Revealed preferences for equal college access may be due to beliefs that equal access increases societal income or income equality. To isolate preferences for those goods, we implement an online discrete choice experiment using social statistics generated from true variation among commuting zones. We find that, ceteris paribus, the average income that individuals are willing to sacrifice is (1) $4,984 to increase higher education enrollment by 1 standard deviation (14 percent); (2)$1,168 to decrease rich/poor gaps in higher education enrollment by 1 standard deviation (8 percent); and (3) $2,900 to decrease the 90/10 income inequality ratio by 1 standard deviation (1.66). In addition, we find that political affiliation is an important moderator of preferences for equality. While both Democrats and Republicans are willing to trade over$4,000 to increase higher education enrollment by 1 standard deviation, Democrats are willing to sacrifice nearly three times more income to decrease either rich/poor gaps in higher education enrollment or the 90/10 income inequality ratio by 1 standard deviation.

Suppose the government found itself with an unexpected budget surplus, and policy makers consider three policies for spending this surplus. The first policy considered is intended to reduce college attendance gaps between high- and low-income individuals, which could be accomplished by expanding financial aid for low-income students (Dynarski 2003) while holding admissions rates constant. The second policy is intended to decrease income inequality, which could be accomplished with an unconditional cash transfer to low-income individuals.1 The third policy is intended to increase income for everyone, which could be accomplished by a uniform tax rebate. In this stylized example, the policy maker faces a decision between increasing equality of college access, equality in income, or average income.

Supposing the social planner knows the actual costs and effects for each of the policies, two additional pieces of information are needed to determine which of the policies should be pursued. First, the policy maker needs to know how much individuals value each of the societal variables. Second, to make comparisons across different social variables, the policy maker needs common units of measurement. With this information, it would then be possible to quantify how much societal income individuals would be willing to spend to improve each social value.

In this paper, we are concerned with individual preferences for equality of college access, and how those preferences relate to preferences for other societal variables, including income and income equality. Traditionally, data about preferences for distributions of social variables have been collected from opinion surveys, such as the General Social Survey in the United States and the World Values Survey at the international level. Meanwhile, the academic community has focused mostly on understanding preferences for equality in income and has not, to our knowledge, considered multidimensional preferences for distributions of other variables, such as access to higher education (Clark and D'Ambrosio 2015).

Information regarding individual preferences for multiple social variables is not easily obtained from traditional opinion surveys, because of omitted variable bias. First, preferences for equal college access can be confounded by preferences for either efficiency or equality in income. For example, an individual who is interested in improving college access for low-income students may believe that increased access has positive spillovers on both efficiency and income equality, and is for those reasons desirable and not desirable per se. Second, individuals make unobserved assumptions about the societal costs that a preferred distribution of college access or income would require. Respondents may prefer equal income distributions, all else constant, but because they believe that equality distorts incentives, they also expect societal costs to be large and, therefore, their revealed preferences for equal income will appear attenuated (Piketty 1995).

To recover preferences, we implement a survey-based discrete choice experiment (DCE) that identifies social preferences for equal access to higher education, efficiency, and income equality. Survey respondents are asked to select between one of two societies. For each society a respondent sees, we randomly assign the values of four societal statistics: average median family income (societal income), the ratio of average income of the 10 percent richest to the 10 percent poorest (90/10 income ratio or income inequality), the enrollment rate in higher education (average education), and the difference in higher education enrollment rates between children from families in the 90th and 10th income percentiles (opportunity for higher education). Variation for these statistics is derived from true variation among commuting zones in the United States, using Census data and the education mobility data from Chetty et al. (2014). Because societal statistics are randomly assigned, we avoid biases due to beliefs about the relations among societal values or about the costs of equality. With these data, we obtain measurements of how much average household income individuals are willing to sacrifice to improve other social values, thus providing a common metric for making comparisons across different domains.

We find that (1) individuals are willing to decrease average income by $4,984 to increase enrollment in higher education by 1 standard deviation (SD) (14 percent); (2) the average individual is willing to exchange$1,168 of average income to decrease gaps in college enrollment by 1 SD (8 percent); and (3) the average individual is willing to exchange $2,900 of average income to decrease the 90/10 income inequality ratio by 1 SD (1.66). Additionally, we evaluate “Rawlsian trades”—so named because of the distributive priority Rawls gives to equality of opportunity over income equality in his theory—and find the average individual is willing to increase gaps in college access by 2.49 SDs to reduce the 90/10 income ratio by 1 SD. We identify meaningful differences based on political affiliation. Although right-leaning voters care less about inequality (Kuziemko et al. 2015), this preference may be due to beliefs about societal costs and not inequality per se. Additionally, we know little about whether preferences for equality in college access and income correlate with political affiliation. We find that Republicans have nearly lexicographic preferences for average income, meaning they are unwilling to trade any units of income for equality in either dimension. Thus, Republicans are not equality averse because of perceived costs but because societal income is the most important social variable in their social welfare functions. We do, however, find overlap among partisans, as both Democrats and Republicans are willing to trade meaningful quantities of average income (over$4,000) to increase enrollment in higher education by 1 SD (14 percent). These results suggest, between parties, there is an overlapping consensus with respect to increasing average levels of education and a large chasm with respect to equalizing educational opportunities or income.

Our primary result is that U.S. residents are willing to exchange meaningful amounts of average income for other social variables, including overall levels of education (which is often viewed purely as a vehicle for increasing economic growth) and reductions in inequality. Second, our results help clarify some confusion about the relation between access to higher education and equality of income. When considered in isolation, individuals may indicate greater preferences for college access relative to equal income; however, our results indicate that some of this rank-ordering is attributable to omitted variable bias. When respondents consider societal variables simultaneously, they are willing to pay over twice as much for equivalent reductions of income inequality relative to college enrollment inequality. This implies that if there is a public policy choice between a tax credit to reduce income inequality by 1 SD or an education intervention to reduce college enrollment gaps by 1 SD, all else constant, the preferred policy choice would be the tax credit.

The next section reviews the most relevant background literature, and section 3 provides a theoretical and empirical justification for the focus on college access. Section 4 details the experiment that was implemented. Section 5 describes the data and the econometric methodology, and section 6 provides and discusses the results.

In general, academic research has focused on preferences for income equality and not equal educational opportunity. Clark and D'Ambrosio (2015) classify research about preferences for income equality into two fields: comparative and normative. In the comparative case, individuals think of themselves as the relevant reference group and consider whether their place in a specific distribution of income is better or worse than alternative distributions. In the normative case, the relevant reference group is an ideal standard; therefore, individuals consider whether a distribution of income is better or worse relative to the standard and not with respect to their own position.

Our paper is most closely related to the normative case. In this branch of research there are two approaches. The first one estimates empirical correlations between a society's level of income equality and its members’ observed level of well-being. Contextual factors—such as credit constraints (Benabou 2000), observed social mobility (Piketty 1995; Alesina, Stantcheva, and Teso 2018), and expected social mobility (Benabou and Ok 2001; Alesina and La Ferrara 2005)—can then be used to explain preferences for distributions of income. D'Ambrosio and Clark (2015) provide a summary of such research and show that results differ depending on the data source, country of analysis, and the inequality metric used. The heterogeneity in results is not surprising, given that different groups (e.g., socioeconomic, political) residing in different contexts have different beliefs about the relevance of income inequality (Grosfeld and Senik 2010).

Benjamin et al. (2012) caution against the use of willingness-to-pay (WTP) statistics based on assessments of subjective well-being. The reason is that respondents understate the importance of money in measures of subjective well-being relative to when they are presented with choice sets. When presented with choice sets (even hypothetical ones), respondents systematically weight income gains more highly than when they are asked whether an equivalent income gain will improve their well-being. These results suggest that forced choice experiments may be a superior way to elicit WTP for other social variables.

The second approach uses experiments to estimate individuals’ WTP for equality. To separate respondent preferences for equality from their beliefs about the costs of equality, Johansson-Stenman, Carlsson, and Daruvala (2002) provide individuals with hypothetical societies for their future grandchildren and randomly set a uniform distribution of income. They find high levels of inequality aversion in their sample. Similarly, Amiel and Cowell (1999) and Pirttilä and Uusitalo (2010) use a leaky bucket experiment, which imposes a societal cost to redistribute income, and find a wide range of inequality aversion.

Inequality aversion varies among political partisans. Indeed, research has provided considerable evidence that liberals and conservatives have what appear to be fundamental differences in preferences for income equality. Data from the General Social Survey show that Democrats are twice as likely as Republicans to favor governmental action to remedy inequality.2 Data from the Pew Research Center show that Republicans are twice as likely as Democrats to say that a person is rich because of his or her own efforts and nearly three times as likely to say that a person is poor because of lack of effort.3

Researchers have also shown that individuals respond to information differently based on political identification. Kuziemko et al. (2015) randomly provide accurate information about levels of inequality in the United States to a sample of respondents through Amazon's Mechanical Turk (MTurk) interface, and find this information changes how much individuals care about inequality but does not change support for redistribution policies. They also show that liberals care more about inequality overall, and the effect of presenting information to them is larger. Alesina, Stantcheva, and Teso (2018) provide individuals with accurate information about social mobility, and find that liberal respondents increase their support for redistribution when presented pessimistic data about mobility, whereas conservative respondents are inelastic to information. To our knowledge, empirical research regarding variation in inequality aversion between political partisans has not addressed whether this variation is explained by beliefs about costs or preferences for equality.

Finally, Lü (2013) tests whether educational opportunity mediates inequality aversion. The author defines educational opportunity as the difference in the rate of college enrollment between individuals in high- and low-income districts. The relative differences in college attendance are randomly assigned, and income differences are held constant. Respondents then report whether they believe the income differences between the two districts are too large. Lü finds that as access to higher education becomes more equal, respondents are less likely to report that the income differences are too large.

Our goal is to distinguish preferences for equal access to higher education from preferences for society's overall level of income, average education, and income equality. We operationalize equal access to higher education as the relative difference in the probabilities that individuals from different parental income percentiles (the 10th and 90th percentiles) attend college. Under certain conditions, such a definition of equal access converges with the traditional notion of fair equality of opportunity articulated by Rawls in Theory of Justice and in political philosophy more broadly (Arneson 1999; Brighouse and Swift 2008; Rawls 2009). This conception of access is also widely used in empirical applications. For example, along with income mobility, Chetty et al. (2014) measure equality of opportunity as the probability of college attendance conditional on parental income.

Debate about whether or not public policy should promote equal access to higher education or income equality is salient in both public policy and political philosophy. Tuition-free higher education was a prominently featured campaign issue during the Democratic primaries of 2016. As of April 2016, a Gallup survey of 2,024 adults found that 47 percent supported tuition-free higher education, and less reliable polling data indicate this support has grown.4

Meanwhile, educational attainment is associated with increased earnings and lower unemployment. As of 2016, the unemployment rate for those with a bachelor's degree was 2.6 percent, compared with 5.2 percent for those with a high school diploma. Median weekly earnings were 1.67 times higher for these same groups.5 A common policy proposal is to provide subsidies to low-income students to attend college. Dynarski (2002) estimates that a $1,000 subsidy increases college attendance by 4 percent. As of August 2019, the federal expenditures on Pell Grants is$28.2 billion (College Board 2019). Estimates of the population costs required to close the college attendance rate gap are not easily obtained.

In political philosophy, the origin of the debate can be traced back to Rawls's (2009) relative ranking of the two principles of distributive justice: fair equality of opportunity and the difference principle. For our purposes, we can think of the difference principle as any preferred distribution of income, such as equality, and the fair equality principle as ensuring equal access to higher education. In the Rawlsian schema, the difference principle is lexically subordinate to the fair equality principle, meaning that the conditions of fair equality are to be satisfied before attention is paid to the difference principle. Thus, for Rawls, it is allowable to trade equality of income for educational opportunity.

Against this view, Arneson (1999) has argued that equal opportunity principles have a meritocratic bias. That is, equal opportunity principles that eliminate barriers based on social class (and other characteristics) leave open barriers based on ability. Because discrimination based on ability has no greater moral justification than discrimination on the basis of social class, equal opportunity principles need to be given either lower distributive priority or discarded. Such a concern is easily applied to higher education subsidies, as those would favor the skilled. Other philosophers have offered various reasons to promote equal opportunity. Each argument has a common feature, which is to identify a benefit promoted by opportunity that is of greater value than the “consumption interest” (Taylor 2004, p. 337) promoted by distributing shares of income. For Shields (2015), the benefit is autonomy; for Shiffrin (2003), the benefit is democratic equality; and for Taylor (2004), the benefit is self-realization. Despite the ongoing disagreement among political theorists, U.S. residents, and policy makers, our analysis is the first to conduct an empirical test to determine whether individuals prioritize equality of access to higher education or income equality.

### Empirical Problem: Omitted Variable Bias

Typical opinion surveys ask respondents the extent to which they agree with various social objectives. For example, the General Social Survey 2016 asks participants to rate the priority the government should give to reducing income inequality. Because individuals might have different beliefs about the costs and mechanisms required to produce different social objectives, it is difficult to interpret the answers to these surveys as proper measures of social preferences.

To see how differences in individual beliefs can affect survey results, consider a simple survey where individuals are asked if they support a governmental action to improve a social variable $X$. We can characterize individuals as having two random parameters that influence their answer:

1. The society's income $αb$ that the respondent believes to be traded off in order to achieve $X$, and

2. The society's income $αt$ that the respondent is willing to trade off to achieve $X$.

Given those parameters, the respondent is only willing to support $X$ if she believes the income $αb$ needed to produce $X$ is less than the income $αt$ she is willing to trade. To illustrate the omitted bias problem, assume that $αb$ and $αt$ are independently distributed following exponential distributions of parameters $βb$ and $βt$, respectively.6 The expected value of an exponential distribution is its distributional parameter and the expected support for the policy reported in the simple survey would be equivalent to:
$E[SupportforX|βt,βb]=∫0∞∫0αtf(αt,αb|βt,βb)dαbdαt=βtβt+βb.$
(1)

Notice the expected support for $X$ is a function of both beliefs and preferences. In fact, we obtain different results depending on $βb$. If $βb=βt$ then the expected support will be 0.5. Conversely, if $βb→0$ (no income sacrifice for $X$) then individuals will have perfect support. Finally, if $βb→∞$ then support approaches zero.

Thus, unobserved beliefs ($βb$) about costs can bias results of simple opinion surveys. Moreover, these surveys do not provide the amount of income that respondents are willing to trade ($βb$) for $X$. Through randomization, our survey improves upon simple surveys by imposing the costs needed to produce societal variables. Randomization therefore allows identification of unbiased estimates of $βt$, or the respondents’ willingness to support $X$.

### Discrete Choice Experiment

We use a DCE to randomly assign societal values, along four dimensions, to two different hypothetical future societies.7 Between these two societies, respondents must decide which one is preferable.8 The four dimensions isolated are (1) societal income; (2) income inequality; (3) average education; and (4) equal access to higher education.

The survey experiment consists of two sections. In the first, respondents are presented with descriptive information about the four societal variables and asked a series of diagnostic questions to determine whether they understand the data. Regardless of whether respondents answer the diagnostic questions correctly, the survey tells them the correct answer.9

In the second section, respondents are given information about contemporary U.S. statistics in each of these dimensions. Respondents are then asked to choose between two hypothetical future societies, A and B, in which values for each of the four variables are randomly assigned to each society. For example, societies A and B may both be assigned the same level of income but society A has high levels of income inequality whereas society B has large gaps in college access. Respondents choose which bundle of randomly assigned values is optimal, according to their own welfare criteria.

We highlight two additional features of the DCE. First, because asking respondents multiple questions is more cost effective than repeatedly introducing the survey to new respondents, we give them four versions of the choice experiment, in which societal values are randomly assigned for each new question. Standard errors are therefore clustered at the respondent level. Second, to minimize primacy and recency effects, the four societal attributes were presented in a randomized order across respondents (Hainmueller, Hopkins, and Yamamoto 2014).

### Social Welfare Variables Construction

Respondents are presented with information about a society's overall level of income and human capital development, as well as levels of income and equality of access to higher education. These variables are constructed based on means and SDs from U.S. commuting zones (CZs) using Chetty et al. (2014) data available on the Equality-of-Opportunity.org Web site. Respondents are asked to choose values that conform to different combinations of CZ-level family income per capita, income inequality, level of higher education, and educational mobility. Effectively, respondents are randomly assigned CZ descriptive characteristics and are asked which bundle of descriptive statistics is most desirable.

The statistics presented to respondents are household income per capita, the percentage of persons aged 25 years and above with at least a bachelor's degree, the 90/10 income inequality ratio, and the percent of children from the 90th income percentile who attended a four-year college program by age 21 years, minus the percent of children from the 10th percentile. To generate the values to be presented, we take values for each variable at the national level and set those as midpoints. For variation, we calculate the CZ-level SDs using comparable statistics from the Chetty et al. (2014) data. We then add/subtract one-half and one times the respective SDs to the average values. Therefore, lowest/highest values are the average minus/plus one times the SD, for a total of five values per variable. For purposes of easier interpretation, we modify the values slightly by rounding. Table 1 shows the final set of variables values that are assigned to respondents.10

Table 1.
Discrete Choice Experiment, Randomization Values Actual
VariableMean − 1 SDMean − 0.5 SDMeanMean + 0.5 SDMean + 1 SD
Income per capita $36,000$39,000 $42,000$45,000 $48,000 Inequality income 8.8 9.6 10.5 11.3 Percent college educated 14% 21% 28% 35% 42% Inequality higher education 46% 50% 54% 59% 63% VariableMean − 1 SDMean − 0.5 SDMeanMean + 0.5 SDMean + 1 SD Income per capita$36,000 $39,000$42,000 $45,000$48,000
Inequality income 8.8 9.6 10.5 11.3
Percent college educated 14% 21% 28% 35% 42%
Inequality higher education 46% 50% 54% 59% 63%

Notes: Descriptive statistics for the four societal variables randomly assigned to respondents. All values taken from Chetty et al. (2014) from the Equality-of-Opportunity.org project. Mean corresponds to national mean and variation is based on the estimated between-commuting zone standard deviation. SD = standard deviation.

### Data

Data for the survey are collected using Amazon's MTurk interface, with the sample drawn from persons living in the United States. Currently, MTurk is an established online platform that can be used to carry out social and survey experiments. For instance, Berinsky, Huber, and Lenz (2012) show that MTurk samples are more representative than in-person convenience samples and less representative than nationally representative probability samples used by firms like YouGov. Importantly, Berinsky, Huber, and Lenz are able to replicate multiple attitudinal experiments previously conducted, with nationally representative sampling designs, using MTurk data. In addition, Kuziemko et al. (2015) find that the unweighted MTurk sample for their study was as representative of U.S. Census data as unweighted samples from a nationally representative sample of U.S. adults contacted by Columbia Broadcasting Company. Finally, Levay, Freese, and Druckman (2016) find that differences in political attitudes between the population-based American National Election Studies and an MTurk sample can be substantially reduced once one includes controls for demographic variables.

Chandler, Mueller, and Paolacci (2014) raise three concerns regarding the use of MTurk data. First, respondents may participate multiple times on the same survey; second, respondent performance on diagnostic items, such as cognitive reflection tasks, may be inflated due to conceptually related experiments; third, researchers may utilize post hoc data cleaning. Our survey is designed to mitigate these threats. First, although our survey was administered in two waves, we used JavaScript to pre-screen and exit respondents if their unique WorkerID appeared in the second wave. Second, the diagnostic items we use to ensure attention and comprehension are task-specific to the survey instrument and not generic cognitive reflection tasks. Finally, all respondents who completed the survey were included in the main analysis; no post hoc data cleaning was conducted.

The survey was posted in two waves on MTurk, 5 January and 12 January 2017. We collected complete responses from 999 MTurk participants, at a rate of $0.75 per response.11 Table 2 shows descriptive statistics for survey participants, comparable U.S. Census data for 2010, and the Kuziemko et al. (2015) MTurk sample (N = 3,741). Table 2. Descriptive Statistics: (1) Analytic MTurk Sample, (2) 2010 U.S. Census, and (3) Kuziemko et al. (2015) MTurk Sample2010 U.S. CensusKuziemko et al. (2015) VariableFrequencyPercentagePercentagePercentage Sex Female 420 42.17 50.8 57.2 Male 576 57.83 49.2 42.8 Race/Ethnicity Black 72 7.24 12.6 7.8 Other 123 12.37 17.7 7.6 White 799 80.38 63.7 77.8 Age, years 18—29 358 35.87 13.0 (18 to 24 years) 35.41 (sample mean) 30—44 445 44.59 35.0 (25 to 44 years) 45—64 164 16.43 34.8 (45 to 64 years) 65 or older 31 3.11 17.1 (65+ years) Educational attainment Associate's or two-year college degree 95 9.52 5.52 Did not finish high school 0.5 11.6 Four-year college degree 384 38.47 19.49 43.3 (at least college) Graduate or professional degree 121 12.12 11.19 High school diploma or equivalent 109 10.92 28.95 Some college, no degree 252 25.25 19.1 Technical or vocational school after high school 32 3.21 4.04 Party affiliation Democrat 592 59.3 44.8 67.5 Republican 306 30.6 44.3 MTurk Sample2010 U.S. CensusKuziemko et al. (2015) VariableFrequencyPercentagePercentagePercentage Sex Female 420 42.17 50.8 57.2 Male 576 57.83 49.2 42.8 Race/Ethnicity Black 72 7.24 12.6 7.8 Other 123 12.37 17.7 7.6 White 799 80.38 63.7 77.8 Age, years 18—29 358 35.87 13.0 (18 to 24 years) 35.41 (sample mean) 30—44 445 44.59 35.0 (25 to 44 years) 45—64 164 16.43 34.8 (45 to 64 years) 65 or older 31 3.11 17.1 (65+ years) Educational attainment Associate's or two-year college degree 95 9.52 5.52 Did not finish high school 0.5 11.6 Four-year college degree 384 38.47 19.49 43.3 (at least college) Graduate or professional degree 121 12.12 11.19 High school diploma or equivalent 109 10.92 28.95 Some college, no degree 252 25.25 19.1 Technical or vocational school after high school 32 3.21 4.04 Party affiliation Democrat 592 59.3 44.8 67.5 Republican 306 30.6 44.3 Notes: This table compares descriptive statistics for the analytic MTurk sample, the 2010 U.S. Census, and the larger MTurk sample obtained in Kuziemko et al. (2015). Statistics on political affiliation are taken from Gallup 2019 (year 2010). The data in our sample are especially overrepresentative of white, the young, college-educated, and Democratic individuals. Our data more closely resemble the larger MTurk sample collected by Kuziemko et al. (2015). In their sample, women are overrepresented by the same amount men are overrepresented in our data.12 White participants constituted 78 percent of the Kuziemko et al. (2015) sample compared with 81 percent in our data. The average age of their respondents was 35 years, whereas our average age (based on the median values of the “binned” age data) is 36 years. Meanwhile, 43 percent of their sample has at least a college degree, whereas 51 percent of our sample does. Finally, 68 percent of respondents in their sample voted for Barack Obama, whereas 66 percent of our sample either self-identify as Democrat or voted for a Democrat in the previous election. Overall, these statistics confirm that our data are not representative but are typical of MTurk respondents. In our main econometric specifications below, we weight the data to be representative of the joint distribution of two variables most implicated in the research questions: educational attainment and political affiliation. Educational attainment is taken from the U.S. Census 2010, and political affiliation is taken from the 2010 Gallup poll.13 Because party affiliation is not recorded in the U.S. Census, we estimate the joint distribution of these two variables using the raking method described by Deville, Särndal, and Sautory (1993) and implemented in Kolenikov (2017). ### Econometric Methods So far, we have defined and motivated interest in four statistics. We now describe our econometric models for estimating how much respondents are willing to trade for these social variables. To estimate utility parameters, we use choice modeling methods. We first estimate a nonparametric ordinary least squares (OLS) model to obtain raw estimates of respondent preferences for different combinations of social welfare variables. We then model the data using a Cobb-Douglas utility function, allowing us to estimate the relevant tradeoffs, which can then be represented as indifference (or iso-welfare) curves. The Cobb-Douglas model imposes additional functional form assumptions on the data; thus, the raw estimates from the OLS model provide information as to whether these assumptions are reasonable. (See Train [2003, pp. 62–63] for additional discussion on the relationship between choice models and Cobb-Douglas equations.) In the nonparametric approach, we estimate the normalized level of utility as the probability that society $X$ (independently of whether society A or society B is presented in the question) is chosen. The model includes interactions of indicator variables that correspond to combinations of societal values that a society could have. For example, five levels of average family income and college attendance gaps were randomly assigned to respondents. The interaction of these five variables results in twenty-five parameter estimates. The following regression model formalizes the approach: $1iXischosen=∑j=15∑k=15δjk1jk..X+∑l=15ρl1..l.X+∑m=15σm1...mX+ɛiX,$ (2) where $1i[Xischosen]$ is an indicator equal to 1 if society $X$ is chosen by individual i and 0 otherwise. Meanwhile, $1jklmX$ is an indicator equal to 1 (0 otherwise) if society $X$ has j level of income, k level of income inequality, l level of average education, and m level of equal access to higher education. Therefore, the coefficients $δjk$ represent fixed effects for each combination of income and income inequality (of which there are twenty-five). Such fixed effect coefficients are equivalent to utility values of each combination of income/income equality. The coefficients $ρl$ and $σm$ capture the utility of each level of average education and equal access, respectively. In separate models, we exchange k income inequality with l average education or m equal access, which provide combinations of the interactions of income/average education and income/equal access, respectively. The final specification replaces j level of income with m equal access, which provides the trade-off between equal income and equal access to higher education (i.e., “Rawlsian trades”). Finally, $ɛiX$ is an individual error term related to heterogeneity in preferences for $X$. Because the choice sets are randomly assigned to individuals, $E[ɛiX]=0$ and, therefore, the OLS model is an unbiased estimator of the normalized utility levels (Hainmueller, Hopkins, and Yamamoto 2014). Although the econometric model (equation 2) is flexible and provides interval-scaled estimates for different combinations of societal values, it does not allow us to estimate an indifference curve, nor does it take advantage of the actual structure of the data generation process. Therefore, our second methodological approach is the traditional choice model of McFadden (Train and McFadden 1978; McFadden, 1980). We begin by translating the societal preferences of an individual i for society A into a Cobb-Douglas utility function of the form: $UiA=α0+αYlnYA+βYlnYAIneq+αElnEA+βElnEAIneq+ɛiA,$ (3) where $αY$ and $αE$ are coefficients corresponding to preferences for levels of income and average education, and $βY$ and $βE$ represent the negative preference for inequality of income and educational opportunity, respectively.14 We also include a constant $α0$ and an error $ɛiA$, which represents the individual heterogeneity in preferences for societies. As the survey asks individuals to choose between two societies, A and B, for society A to be chosen, it must be the case that $Ui(A)-Ui(B)>0$. Given the functional assumption, this amounts to the following equation: $αYlnYAYB+βYlnYAIneqYBIneq+αElnEAEB+βElnEAIneqEBIneq+ηiAB>0,$ (4) where the error term $ηiAB=ɛiA-ɛiB.$ There are four features of equation 4 to highlight. First, if we assume that each error $ɛi$ follows a normal distribution, then $ηiAB$ would also be normally distributed and, therefore, the parameters can be estimated by a Probit Maximum Likelihood Estimator. Second, given that each pair of societies is randomly assigned across individuals, the estimates are unconfounded by preferences for equal college access and societal income. Third, because each society has the same set of features, there is not a constant in the model and, consequently, we do not include one in our estimation. Fourth, the Cobb-Douglas model imposes the functional form of decreasing marginal returns to each variable, therefore, the marginal rate of substitution (MRS) varies in the same proportion as the ratio between social statistics and the ratio of the utility parameters of each variable. In this section we present results. Results from equation 2 allow us to plot the ordered preferences that respondents have for the social welfare variables, and results from equation 4 allow us to estimate MRS statistics and indifference curves. We then test for heterogeneous preferences based on political affiliation and educational attainment. ### Nonparametric Results We start with estimates of the preferences for each social value from equation 2. These results allow us to rank different combinations of social statistics. Figure 1 shows a contour that summarizes the interactions $δjl$ (income and education levels), $δjk$ (income and income inequality), $δjm$ (income and equal access), and $δkm$ (income inequality and equal access). In each model, twenty-five estimates are available. Cells in white indicate that an assigned combination of societal values (e.g., income$45,000 and 90/10 income ratio 10.5) is less preferred. Darker shading indicates a stronger preference.15
Figure 1.

Nonparametric Estimates Social Welfare Preferences, Contour Plots, Weighted Sample

Notes: Each panel represents a pairwise trade among social variables. Shaded cell regions indicate strength of preference in standard deviation units for pairwise combinations of social variables. Black indicates greater utility; white indicates less utility. Utility estimates based on equation 2. Point estimates and standard errors shown in tables D.1, D.2, D.3, and D.4 in the online appendix.

Figure 1.

Nonparametric Estimates Social Welfare Preferences, Contour Plots, Weighted Sample

Notes: Each panel represents a pairwise trade among social variables. Shaded cell regions indicate strength of preference in standard deviation units for pairwise combinations of social variables. Black indicates greater utility; white indicates less utility. Utility estimates based on equation 2. Point estimates and standard errors shown in tables D.1, D.2, D.3, and D.4 in the online appendix.

As expected, higher income per capita, higher levels of college enrollment, lower income inequality, and more equal access to higher education are preferred, as indicated by the black shading in the upper right quadrants and the white in the lower left quadrants of each panel. These results demonstrate that respondents understood the survey and were providing preferences that were correctly ordered.

More interestingly, we can observe which social statistics appear to be more relevant to individuals. Because variables were generated based on observed SDs across CZs in the United States, the shaded cell regions indicate strength of preference in SD units. In general, individuals are willing to trade equivalent units of income for average education (figure 1, panel a), indicated by the uniformity along the diagonal from the upper-left to the lower-right. However, for income equality (figure 1, panel c) and equal access to higher education (figure 1, panel b), preferences for income outweigh equivalent preferences (in SD units) for equality (e.g., $45,000 income and a 90/10 income ratio of 10.5 is preferred to$39,000 income and a 90/10 income ratio of 8.8). Indeed, preferences for college access equality are nearly lexicographic, as increases in estimated utility largely result from increases in societal income along the vertical axis.

Linear probability models are common estimators for DCEs, but they have limited value if the objective is to recover the MRS (i.e., WTP) and to make comparisons across variables. We now turn to results from equation 4, which provide the statistics of interest but require parametric assumptions.

### Parametric Results

Having displayed how bundles are ranked, we can now move on to direct estimation of the indifference curve. We first present direct estimates from equation 4 in panel A of table 3. We display estimates from the unweighted and weighted data in columns 1 and 2, respectively.

Table 3.
Cobb Douglas Results, Main Effects, and Marginal Rate of Substitution (MRS)
Panel A: Probit Coefficient Estimates
UnweightedWeighted
∆ ln(income) 4.280*** 4.340***
(0.206) (0.262)
∆ ln(Inc. Inequality) −1.943*** −1.733***
(0.159) (0.206)
∆ ln(Educ.) 1.061*** 1.030***
(0.056) (0.064)
∆ ln(Educ. Inequality) −0.968*** −0.814***
(0.157) (0.198)
Panel B: Marginal Rate of Substitution
MRSInequality Inc.,Income −1.986*** −1.747***
(0.170) (0.217)
MRSInequality HE,Income −0.176*** −0.146***
(0.029) (0.035)
MRSAvg. HE enrollment,Income 0.372*** 0.356***
(0.022) (0.026)
MRSInequality Inc.,Inequality HE 11.294*** 11.980***
(1.910) (3.003)
N 3,996 3,996
Panel A: Probit Coefficient Estimates
UnweightedWeighted
∆ ln(income) 4.280*** 4.340***
(0.206) (0.262)
∆ ln(Inc. Inequality) −1.943*** −1.733***
(0.159) (0.206)
∆ ln(Educ.) 1.061*** 1.030***
(0.056) (0.064)
∆ ln(Educ. Inequality) −0.968*** −0.814***
(0.157) (0.198)
Panel B: Marginal Rate of Substitution
MRSInequality Inc.,Income −1.986*** −1.747***
(0.170) (0.217)
MRSInequality HE,Income −0.176*** −0.146***
(0.029) (0.035)
MRSAvg. HE enrollment,Income 0.372*** 0.356***
(0.022) (0.026)
MRSInequality Inc.,Inequality HE 11.294*** 11.980***
(1.910) (3.003)
N 3,996 3,996

Notes: Standard errors clustered by respondent in parentheses. MRS measured at the mean values. Probit coefficients based on equation 4. MRS estimates based on equation 5. Weighted estimates based on joint distributions of adult education and political affiliation using raking method of Deville, Särndal, and Sautory (1993) and implemented by Kolenikov (2017). HE = higher education.

***p < 0.01.

As expected, based on results from figure 1, increases in income and average education have positive effects on utility, and increases in the statistics measuring inequality have negative signs. All point estimates are statistically significant at p < .01.

The estimates of the Cobb-Douglas parameters allow us to map the indifference curves, which are drawn using the utility levels at different points of the y-axis. These parametric results mimic the contour figures generated from the nonparametric models: Average education is more relevant than income inequality, and income inequality appears more relevant than equal access to higher education. These results indicate that independent improvement in income equality is preferred to equivalent (in SDs) independent improvement in educational equality, as shown by the fact that the indifference curve is steeper in figure 1, panel c, than in figure 1, panel b. Indeed, when compared directly in figure 1, panel d, we see that respondents are willing to trade approximately 2 SD units of equal access to higher education for 1 SD unit of income inequality.

In figure 2, we graphically display the indifference curves that describe the trade-offs individuals are willing to make between social values. Although these figures are informative, they do not give a statistic of the exact trade-offs. For that purpose, we present the estimation results of equation 4 in panel B of table 3, which are the MRS (or WTP) statistics for certain social variables. The MRS can be easily recovered from the Cobb-Douglas utility as:
$MRSx,y=CoefficientxCoefficienty·yx,$
(5)
where y is the average societal income; x is a vector of the other societal variables of interest (average education and the two inequality statistics). The ratio indicates how much respondents are willing to pay in social income for values of x. In the special Rawlsian trade-off, y is set to equal access, and x is equal income; this MRS statistic indicates how much respondents are willing to trade equal access for equal income. Therefore, if we assume the mean values of x and y provide a reasonable approximation to estimate the MRS,16 the WTP can be expressed as the average income individuals are willing to sacrifice.17 The findings indicate:
• Individuals would be willing to decrease average income by $1,460 to reduce the gap in higher education from 54 percent to 44 percent. This implies that individuals would have a WTP of$1,168 for a 1 SD decrease in the higher education enrollment gap statistic.

• Individuals would be willing to decrease average income by $1,747 to decrease the 90/10 income inequality ratio from 9.6 to 8.6. This implies that individuals would have a WTP of$2,900 for a 1 SD decrease in the income inequality statistic.

• Individuals would be willing to decrease average income by $3,560 to increase higher education enrollment from 28 percent to 38 percent. This implies that individuals would have a WTP of$4,984 for a 1 SD increase in the average education statistic.

• Individuals would be willing to increase the higher education enrollment gap by 12 percent to decrease the 90/10 income ratio from 9.6 to 8.6. This implies that individuals would have a WTP of 2.49 SD of the higher education enrollment gap statistic for a 1 SD decrease in income inequality statistic.

Figure 2.

Log Linear Estimates Social Welfare Preferences, Indifference Curves

Notes: Each panel represents a pairwise trade among societal variables. Indifference curves derived from estimates from equation 4.

Figure 2.

Log Linear Estimates Social Welfare Preferences, Indifference Curves

Notes: Each panel represents a pairwise trade among societal variables. Indifference curves derived from estimates from equation 4.

As shown, individuals are willing to sacrifice important amounts of income to improve other social parameters. Indeed, educational attainment, which is often encouraged for its effects on economic growth, is independently supported; individuals are willing to sacrifice social income for an educated population. In that sense, economic growth should not be the sole focus of policy, and public policy decisions that require trade-offs between efficiency and other outcomes ought to be considered.

These results are robust to concerns about respondent-survey interactions. First, as respondents are asked the same question four times, they may lose interest and anchor on familiar variables; however, we see little difference in responses between the first and second two questions (tables D.5 and D.6 in the online appendix). Second, respondents may not comprehend the inequality statistics and favor the more familiar average income statistic. Individuals who respond correctly to the diagnostic questions express stronger WTP to reduce inequalities (tables D.7 and D.8 in the online appendix).

### Heterogeneous Preferences

We now turn to whether there is heterogeneity in the social preferences identified here. We identify heterogeneous effects based on political affiliation and respondent educational attainment. Both attributes are relevant for the variables included here. Differences in preferences for societal variables between right-leaning and left-leaning voters may be due to differences in beliefs about the costs of equality or in preferences for equality.18 Our survey design disentangles those competing explanations. Educational attainment is relevant because it both correlates with individual income and may influence the preferences for education variables.19

Results for political affiliation, showing important differences in the egalitarian preferences across political groups, are presented in table 4. 20 The estimates show that, compared to Republicans, Democrats are willing to give up nearly three times the amount of average income for either of the equality measures. These differences in the WTP are statistically significant at p < .01. Democrats also have a greater WTP for average educational attainment (p < .05); however, the magnitude of this difference is not large. Both groups are willing to sacrifice important amounts of income (over $4,000) to increase the average higher education enrollment by 1 SD (14 percent). This result suggests the presence of an overlapping consensus between parties with respect to increasing average levels of education—however, the parties are far apart with respect to equalizing income or educational opportunities. Finally, it is interesting to note that both groups give greater weight to income equality relative to access to higher education, despite having different preferences for equalities of both kinds. Table 4. Marginal Rate of Substitution (MRS), Respondent Political Affiliation ParameterDemocratRepublicanDemocrat − Republican MRSInequality Inc.,Income −2.575*** −0.893*** −1.683*** (0.243) (0.252) (0.350) MRSInequality HE,Income −0.237*** −0.082* −0.154** (0.040) (0.046) (0.061) MRSAvg. HE enrollment,Income 0.407*** 0.294*** 0.113** (0.031) (0.032) (0.045) MRSInequality Inc.,Inequality HE 10.888*** 10.830* 0.058 (1.858) (6.327) (6.594) N 2,368 1,224 3,592 ParameterDemocratRepublicanDemocrat − Republican MRSInequality Inc.,Income −2.575*** −0.893*** −1.683*** (0.243) (0.252) (0.350) MRSInequality HE,Income −0.237*** −0.082* −0.154** (0.040) (0.046) (0.061) MRSAvg. HE enrollment,Income 0.407*** 0.294*** 0.113** (0.031) (0.032) (0.045) MRSInequality Inc.,Inequality HE 10.888*** 10.830* 0.058 (1.858) (6.327) (6.594) N 2,368 1,224 3,592 Notes: Standard errors clustered by respondent in parentheses. MRS measured at the mean values. Probit coefficients based on equation 4 shown in online table D.9. MRS estimates based on equation 5. Standard errors for tests of significance among partisans calculated using the delta method. HE = higher education. ***p < 0.01; **p < 0.05; *p < 0.1. Results based on educational attainment are presented in table 5. 21 Respondents with college degrees have greater WTP for reductions in income inequality than those with some college education. Conversely, those with no college experience have greater WTP for reductions in income inequality than the college educated. Thus, WTP for income equality are not monotonic according to educational attainment. Meanwhile, WTP statistics for access to higher education are very similar for all educational groups. This finding is interesting because political affiliation influences preferences for both income equality and access to higher education, while educational attainment (a class status indicator) influences only preferences for income equality. If preferences for equal college access are class-insensitive, then it may be easier to obtain a consensus for policies promoting equal access to higher education, despite the fact that preferences for equal access are weaker on average. This feature of access to higher education may be a second explanation (in addition to perceived spillover benefits) for its prominence in U.S, society. Finally, college-educated respondents have greater WTP for levels of college enrollment than those with no college education, but there is no difference when compared to those with some college experience. Table 5. Marginal Rate of Substitution (MRS), Respondent Level of Education ParameterCollege or MoreSome CollegeLess than CollegeCollege − SomeCollege − Less MRSInequality Inc.,Income −1.968*** −2.921*** −1.090*** 0.952* −0.878* (0.225) (0.450) (0.397) (0.503) (0.457) MRSInequality HE,Income −0.194** −0.209*** −0.206*** 0.015 0.012 (0.038) (0.072) (0.068) (0.081) (0.078) MRSAvg. HE enrollment,Income 0.392*** 0.394*** 0.211*** −0.002 0.181*** (0.030) (0.055) (0.034) (0.063) (0.046) MRSInequality Inc.,Inequality HE 10.150*** 13.991*** 5.280** −3.841 4.870 (2.086) (4.696) (2.413) (5.138) (3.189) N 2,020 1,008 456 3,028 2,476 ParameterCollege or MoreSome CollegeLess than CollegeCollege − SomeCollege − Less MRSInequality Inc.,Income −1.968*** −2.921*** −1.090*** 0.952* −0.878* (0.225) (0.450) (0.397) (0.503) (0.457) MRSInequality HE,Income −0.194** −0.209*** −0.206*** 0.015 0.012 (0.038) (0.072) (0.068) (0.081) (0.078) MRSAvg. HE enrollment,Income 0.392*** 0.394*** 0.211*** −0.002 0.181*** (0.030) (0.055) (0.034) (0.063) (0.046) MRSInequality Inc.,Inequality HE 10.150*** 13.991*** 5.280** −3.841 4.870 (2.086) (4.696) (2.413) (5.138) (3.189) N 2,020 1,008 456 3,028 2,476 Notes: Standard errors clustered by respondent in parentheses. MRS measured at the mean values. Probit coefficients based on equation 4 shown in online table D.10. MRS estimates based on equation 5. Standard errors for tests of significance among educational level calculated using the delta method. HE = higher education. ***p < 0.01; **p < 0.05; *p < 0.1. In this paper we have estimated social preferences for efficiency, educational attainment, income equality, and equal access to higher education. Not surprisingly, average income is an important aspect of respondents’ social welfare functions. More interestingly, respondents are willing to exchange societal income to increase levels of educational attainment (meaning that educational attainment is not desired purely for economic reasons) as well as both aspects of equality (meaning that respondents have distributive concerns). Moreover, respondents display a stronger independent preference for income equality relative to expanding access to college. This finding contradicts the traditional notion that equal access to higher education is more important than income equality in the United States. Quite possibly, college access is believed to have positive effects on economic growth and income equality; for this reason, narrowing the income gap in college attendance has large popular support, despite its having relatively low independent value. Finally, we emphasize that the implemented discrete choice experiment has useful features that can be replicated in subsequent research. First, we use true variation in income, education, and inequality statistics. Second, by randomly assigning societal income, we impose a budget constraint, which provides a common metric for making comparisons across different social variables. Third, we integrate different dimensions of societal well-being into a common framework. Although discrete choice experiments are prevalent in political science and some subdisciplines of economics, they have not been used to identify the types of social preferences evaluated here. Consequently, additional research with different samples and social statistics could provide a deeper understanding of social preferences for efficiency, income equality, and other variants of equality of opportunity, in addition to other social concerns. 1. Imbens, Rubin, and Sacerdote (2001) find increases in unearned transfers have small effects on earned income, particularly among individuals with low earnings. 4. See Gallup (2016) and Bankrate (2016), respectively. 5. See Bureau of Labor Statistics Employment Projections (https://www.bls.gov/emp/). 6. An exponential distribution of parameter $β$ has a probability density function $f(x|β)=1βe-x/β$. 7. Although respondents may still consider the social status of their children, it is not clear they should be fully veiled. First, what constitutes a veiled experiment is ambiguous and preferences vary by the specification (Amiel, Cowell, and Gaertner 2009). Second, there is evidence that nonveiled respondents have greater justice concerns than veiled respondents (Herne and Suojanen 2004; Traub et al. 2005). 8. Discrete choice experiments are a method for studying social preferences for discrete outcomes and are widely used in different research areas (see Vossler, Doyon, and Rondeau 2012 for a summary). 9. For the diagnostic questions about income equality and equal college access statistics, 79.4 and 61.2 percent of respondents answered correctly, respectively, and 71.1 percent of respondents answered a final diagnostic question correctly that asked to identify the difference between two societies in a simulation of the survey. Screen shots of the survey platform are available in a separate online appendix that can be accessed on Education Finance and Policy’s Web site at https://www.mitpressjournals.org/doi/suppl/10.1162/edfp_a_00271. 10. Additional details about these data and the construction of these variables are available in the online appendix. 11. A sample size of 999 was deemed sufficient based on previous literature (de Bekker-Grob et al. 2015). Based on the number of choice tasks, attributes, and attribute levels, Orme (1998) recommends a sample size of 313. Average completion time was 6 minutes 52 seconds; therefore, the hourly rate was$6.54.

12.

Our sample has more male participants than other MTurk samples that have been evaluated (Berinsky, Huber, and Lenz 2012; Huff and Tingley 2015).

13.

The Gallup poll dichotomizes party affiliation by separating independents (about 38 percent of the sampled respondents) into whether the respondent leans Republican or Democrat. We dichotomize political affiliation similarly. See Gallup (2019).

14.

A negative coefficient on $βE$ indicates disutility for higher levels of the 90/10 higher education attainment gap—that is, inequality of access to higher education.

15.

Estimated coefficients and standard errors are shown in tables D.1, D.2, D.3, and D.4 in the online appendix. Results from the unweighted data are available in figure C.1 in the online appendix.

16.

In other words, that the MRS is stable across different values of x and y; based on the results from figure 2, this assumption seems reasonable.

17.

Standard errors for the MRS statistics are calculated using the delta method. All results in the itemized list below are statistically significant at p < .01.

18.

Our survey asked participants two questions about their political affiliation: (1) if they self-identify as one of the major political parties, and (2) which political party they most recently voted for. We code as “right-leaning” a respondent who self-identified/voted Republican or Libertarian. We code as “left-leaning” a respondent who self-identified/voted Democratic or Green. Our identification of political affiliation reduces the sample from 3,996 observations to 3,592.

19.

Educational attainment is coded as 0 for a four-year college degree or more; 1 for “some college”; 3 for a high school diploma or less. We exclude trade and vocational schools from the analysis. This reduces the sample to 3,484 observations.

20.

Table D.9 in the online appendix displays model coefficients.

21.

Table D.10 in the online appendix displays model coefficients.

We want to thank Randall Reback and Ilyana Kuziemko, as well as three anonymous referees, for their insightful comments. All errors are our own.

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