predict $(y_{ijt},\tau -h_{ijt})$ pairs for the $j=1,\ldots J$ potential choices used in the labor supply model. To do so, we first estimate an Heckman-corrected wage equation (instrument is non-labor income and the presence of children aged 0–2) in order to predict wage rates $w_{it}$ (wages are unobserved for non-workers). Then we numerically compute disposable income $y_{ijt}=\psi _{t}(w_{it}h_{ijt},\mu _{it},\zeta _{it})$ for the J discrete labor supply values of $h_{ijt}$ (see Bargain et al. 2014).

Identification and limitations The econometric identification of ordinal preferences requires some discussions (see also Akay et al. 2015). For labor supply models, a well-known difficulty pertains to the role of omitted preference shifters that may affect both wage rates and work preferences. For instance, hard-working types may work a lot also because they tend to have higher wage rates, i.e. an underestimation of preferences for leisure. For the SWB model, a similar type of bias may exist. For instance, actual heterogeneity in work preferences may be correlated with other unobserved determinants of well-being. If hard workers are more likely to experience positive shocks to SWB, then the bias goes in the same direction as for labor supply, i.e. work aversion is underestimated. However, the bias could go the other way. We suggest three strategies to reduce these concerns. First, we account for individual heterogeneity $x_{it}$–notably relevant personality traits, i.e. conscientiousness and neuroticism—in work preferences and, for the SWB equation, in the separately additive term $z_{it}$. Second, we account for random preference-for-leisure parameters (note, however, that $\phi _{i}$ is normally distributed and, hence, cannot capture the true distribution of omitted variables). Finally, and most importantly, we use spatial and temporal variation in factors that affect the net wages. As used in the labor supply literature, it corresponds to spatial variation in tax-benefit rules (Hoynes 1996) and time variation in these rules over 1996–2005 (i.e., tax-benefit reforms, as in Blundell et al. 1998). The period covered in our data includes quite much variation in tax-benefit rules to improve identification (see a detailed account in Akay et al. 2015). These approaches are the best we can do in the present setting. Nonetheless, one can never exclude that remaining biases cause some of the observed differences between preferences derived from both methods.

1.2 A.2 Models estimation results

See Table 3.

Table 3 Models’ estimates

B Online appendix

1.1 B.1 Indifference curves by broad groups

We derive indifference curves in the income-leisure space for every individual in our sample. For the whole population (graph A) or within each group (graphs B–H), we average individual indifference curves through a common point set at 40 h of leisure and $\overline{y}(40)$ (the sample mean net income at this leisure level) (Fig. 8).

Fig. 8

Indifference curves with revealed vs. subjective preferences. Note: solid (dash) lines indicated indifference curves for revealed (subjective) preferences. Indifference curve representations on these graphs are obtained using estimated parameters of the income-leisure utility functions, overall or for particular groups (e.g. women), and averaging individual indifference curves drawn through a common point, defined as $(\overline{y}(40),40)$ On the graphs, weekly leisure points range from 20 to 80 h, corresponding to weekly work hours from 60 (overtime) to 0 (inactivity)

1.2 B.2 Reranking by broad groups

See Figs. 9, 10.

Fig. 9

Welfare rank correlation (rent metric) by groups, using group-specific ranks. Note: for the Rent metric, the graph compares welfare ranks with revealed versus subjective preferences, i.e. income-leisure ordinal preferences from actual choices versus from SWB experienced at these choices. Observations are grouped by demographic type, using group-specific ranks

Fig. 10

Welfare rank correlation (rent metric) by groups, using overall ranks. Note: for the Rent metric, the graph compares welfare ranks with revealed versus subjective preferences, i.e. income-leisure ordinal preferences from actual choices versus from SWB experienced at these choices. Observations are grouped by demographic type, using overall ranks

1.3 B.3 Results for the wage metric

See Figs. 11, 12 and Table 4.

Fig. 11

Welfare rank correlation (wage metric): whole sample. Note: for the Wage metrics, these graphs compare the welfare ranks obtained with revealed vs. subjective preferences, i.e. income-leisure ordinal preferences from actual choices vs. from the SWB experienced at these choices. Preferences are modelled using box-cox utility functions with preference heterogeneity (male, age, education, presence of young children, London, non-white, migrant, conscientious, neurotic)

Fig. 12

Welfare rank correlation (wage metric) by gender, using overall ranks. Note: for the Wage metric, the graph compares welfare ranks with revealed versus subjective preferences, i.e. income-leisure ordinal preferences from actual choices versus from SWB experienced at these choices. Observations are grouped by gender type, using overall ranks

Table 4 Characteristics of the most deprived (wage metric)