Subjective beliefs about the income distribution and preferences for redistribution

Abstract

We investigate whether beliefs about the income distribution are associated with political positions for or against redistribution. Using a novel elicitation method, we assess individuals’ beliefs about the shape of the income distribution in the United States. We find that respondents’ beliefs approximate the actual distribution on average. However they tend to overestimate the median income and underestimate the level of inequality. Surprisingly we find that beliefs about overall inequality, measured in terms of income dispersion, play only a marginal role in political positions as well as prospects of future wealth. Political preferences, however, are predicted by first, beliefs about the level of income of the poorest members of society, and second, a belief in an open society with equal opportunities for all. Support for redistribution is lower for people who give higher estimates of the income level of the poorest members of society and for people who perceive that opportunities for upward mobility are available.

Appendices

Appendix 1: Variables description

See Table 7.

Table 7 Description of the explaining variables

Appendix 2: Description of the sampled counties

See Table 8 and Fig. 4.

Table 8 Detail of the selected counties

Fig. 4

Census regions and divisions

Appendix 3: Survey sample

Tables 9 and 10 below compares the survey sampling firms panel demographics to our sample. The largest differences is observed for gender with more female respondents than in the overall panel. We have already experienced such a gender imbalance in previous uses of this firms panel as well as other commercial panels and panels we have curated ourselves. This suggests that it may be due to a general gender differences in the propensity to participate to a survey rather than a selection induced specifically by our topic. We also observe a smaller number of young participants, a larger number of participants with high income. We have now added this information to the description of our sample.

Table 9 Comparison of the study sample with the sampling firm panel demographics

We retained 82 % of the initial sample and eliminated respondent who looked that they may not have taken the task seriously. Table 10 compares the answers of both samples (retained and not retained). On most answers, there are no significant differences. The standard deviation of the distribution elicited by the DB is significantly higher in the retained sample relative to the non retained sample. It is likely to be a mechanical effect of the rule we chose: we eliminated participants who clicked less than 5 times on the DB. This is likely to eliminate participants who created DB distributions with only limited dispersion. The retained sample also display a belief which is (marginally) significantly higher than for the non retained sample. Overall, our choice to retain the sample does not lead to a sample of respondents with very different answers. In particular, there are no significant differences in regard to the answers to the political questions.

Table 10 Comparison of the retained sample with the non retained sample

Appendix 4: Structural estimation

Estimating a parametric distribution from DB data requires taking into account that the DB allows participants to give an estimate of the percentage of households in a series of brackets 10,000 dollars wide each, up to the highest bracket “$205k and above”. To summarize beliefs about the income dispersion in one parameter, we model the DB observations as coming from a lognormal distribution with mean and standard deviation $\mu$ and $\sigma$. To estimate these parameters for each participant, we maximise the log-likelihood function for each individual i:

$$\begin{aligned} \ell (\mu _i,\sigma _i|M_i)=\sum _{k=1}^{100}\sum _{j=1}^{22} \ln \left( \varPhi \left( \frac{\ln (\overline{b}_j)-\mu _i}{\sigma _i}\right) -\varPhi \left( \frac{\ln (\underline{b}_j)-\mu _i}{\sigma _i}\right) \right) {\mathbbm {1}}_{\{m_{ki}\in [\underline{b}_j,\overline{b}_j]\}} \end{aligned}$$

where $M_i$ is the vector of observed marker values $m_{ki}$ for the individual i, with k being the id of the marker for each participant, j the id of the bracket and $\underline{b}_j$, $\overline{b}_j$ respectively the lower and upper bounds of bracket j (with $\underline{b}_1=0$ and $\overline{b}_{22}=+\infty$).

This model allows us to estimate how different participant characteristics correlate with participants’ beliefs about the shape of the distribution. To do so, we sum the individual log likelihood over the whole sample:

$$\begin{aligned} \mathcal {L}(\mu ,\sigma |M)=\sum _{i=1}^N \ell (\mu _i,\sigma _i|M_i) \end{aligned}$$

(5)

where M is the vector of all observed marker values $m_{ki}$ in the sample. In order to estimate links between individual and local characteristics of participants and their beliefs, we parametrize the coefficients as linear functions of vectors of observed variables $X_1$ and $X_2$ respectively:

$$\begin{aligned} \mu&=\beta _1X_1\nonumber \\ \sigma&=\beta _2X_2 \end{aligned}$$

(6)

Table 11 Beliefs about the moments of the distribution from the distribution builder

Table 11 shows the results of the estimations of parameters $\mu$ and $\sigma$ from the lognormal distribution by maximizing the likelihood (5). The parameters are written as linear functions of variables characterizing the individual and local characteristics following Eq. (6). To take the non-independence of observations within participants into account, we use a robust matrix of variance clustered by participants. We find that education and age are significant, while no local variable is significant.

Appendix 5: Median comparison

An interesting feature of our design is the elicitation of the subjective beliefs about the median household income using two different methods: a direct question and the Distribution Builder. Figure 5 shows the scatterplot of the individual answers to these two methods. There is clearly substantial variation across the two elicitation methods reflected in the overall correlation of 0.6 between the two types of answers. We think that these difference can be due to the abstract nature of the direct question which requires participants to think about the notion of percentiles. This may lead to more noisy answer from guesses. Another possibility is that people may take more or less care in answering each question. Overall 60 % of participants estimates about the median via these two methods are within $10,000 from each other and 78

Fig. 5

Individual answers about the median in the questionnaire and in the DB. p values indicated in brackets