Perceptions of Distributive Justice in Latin America During a Period of Falling Inequality

This paper explores perceptions of distributive justice in Latin America during the 2000s and their relationship with income inequality. In line with the fall in income inequality in the region, the paper documents a widespread, although modest, decrease in the share of the population that believes income distribution is unfair. The fall in the perception of unfairness holds across very heterogeneous groups of the population. Moreover, perceptions evolved in the same direction as income inequality for 17 of the 18 countries for which microdata are available. The analysis reveals that unfairness perceptions are more correlated with relative measures of income inequality than absolute ones, and that individual characteristics are correlated with distributive perceptions. On average, individuals who are older, more educated, unemployed, and left-wing tend to perceive income distribution as more unfair. The paper shows that the decrease in unfairness perceptions during the past decade was due to changes in inequality, rather than to composition effects. Finally, the paper shows that individuals who perceive income distribution as very unfair are more prone to mobilize and protest.

This paper explores perceptions of distributive justice in Latin America during the 2000s and their relationship with income inequality. In line with the fall in income inequality in the region, the paper documents a widespread, although modest, decrease in the share of the population that believes income distribution is unfair. The fall in the perception of unfairness holds across very heterogeneous groups of the population. Moreover, perceptions evolved in the same direction as income inequality for 17 of the 18 countries for which microdata are available. The analysis reveals that unfairness perceptions are more correlated with relative measures of income inequality than absolute ones, and that individual characteristics are correlated with distributive perceptions. On average, individuals who are older, more educated, unemployed, and left-wing tend to perceive income distribution as more unfair. The paper shows that the decrease in unfairness perceptions during the past decade was due to changes in inequality, rather than to composition effects. Finally, the paper shows that individuals who perceive income distribution as very unfair are more prone to mobilize and protest.

Introduction
One of the most salient features of the 21st century is the rising concern about economic inequality, to the point that it is assessed as 'the defining challenge of our time.' 4 Inequality has been observed with concern by multilateral organizations, politicians and religious leaders. 5 The concerns about inequality are not only based on efficiency arguments, but especially on a moral ground. Anecdotal evidence suggests that concerns about inequality extend to the general population. For instance, protests such as 'Occupy Wall Street' are manifestations of the discontent with the wide income gaps. However, research on how the general population thinks about inequality, and how factors like age, gender, or education relate to our views on what is fair and unfair is still scarce.
Central to this paper is the concept of social justice or fairness and the underlying desire to live in a just world. 6 Since the seminal paper of Rabin (1993), the concept of fairness has been increasingly important in the field of economics. Fehr and Schmidt (2003) provide an extensive review of the experimental evidence related to the desire for fairness. The authors show how in dictator games, participants share part of their endowments even though they could keep it all. Similarly, in ultimatum games, participants accept a monetary loss to penalize behavior that is not considered fair, and in gift exchange games, participants are averse to inequitable outcomes.
The desire for fairness seems to transcend cultural differences. Throughout Jerusalem, Ljubljana, Pittsburgh, Tokyo, the Machiguenga of the Peruvian Amazon, and 15 other small-scale societies, ultimatum game offers are always positive, and payoffs that are not considered fair are punished by rejecting positive offers at considerable rates. 7 Evidence from psychology suggests the desire for fairness is ingrained in human nature. Children as young as three years old react negatively to unfair distributions (Loblue et al, 2011), 8 and children's aversion to inequities also transcends borders (Blake et al., 2015). Insights from biology suggest preferences for fairness might have evolutionary origins. In their famous experiment, Brosnan and de Waal (2003) find that capuchin monkeys reject unequal payoffs, a finding that has been replicated in other species, such as dogs (Range et al., 2009) and birds (Wascher and Bugnayar, 2015). Bjornskov et al. (2013) show that people who perceive their society as fairer exhibit higher levels of subjective well-being and, in the context of 3 distributive justice, Corneo and Fong (2008) find that US households put a monetary value on social justice of about a fifth of their disposable income.
In this paper, we study the general population's beliefs about distributive justice, i.e., the perception of whether income distribution is fairly distributed, in the context of a pronounced decline in the income inequality in Latin America (LA), a highly unequal region. Our approach is to combine income microdata originated from household surveys with perceptions data from opinion polls surveys. We exploit the heterogeneity across years, countries, and individuals within countries to analyze how our views of fairness relate to the actual levels of income inequality.
Evidence of the relationship between fairness perceptions and income inequality, particularly in LA, is rather scarce. In Argentina, Rodriguez (2014) finds that people who consider their income to be fair tend to perceive lower levels of inequality. The work closest to this paper is CEPAL (2010), which shows that perceptions of distributive inequity in LA remained persistently high during the 1997-2007 period, consistent with the high levels of inequality of the region.
In the first part of the paper we document a series of stylized facts. After a decade of increasing disparities in LA, the 2000s saw a remarkable decrease in the levels of inequality. Despite this, the region continues to be one of the least egalitarian in the world, with levels of inequality comparable to those of Africa (Alvaredo and Gasparini, 2015). To the best of our knowledge, we are the first to show that unfairness perceptions fell during the 2000s in line with the evolution of income inequality, although we find that unfairness perceptions are not very responsive to changes in inequality. During the 2002-13 period, a 1 percentage point decrease in the Gini coefficient was associated with a 1.4 percentage point decrease in the share of the population perceiving the distribution as unfair or very unfair.
The evolution of unfairness and inequality was consistent across countries: perceptions moved in the same direction as the Gini coefficient for 17 of the 18 countries of the region for which microdata are available. We also show that this change was widespread across very heterogeneous groups of the population, and that the decline in unfairness perceptions was driven mainly by a reduction in the intensity of such beliefs (i.e., compared to ten years ago, fewer people perceive the distribution as very unfair).
Next, we shed some light on the discussion of whether inequality should be measured with relative vs. absolute indicators, by analyzing which indicators are more correlated with unfairness perceptions. We show that relative indicators-and in particular, the Gini coefficient-are the ones mostly correlated with people's perception of fairness.
In the second part of the paper we explore how individual factors and belief systems affect how inequality is perceived. We find that older, unemployed and more educated people are more likely to perceive income distribution as unfair. A decomposition exercise provides evidence on the relative contribution of composition effects vis-à-vis changes in aggregate inequality trends, to explain the decline in unfairness perceptions during the last 4 decade. Regarding beliefs and unfairness, consistent with theories of fairness, we find that people leaning to the right of the political spectrum, Catholics, and optimists are more likely to believe income distribution is fair. Finally, we analyze the link between fairness perceptions and propensity to protest, and show some suggestive evidence that people who believe inequality is very unfair are more prone to mobilize.
The rest of the paper is organized as follows. In section 2 we document some stylized facts about distributive justice perceptions and the evolution of income inequality. In section 3, we shed some light on the discussion of whether income inequality should be measured with absolute or relative measures by studying the relationship between perceptions data with different indicators of income inequality. In section 4 we analyze whether individuals' unique backgrounds shape their perception of fairness, by analyzing how individuals' characteristics relate with perception of distributive justice; and compare the relative importance of the demographic variables vis-à-vis aggregate trends of inequality to explain the observed changes in fairness perceptions. In section 5 we analyze the relationship between different beliefs systems and unfairness, while in section 6 we explore the link between fairness perceptions and social cohesion. Section 7 concludes.

Income inequality and fairness: Some stylized facts
Latin America has long been characterized as a region with high levels of income inequality, among the least egalitarian regions in the world. Among the ten most unequal countries of the world for which household survey data are available, eight of them are in LA, and the rest in Sub-Saharan Africa (World Bank, 2016), probably the most unequal region in the world (Alvaredo and Gasparini, 2015). Although the disparities between the poor and rich are still large, after a period of increasing inequality during the 1990s, the region experienced a 'turning point' in the 2000s, when income inequality saw a widespread decrease across the countries of the region. 9 The social gains in terms of inequality contrast with what happened in other developing regions in the world, where the declines in inequality were much more modest (e.g., such as in the Middle East and North Africa), or even increased (such as in East Asia and Pacific, cf. Alvaredo and Gasparini, 2015, p. 29), and also contrasted with the increases in inequality experienced by developed countries (cf., Atkinson, Piketty and Saez, 2011).
In this section, we replicate the widespread decrease in income inequality in LA, and show how perceptions about fairness moved in the same direction. Our primary data set for income inequality comes from a regional data harmonization effort known as SEDLAC (CEDLAS and World Bank), which increases the cross-country comparability from official household surveys. 10 5 Figure 1 shows a scatterplot of the Gini coefficient of the per capita household income (in 2005 USD PPP) of 18 LA countries for which comparable data are available both at the beginning of the 2000s and one decade later (we use years close to 2002 and 2013). The figure includes a 45-degree line denoting all the points for which the Gini coefficient is the same in both years, and points to the right of this line denote decreases in income inequality. As is immediately apparent from Figure 1, with the exception of Costa Rica, all countries of the region experienced a decrease in income inequality. The regional trend is consistent with the cross-country evidence: the average Gini coefficient has decreased every year since the beginning of the decade, declining from 0.54 in 2000 to 0.47 in 2015. Moreover, as Rodríguez-Castelán et al. (2016) note, the decline in income inequality of the region is robust to the inequality indicator used and to the method of aggregation of the countries.
We complement the 'objective' evolution of income inequality with data from public opinion polls from Latinobarómetro, which has conducted surveys in 18 Latin American countries since the 1990s, interviewing about 1,200 individuals per country about individual socioeconomic background and preferences regarding political and social issues (including inequality). The surveys are representative at the national level for the population over 18 years old. 11 In every country, Latinobarómetro asks "How fair do you think income distribution 6 is in [country]? Very fair, fair, unfair or very unfair?" Using this question, we construct dichotomic variables reflecting whether the individual believes income distribution is unfair or very unfair. 12 Our baseline definition of unfairness perceptions includes all the individuals who perceived income distribution as unfair, i.e., we include those who answered both 'unfair' and 'very unfair', but also show the results are robust to a narrower definition of unfairness (i.e., considering only those who answered 'very unfair'). Figure 2 shows the percentage of each country's population that believes income distribution is either unfair or very unfair in 2002 and 2013. There are several things to note about Figure 2. First, the percentage of the population that believes income distribution is unfair is strikingly high in both points in time. The regional average was as high as 86.6% in 2002 (with Argentina peaking at 97.7% of the population, in the midst of a severe crisis). Even in Venezuela, the country with the smallest perception of unfairness in 2002, three out of four individuals (74.5%) perceived inequality as unfair in 2002. Although lower, the share of the population unsatisfied with income distribution was still astoundingly high in 2013, when about 72.8% of the population thought inequality was unfair or very unfair.
to analyze the relationship between inequality and subjective well-being; and Bonnet et al. (2012) to study satisfaction with the privatization of state-owned companies in Latin America. 7 Second, there was a widespread decrease in the share of the population that perceived income distribution as unfair. Relative to the previous decade, in 2013 fewer people perceived income distribution as unfair in 16 of the 18 countries analyzed. The change in perceptions ranges from modest decreases, such as in Chile, where the decline was of less than one percentage point, to remarkable reductions, such as in Ecuador, where perceptions about unfairness declined from 87.5% to 38.6% in the 2002-13 period.
Lastly, with the exception of Honduras-where, despite falling inequality, the population perceived the distribution as more unjust-in the rest of the countries both variables moved in the same direction. To see this more clearly, in Figure 3 we show jointly the change in the perceptions of unfairness (as measured by the percentage point change in the share of the population reporting income distribution is unfair or very unfair), and the change in the Gini coefficient during the 2002-13 period. As can be easily seen from Figure  3, most LA countries lie in the third quadrant, where both inequality and unfairness perceptions decreased. The relation between unfairness perceptions and the Gini coefficient is strong both across countries and time. In Figure 4 panel (a), we show the cross-country correlation between unfairness perceptions and income inequality in all the years for which both 8 indicators are available, while in panel (b) we show the average regional trend over the 1997-2015 period. 13 Gini coefficient (RHS) % Unfair or very unfair (LHS) 9 were calculated through linear interpolations. Panel (b) shows the unweighted average Gini coefficient of LA and unfairness perceptions since 1997. To ensure the same set of countries is analyzed over time, a linear extrapolation of inequality indicators was made in the years in which income microdata was not available.
Figures 4a and 4b indicate that income inequality and unfairness perceptions are closely related. The linear correlation between the Gini coefficient and the unfairness perceptions across countries is 0.39, while the Spearman correlation between the ranking of countries is 0.45 (in both cases, p<.01). The correlation over time is stronger than across countries. The linear correlation of the series plotted in Figure 4.b is notably high (0.80), and the correlation between the Gini coefficient and perceptions is very similar if we consider the share of individuals who responded that income distribution is very unfair (0.79).
Our results point to a low elasticity of unfairness perceptions to income inequality. 14 Pooling the data from all the countries, we find that, during the 2002-13 period, a one percentage point decrease in the Gini coefficient was associated with a 1.4 percentage point decrease in the share of the population perceiving the distribution as unfair or very unfair. 15 To put this number in context, this means that, at the pace of inequality reduction of the 2000s, it would roughly take LA more than another decade to reduce the population that perceives income inequality as unfair to 50%.
The decrease in unfairness perceptions-from almost 90% in 2001 to 72.8% in 2013does not seem to be driven by any particular group of the population, but is rather a widespread phenomenon. To see this, in Figure 5 we present the perceptions of fairness by dividing the population into several subgroups: according to their age, gender, educational achievement and labor status.  Not only injustice perceptions fell during the last decade, but the intensity of beliefs also diminished over time. To see this, Figure 6 shows the evolution of the different possible answers to the question of unfairness perceptions. LA, 1997LA, -2015 Note: This figure presents the average across 18 LA countries of the share of individuals that perceived income distribution as very unfair, unfair, fair, and very fair over the 1997-2015 period.

Figure 6. Intensity of unfairness perceptions in
As can be seen from Figure 6, the decrease in unfairness perceptions was driven mainly by strong beliefs about unfairness (i.e., people who perceived inequality as very unfair). While in 2001, 37.4% of the population thought income distribution was very unfair, this figure decreased to 25% in 2015. In contrast, weak beliefs about unfairness (i.e., the population that responded income distribution was only 'unfair'), have been more volatile, remaining relatively constant during the 2000s (from 51.4% in 2001 to 49% in 2015). On the other hand, the share of the population believing in a fair distribution increased from a meager 9.5% in 2001 to a sizable 22.6% in 2015, while strong beliefs on fairness (i.e., 'very fair'), have remained under 5% throughout all the 2000s.

Is fairness absolute or relative?
In the previous sections, we showed that a large, albeit decreasing, share of the population believes income distribution is unfair, and that such levels and evolution are consistent with a high, but also declining Gini coefficient. Despite being the most widely used indicator to measure income inequality, the general population's views on income distribution might, in fact, be better captured with other indices.
The literature on inequality measurement makes a crucial distinction between two types of indicators: the relative (such as the Gini coefficient) and absolute ones (such as the variance). The main distinction between them is that relative indicators fulfill the scale- In practical terms, this means that if the income of the entire population increases by the same percentage, relative indicators will remain unchanged, while absolute indicators might increase significantly. The question on which indicator should be used in practice has led to a heated debate in the literature. Milanovic (2016) provides several arguments to defend the use of relative indicators in practice, but the fact that they are better from a technical point of view does not say anything about how the general population perceives fairness. 16 Understanding whether people think about distributive fairness through the lens of relative or absolute indicators is more than a technical measurement issue or an economist's whim. As Ravallion (2003) and Atkinson and Brandolini (2008) note, it has profound consequences about how we think of important issues such as the distributive effects of globalization or trade openness. As measured by absolute indicators, globalization has deteriorated the income distribution since the absolute income differences between the rich and the poor have increased, but under the lens of relative measurement, income inequality has been reduced, since the poor have grown proportionally more than the rich in relative terms.
We take an agnostic approach and let the data show which inequality indicators are more correlated with the perceptions of distributive justice. To do this, we calculate 13 different measures of income inequality for all the countries in our sample, and correlate all the indicators with the share of the population that believes income distribution is unfair over time. 17 Table 1 shows the results for the three different ways of calculating the correlation between the perceptions and inequality indicators at the regional level: (i) pooling all the data (i.e. taking simultaneously the indicators of all the countries and calculating the correlations with that pool of data, columns 1-3); (ii) calculating the average of the indicators across all the countries in every year, and then calculating the correlation between the average values of the indicators (columns 4-6); and (iii) calculating the correlations between inequality indicators and perceptions at the country level and then averaging the results (columns 7-9).
Our results suggest perceptions of unfairness are more correlated with relative indicators rather than absolute ones (Column 1 of Table 1). In fact, the Gini Coefficientprobably the most used inequality indicator in the literature-is the one with the highest explanatory power. 18 On average the Gini coefficient explains about 15 percent of the variability of the perceptions about unfairness, as measured by the R-squared. On the other hand, the absolute indicators of inequality correlate negatively with the unfairness perceptions, and the explanatory power of such indicators is lower than of the relative indicators. It is interesting to note that indicators often mentioned in the mass media, such as the ratio between the richest 90% and the poorest 10%, exhibit low explanatory power, although this may be due to mismeasurement of the top incomes. The results of the high correlation between unfairness perceptions and income inequality seem to be driven by the population that perceives inequality as very unfair (columns 2, 5, and 8), rather than just unfair (columns 3, 6, and 9), as the correlations in the latter are close to zero for almost all indicators.
These results are consistent with experimental evidence from Amiel andCowell (1992, 1999) who show that support for the scale-invariance axiom was greater than for translation invariance, reflecting greater support for relative inequality indicators. Moreover, the results are also consistent with graphical evidence that shows decreasing relative inequality, but rising absolute inequality during the 2000s in LA ( Figure 4 and Figure 7, respectively). Since unfairness perceptions also declined over time, the relative indicators do a better job of tracing such evolution.

Fairness through the eyes of people
In this section, we explore how individuals' characteristics relate to their views on inequality. As shown in the previous section, most of the change in perceptions over the last decade was driven by the share of the population that perceived income distribution as being very unfair, thus we focus on explaining the correlates of such measure, although we also show the results for a broader definition of unfairness.

DATA
Our sample of individuals comes from pooling all LA countries from nine different waves of Latinobarómetro over the 1997-2015 period. Appendix Tables A1-A3 show basic descriptive statistics of the sample. Roughly half of respondents are women (50.9%), the average age was 39.4 (most interviewees-38%-were aged 25-40). Over half of the sample (57.3%) reported being married or in a civil union, and are adherents to Catholicism (70.7%).
About 90 percent of the sample are literate, the majority of respondents (76%) completed at least primary school, while a third of them (32.3%) had secondary education or more. Almost two-thirds of the sample (64%) were part of the labor force, and 9.9% of them were unemployed. Access to basic services among respondents is relatively high: 87.6% of individuals had access to running water inside their dwelling and over two-thirds (69.7%) reported that their dwellings had access to a flush toilet connected to a waste-removal system (i.e., sewerage). Ownership of durable goods ranges from low levels regarding cars and computers (27.3% and 29.6%, respectively) to high levels regarding fridges and mobile phones (79.2% and 76.4%).
To assess the differences between Latinobarómetro's sample and the household surveys' sample (SEDLAC), Appendix Table A4 compares a set of summary statistics in both data sets in 2013. To ensure comparability of the samples, we restrict the calculations to individuals aged over 18, and to countries with data available in both databases. In general, the samples are similar in observable characteristics. For instance, the average age in Latinobarómetro's reduced sample is 40.6 years, while in SEDLAC it is 42.7 years. Similarly, the percentage of males is 48.9% in Latinobarómetro and 47.6% in SEDLAC. The main difference arises from educational attainment. On average, the SEDLAC subsample is more educated (46.1% of the population has secondary education or more, while this figure is 38.8% in Latinobarómetro).

ESTIMATION STRATEGY
To formally assess the relationship between individuals' characteristics and fairness perceptions, we run Logit regressions where the dependent variable takes the value 1 if the individual believes income distribution is very unfair and 0 otherwise. In the baseline specification, we assume that unfairness perceptions can be characterized according to the following equation: where is the variable of interest, namely, whether individual of country during year believes income distribution is very unfair or not; is a vector of individual characteristics that includes the age, sex, civil status, education, and type of job; is the country's Gini coefficient; is a vector of country and subnational fixed effects 19 ; is a vector of year fixed effects and is the error term.
We are interested in the sign and magnitude of and . The first of these coefficients captures the relationship between the individual's characteristics and unfairness perceptions. If unfairness is uncorrelated with observable characteristics, then this coefficient should not be statistically different from zero. On the other hand, captures the relationship between the Gini coefficient and the perceived fairness after controlling for an individual's covariables. If subjective measures of income inequality are significantly correlated with their objective counterparts, we would expect this coefficient to be positive and statistically different from zero. Table 2 summarizes the main results of the Logit regressions under different specifications. Column (1) presents the results controlling only for the Gini coefficient. Column (2) includes basic demographic indicators: age, age squared and gender. Column (3) incorporates dummies for civil status and educational variables, namely, literacy and maximum educational attainment. Column (4) includes dummies for labor market variables: labor force participation and unemployment. Column (5) incorporates access to basic services-running water and sewerage-and asset ownership, namely ownership of a computer, washing machine, telephone and car. Column (6) replicates the same specification as column (5), but with Ordinary Least Squares (OLS). All specifications include country, subnational and year fixed effects.

RESULTS
Our first result is that the Gini coefficient has a positive and statistically significant relationship with unfairness perceptions, consistent with the evidence shown in the previous section. For example, in a country with average characteristics, a decrease of one point of the Gini coefficient (from 0.496 to 0.486) decreases by about half a percentage point the share of the population that believes income distribution is very unfair. Such magnitude is quite similar with the Logit (column 5) and OLS (column 6) estimates, and does not vary much across different specifications (columns 1-5). It is important to stress that the interpretation is not causal. The relationship between income inequality and unfairness perceptions can go both ways. On one hand, higher inequality can increase the share of the population that believes distribution is unfair. But as more people perceive income distribution as unfair, inequality can be affected through several channels (e.g., more demand for redistribution). The results of the regressions also suggest that, holding all other variables constant, older people tend to respond more often that income distribution is very unfair, although the relationship between age and unfairness perception is not linear. This result is similar to that of Bellemare et al. (2008), who find that young individuals have lower aversion to inequity than other groups in an experimental setting.
On average, males are just as likely as females to perceive income distribution as very unfair, while married individuals are less likely to do so. Education seems to be correlated with perceptions of unfairness but only at the highest level of education-for those who have completed primary and secondary school, the coefficients are not statistically different from zero. Being part of the labor force does not seem to be correlated with perceptions of unfairness, but being unemployed does. On average, the unemployed population is more likely to perceive income distribution as unfair. The dummy variables for access to basic services and asset ownership have negative signs. In household surveys, these variables tend to be correlated with household income-although the correlations tend to be lowso a possible interpretation is that relatively richer people (as measured by access to services and assets), are less likely to perceive income distribution as very unfair.
Next, we run a similar set of regressions but, instead of considering only the people who responded that income distribution is 'very unfair,' we also consider the ones who answered only 'unfair.' The output of those regressions is reported in Table 3.
When we use the broader definition of unfairness, the effect of education on perceptions of unfairness becomes stronger: in all the specifications, educational attainment is positively correlated with a sense of distributive unfairness. Moreover, the magnitude of the coefficient increases with the level of qualification: the coefficient of those with tertiary education complete is three times larger than the coefficient of those with only primary education complete. These results are similar to those of Rodriguez (2014), who finds that more years of education are associated with higher perceptions of inequality. The other two main differences with respect to the baseline set of regressions are that the civil status stops being statistically significant, and the male dummy becomes negative and statistically significant (in both cases consistently so across specifications).

DECOMPOSING CHANGES IN UNFAIRNESS OVER TIME
One of the broad takeaways from the regression results is that both the aggregate inequality trends and the individual's characteristics are associated with unfairness perceptions. A natural follow-up question is to ask what factors explain to a greater extent the reduction in the unfairness beliefs over the last decade: the observable characteristics of the individuals or the aggregate inequality trends. To analyze this point, we perform a basic Oaxaca-Blinder decomposition, taking 2002 and 2013 as the two 'groups' to be compared (see Appendix C for further detail on the Oaxaca-Blinder decomposition). The covariables included in the decomposition are analog to those of Column (4) in Table 2. The results are summarized in Figure 8.

Figure 8. Oaxaca-Blinder decomposition of unfairness perceptions in LA, 2002-2013
Note: This figure presents the estimates of the Oaxaca-Blinder decomposition. The dependent variable is a dummy that indicates whether the individual believes income distribution if unfair or not, and the regressors include the Gini coefficient, age, age squared, and dummy variables for: civil status, gender, literacy, maximum educational attainment, labor force participation and unemployment status. Results were calculated pooling data for 18 LA countries. The 'explained' part of the results refers to the endowment effects (changes in the value of the covariables), while the 'unexplained' refers to changes in the coefficients and the interaction terms.
During the 2002-13 period, the share of the population perceiving the distribution as unfair decreased 13.9 percentage points, from 86.9% to 73.0%. 20 The decomposition results suggest that a third of such change (4.5 percentage points) cannot be explained by changes 20 These figures are slightly different from those presented in the previous section due to some observations having missing values in the covariables relevant for the decomposition. in the covariate's values (i.e., changes in the 's of the regression), but rather are a consequence of changes in the elasticity of perceptions to each covariable (i.e., the 's of the regression), while the other two-thirds (9.3 percentage points) can be explained by changes in the covariables' values.
Among the covariables included in the decomposition, the one that explains the decline in the unfairness perceptions is the change in the value of the Gini coefficient, and not changes in the composition of the groups. In fact, although marginal, the demographic component actually contributed to an increase in the unfairness perceptions. This is mostly due to changes in average age and educational attainment. Between 2002 and 2013 both the average age and the maximum educational attainment saw a modest increase in our sample, and since older and more educated individuals are more likely to perceive the distribution as unfair, these changes counteracted part of the decrease in unfairness perceptions.

How beliefs shape fairness perceptions
Ingrained in any judgement of income distribution as unfair is an assessment of the sources of the inequalities. Theories of fairness suggests that societies that perceive that inequality arises from hard work and effort are less likely to perceive distribution as unfair, while societies that believe luck, connections and corruption are the main determinants of income are more prone to see inequality as unfair (see Alesina et al., 2001). 21 Understanding why some people perceive outcomes as a consequence of luck while others think it is due to effort is challenging, although the literature has provided a few clues.
First, political views matter. One of the clear dividing lines between the political 'left' and the 'right' is the views of to what extent luck determines incomes (which, in turn, affect preferences about the extent to which the government should intervene to redistribute from the rich to the poor, as shown by Alesina and Giuliano, 2009). A second view is that beliefs are shaped by interest groups (e.g., Glaeser, 2005). In particular, religion has been identified of a relevant group shaping beliefs (Bénabou and Tirole, 2005). In LA, we would expect Catholicism-the predominant religion-to affect fairness perceptions. Finally, sociology suggests that individuals with motivated beliefs are more likely to perceive hard work and effort as the ultimate determinants of success (e.g. Hochschild, 1981). In line with this research, we would expect people with a more optimistic life outlook to perceive income distribution as less unfair. Summarizing, we identify political views, religion and life outlook as some possible determinants of distributive justice perceptions. We test empirically whether these variables correlate with unfairness perceptions.
To measure political views, we rely on the question "In politics, people normally speak of "left" and "right". On a scale where 0 is left and 10 is right, where would you place yourself?" We interpret values closer to zero (ten) closer to a liberal (conservative) worldview. We create a categorical variable for reported religion, coding the rest of the religions (and lack of religion) as zero. Finally, we proxy life outlook with the question: "In the next 12 months do you think that, in general, the economic situation of your country will be much better, a little better, the same, a little worse or much worse than now?" When using these questions, we control for the current assessment of the country's situation to avoid any spurious correlation. 22 We interpret expectations that the country will be better (conditional on the present situation) as a positive life outlook. Table 4 presents the main results. We control for individual characteristics in all the specifications, and include country and year fixed effects we well. Our results suggest that, as expected, ideologically conservative people are, on average, less likely to perceive income distribution as very unfair (column 1). Catholics are less likely to perceive income distribution as very unfair, even after controlling for other observable individual characteristics (column 2). Finally, people with a more positive (and less negative) future outlook (column 3), are less likely to perceive inequality as unfair, even controlling for the country's current situation (as perceived by the individual). These results are robust to controlling for all the beliefs at the same time (column 4). The Gini coefficient is positive and statistically different from zero in all specifications, although the magnitude decreases notably when all the variables are included, suggesting part of the relationship between the Gini and unfairness perceptions is mediated through other beliefs.
As a robustness check, we run the same set of regressions, but using as the dependent variable all unfairness perceptions. These results are shown in Appendix Table A6. We find that the relationship between Catholicism and unfairness loses its significance, while the self-reported ideology actually changes its sign, which suggests these two results-religion and political ideology-are driven by the population with strong beliefs about unfairness. The rest of the results remain unchanged. As noted previously, we are not inferring any causal relationship out of these results, but rather establishing strong empirical associations as stylized facts. For example, it could be the case that a negative life outlook increases the unfairness perceptions, or that an unfair distribution of income makes people more negative about life in general, or that both variables are caused by a third (omitted) variable.

The relationship between social unrest and fairness perceptions
There is a vast literature that relates economic inequality-and more recently, measures of polarization-to social cohesion, conflict, and activism. 23 More recently, some papers have argued that models that include 'objective' measures of inequality to explain social phenomena such as conflict could be misleading since people do not directly observe the income distribution (or the Gini coefficient), but rather take decisions based on their perceptions of it (e.g. Gimpelson and Treisman, 2015). Thus, this evidence suggests perceived inequality, and not actual inequality, should be the relevant regressor in the models that relate social unrest with inequality. To understand what this implies from an empirical point of view, it is useful to take the measurement-error perspective. Let's assume perceived inequality is equal to real inequality plus an error term:

Perceived inequality = Inequality + Error
If the population's perception of inequality corresponds to the actual level of inequality, then = 0, and the estimations we would obtain of the relationship between conflict and inequality would be unbiased. However, research about how accurately people perceive income inequality reveals systematic cognitive biases. The seminal paper of this strand of the literature is Norton and Ariely (2011), who find individuals dramatically underestimated the current level of inequality. 24 Gimpelson and Treisman (2015) show that ordinary people have little idea about the levels of inequality, its evolution over time, and their place in the income distribution. Individuals consistently arrive to misperceptions of inequality, regardless of the data source, operationalization, and measurement method. In a survey experiment, Cruces et al. (2013) find systematic biases in perceptions of own income rank: a significant portion of relatively poor individuals place themselves in higher positions than they actually occupy. This evidence suggests that the mean of the error term will not necessarily be zero. Thus, if we use the 'objective inequality,' instead of the perceived one as explanatory variable in regressions, the measurement error becomes part of the error term in the regression equation, creating an attenuation bias.
In this section, we test whether unfairness perceptions are positively correlated with social unrest, exploiting the fact that both perceptions and stated activism vary at the individual level. 25 We rely on the following question from Latinobarómetro: "On a scale from 1 to 10 where 1 means "not at all" and 10 "very", how willing would you be to demonstrate and protest about…? (a) Higher wages and better working conditions; (b) Improvement in health care and education; (c) Exploitation of natural resources; and (d) To defend democratic rights." Figure 9 shows the simple cross-country correlations between unfairness perceptions at the country level and the average index of the different measures of stated activism in 2015. Visual evidence suggests that unfairness measures tend to be positively correlated with the social unrest measures, although in some cases the correlation is small. To formally assess the relationship between unfairness and activism, we run OLS regressions, where we use each of the social unrest measures as dependent variables and unfairness perceptions (as very unfair) as the main regressor, including the usual individual and fixed effect controls. Table 5 shows the main results. Note: This table presents estimates of the correlation between measures of demonstrations and unfairness perceptions (very unfair). Coefficients were estimated through OLS. Column (1) presents the results for higher wages and better working conditions. Column (2) to defend democratic right. Column (3) for improvement in healthcare and education. Column (4) for exploitation of natural resources. All regressions control for age, squared age, gender, civil status, maximum educational attainment, labor force participation, unemployment status, access to basic services and asset holding, as well as country, subnational and yearly fixed effects. ***, ** and * denote significance at 10%, 5% and 1% levels, respectively. Robust standard errors in parentheses. Average index Table 5 suggests that the population that perceives distribution as very unfair is more prone to actively demonstrate. Each of the four reasons to mobilize has positive and statistically different from zero coefficients. The magnitudes of the coefficients suggest this effect is larger in the case of protests for jobs, health and education, compared to exploitation of natural resources or to defend democratic rights, where the size of the coefficients is half as large. Table 5 also suggests that, on average, people are less prone to protest in countries with relatively higher levels of inequality. As with previous results, the relationship can go either way. For instance, relatively unequal countries might, in fact, have higher levels of inequality due to a lower propensity of its citizens to manifest against such disparities.
Although these results are encouraging, the analysis relies on 'willingness' to demonstrate. However, people might state they are very eager to protest, while in practice they might not do it. To partially overcome this issue, we analyze the relationship between unfairness and actually having mobilized in the past. In particular, we consider six different types of demonstrations: making a complaint to the media, making a complaint on social networks, signing a petition, refusing to pay taxes and being part of an authorized or unauthorized demonstration. We recode these variables so they take a value equal to 1 if the individual stated she had a past of mobilization, and 0 otherwise. Cross-country visual evidence is provided in Appendix Figure A9 while regression results are shown in Table 6.
Overall, both visual and regression analysis suggests unfairness perceptions are positively and significantly correlated with a past of activism. With the exception of illegal activities (columns 1 and 4), 26 and making a complaint to the media, all other coefficients have the expected sign and are statistically significant. In Appendix Tables A7 and A8 we  replicate the regressions in Tables 5 and 6, but using as the regressor of interest the population that perceived distribution as unfair or very unfair. We observe two main differences. First, some of the coefficients stop being statistically different from zero (e.g., columns 3 and 4 from Table 5). Second, some of the coefficients actually turn negative and statistically significant (e.g., column 2 from Table 5, and columns 1-3 from Table 6). These two facts together suggest that activism is driven by the population with strong views about inequality (i.e., very unfair), and not by those who perceive it as just unfair.
Even though a strikingly high share of the population shares the view that income distribution is unfair, the fight against inequality does not seem to be a top priority among LA citizens. Every year, Latinobarómetro asks respondents what they think is their country's most important problem. Although there is a lot of heterogeneity both across countries and across time, insecurity and unemployment are consistently listed as the top priorities. In these rankings, reducing the high disparities between the rich and the poor is usually listed in the bottom half of the priorities, under other issues like 'education' or 'corruption.' A highly speculative reading of this section is that, the way in which this higher propensity to mobilize could manifest is not with direct demonstrations against inequality (like in the Occupy Wall Street movement), but rather in demonstrations against other types of inequalities (such as inequality in access to education or health), or against the underlying causes of it (such as low wages of some specific segments of the population).

Concluding remarks
There is a growing body of evidence showing that many of the decisions agents make are not based on objective economic indicators, but rather on how these are perceived.
Understanding what people believe about the income distribution is crucial from a policy perspective-not only from a traditional view, in which a just income distribution is seen as a pure public good (Thurow, 1971) and is therefore underprovided by the unregulated free-market economy, but also because interventions that make information less costly can have welfare-improving effects (Roemer, 2003) if there are mismatches between perceptions and reality.
In this paper, we analyzed the perceptions of distributive justice in a context of falling income inequality. If fairness perceptions are interpreted as preferences for some leveling of income, our results suggest a striking majority is in favor of reducing the existing disparities between the rich and the poor, while very few people believe the current distribution is fair and all incomes should be the same.
The positive news is that beliefs moved in line with the evolution of objective indicators: both unfairness perceptions and income inequality declined both across countries and time. The bad news is that three in four LA citizens believe income distribution is unfair, and such perceptions have proved to be quite inelastic to changes in income distribution. What happened during the 2000s in terms of inequality reduction was remarkable, but recent evidence suggests the pace of inequality reduction is not going to be the same in the near future. As inequality reduction in LA stagnates, one can wonder if an income distribution that the majority of the population thinks is unfair can be a steady state in the long run.
We believe that, compared to the vast literature on inequality measurement, as well as its causes and consequences, relatively little emphasis has been given to how inequality is perceived by the general population. This paper intends to bridge this gap in the research agenda. We present the characterization of fairness perceptions in LA not as conclusions but as a starting point for researchers who are interested in income inequality perceptions. The results of this paper also raise a number of puzzling questions for future research: Where do people think the unfairness of income distribution stems from? What has been the role of mass media in shaping these beliefs? Does the general population think separately about the 'micro-justice' (i.e., the income I receive is fair) and the 'macro-justice' of overall patterns of inequality? Would fairness perceptions change if individuals are confronted with accurate information about income distribution? We hope future research helps to clarify these questions.        (3) for improvement in healthcare and education. Column (4) for exploitation of natural resources. All regressions control for age, squared age, gender, civil status, maximum educational attainment, labor force participation, unemployment status, access to basic services and asset holding, as well as country, subnational and yearly fixed effects. ***, ** and * denote significance at 10%, 5% and 1% levels, respectively. Heteroskedasticityrobust standard errors in parentheses.

Appendix B: About the Data
The numbers presented in this paper are based on two harmonization projects, known as Latinobarómetro and SEDLAC (Socio-Economic Database for Latin America and the Caribbean). In this Appendix, we describe how we make both sources compatible.
Our perceptions data come from Latinobarómetro, which has conducted opinion surveys in 18 LA countries since the 1990s, interviewing about 1,200 individuals per country about individual socioeconomic background, and preferences towards political and social issues. Although the survey is conducted every year, not all years include the question regarding fairness of income distribution. The survey was designed to be representative at the national level of the voting-age population (in most LA countries, population aged over 18). In Table  B1 we show what percentage of the voting-age population is represented by the survey in each country for all the years in which the fairness question is available.  A 100  100  100  100  100  100  Ecuador  97  97  100  100  100  100  100  100  100  El Salvador  65  100  100  100  100  100  100  100  100  Guatemala  100  100  100  97  100  100  100  100  100  Honduras  100  100  100  98  100  99  99  99  99  Mexico  93  88  95  100  100  100  100  100  100  Nicaragua  100  100  100  100  100  100  100  100  100  Panama  100  100  100  99  99  99  99  99  99  Paraguay  46  46  46  100  100  100  100  100  100  Peru  52  52  100  100  100  100  100  100  100  Uruguay  80  80  80  100  100  100  100  100  100  Venezuela  100  100  100  100  93  100  100  100  100  Weighted average  68  86  91  100  100  100  100  100  100 Note: This table presents the percentage of the voting age population represented each year in Latinobarómetro overtime. The regional average was calculated by weighting each country's population. N/A means the survey was not conducted in that particular country.
Since our goal is to analyze how unfairness perceptions evolved vis-à-vis changes in income inequality, we put a lot of effort in trying to get income inequality data for each data point for which we have perceptions data available. 43 Our source for income inequality data is SEDLAC, a joint effort of the World Bank and CEDLAS at the National University of La Plata in Argentina. SEDLAC increases crosscountry comparability of selected findings from official household surveys. The welfare indicator used is the total household per capita income in 2005 US$ (PPP) per day. The inequality measures we use include households with zero incomes unless otherwise noted (results are similar with the exclusion of these households). For Argentina and Uruguay, the inequality data correspond to urban areas only.
Whenever possible, we used comparable annual household surveys to estimate inequality indicators. However, some countries did not conduct surveys every year, and some of the household surveys available in certain countries are not comparable across time, usually due to important methodological changes (for instance, due to changes in the sampling scheme or in the set of variables available).
To increase the number of observations available (without pushing the data too much), we made to two partial fixes. First, we filled the data gaps using household surveys of 'close' years in which previously unused data were available. For instance, Chile conducts household surveys on average every two years. We have perceptions data in 1997 but no income inequality data for the same year. Therefore, we use the inequality data from the adjacent year (1998) to compare the perceptions data from 1997. As noted previously, we only do this process of using data from close years if the data from the adjacent year correspond to a year in which the perceptions question was not asked (and therefore, inequality data are not needed in that year). Table B2. Circa years used to fill data gaps

Country
Year without household data Data point used instead