Assessing Colombia's policy of socio-economic stratification: An intra-city study of self-reported quality of life

1 ACCEPTED VERSION Assessing Colombia's policy of socio-economic stratification: An intra-city study of self-reported quality of life Published journal article: Chica-Olmo, J., Sánchez, A. & Sepúlveda-Murillo, F.H. (2020). Assessing Colombia's policy of socio-economic stratification: An intra-city study of self-reported quality of life. Cities, 97. https://doi.org/10.1016/j.cities.2019.102560 1. Introduction Colombian cities are geographically divided into six socio-economic strata (from the lowest stratum 1 to the highest stratum 6), in which dwellings are grouped according to their characteristics and the area where they are located. Taking this classification as a reference, municipal governments allocate subsidies, collect municipal taxes, and charge households different rates for the residential services they provide (DANE 2015). Assuming that the objective of any public policy is to improve citizens' quality of life, we inquire as to whether the classification of Colombian households into socio-economic strata accurately reflects the level of quality of life of households in the city of Medellin. Given the growing interest among economists and policymakers in subjective well-being and its determinants as a more adequate means to measure economic and social progress and monitor well-being in a more comprehensive way (Frey and Stutzer 2017; Odermatt and Stutzer 2018; OˈDonnell et al. 2014), this paper examines Colombia's public policy of stratification in Medellin from the perspective of self-reported quality of life. The study of self-reported quality of life helps to assess the degree to which countries or cities meet the needs of their citizens and to what extent they can flourish or progress in that environment (Veenhoven 2017). Traditional measures of welfare, such as economic growth, have not fulfilled society's need to effectively monitor progress (Frey and Stutzer 2017; Stiglitz et al. 2011; Van den Bergh 2009). Likewise, policymakers increasingly consider the subjective well-being of the population as a possible policy goal (see OˈDonnell et al. 2014; Rojas 2016). There is evidence that improvements in subjective well-being have positive effects for both individuals and society as a whole in many regards, including longer life expectancy (Diener and Chan 2011), increased labour productivity (Oswald et al. 2015), greater participation in voluntary and altruistic activities (Meier and Stutzer 2008) and, in the specific case of Latin America, higher voter turnout (Weitz-Shapiro and Winters 2011). With this in mind, and taking into account the scarcity of studies on the distribution of subjective well-being within Colombia (Hurtado 2016), we aim to test three hypotheses. Firstly, 2 given that the composition of the socio-economic strata in Medellin is not random but takes into account characteristics of the houses and the environment1 which affect perceived quality of life in Latin America's cities (see Ahumada et al. 2019; Gandelman et al. 2012; Medina et al. 2008), we hypothesize that the structure of households in Medellin is hierarchical or nested since the strata are more likely to be comprised of residents who share similar values and interests. To account for this structure, we perform a cross-tabulation analysis of quality of life and strata and estimate the null model with multilevel modelling. Whether nested structures were confirmed, multilevel modelling would be a suitable approach because standard estimation techniques could lead to incorrect conclusions (see Goldstein 2011; Snijders and Bosker 2012). Secondly, we hypothesize that, in addition to the nested structure by strata, the inclusion of economic and non-economic factors identified in the subjective well-being literature would result in a ranking of self-reported quality of life by strata that differs greatly from that of the Colombian authorities. Thirdly, focusing on the economic resources of households as a traditional reference variable of economic and social policies, we hypothesize that changes in economic resources do not have the same effect on self-reported quality of life for households belonging to different strata. Multilevel modelling allows us to check this hypothesis by introducing the stratum slopes of these household resources as random terms and analyse the interaction between stratum and economic resources. Confirming these hypotheses could have policy implications, especially at the local level, because the Colombian authorities use this stratification to differentially charge for residential public utility services such that higher strata households pay more to subsidize utility rates for households in the lower strata. To test these hypotheses, we use data from the Quality of Life Survey 2014 conducted by the Medellin Administrative Department of Planning. Medellin is Colombia's second most populated city with 2.5 million inhabitants in 2017. The availability of this dataset at intra-city level constitutes a strength of our study. In the framework of multilevel models, administrative area, region, or country level is usually chosen due to data availability. However, this does not necessarily represent an individual's daily social interactions precisely (Giordano et al. 2011). In our case, as noted by Farrell et al. (2004), the use of socio-economic strata as the unit of analysis, 1 The stratification methodology applied by the Colombian authorities is analysed in more detail in section 2.2. 3 rather than the city, region, or country (which are expected to contain heterogeneous neighbourhoods), allows for a more fine-grained investigation. The rest of this paper is structured as follows. Section 2 focuses on the conceptual framework, where we review the concept of quality of life, the literature on the contextual effects, and the methodology applied by the Colombian authorities to geographically classify the residential housing into socio-economic strata. Section 3 presents and justifies the dataset and variables used in the analysis. Section 4 describes the empirical strategy under the multilevel modelling approach. Section 5 is dedicated to the main results of our analysis. Lastly, conclusions are drawn in section 6. 2. Conceptual framework 2.1. Quality of life and its determinants The terms ‘well-being’ and ‘quality of life’ may be used interchangeably in the broad sense of living a good life (Veenhoven 2017). Quality of life implies two things. Firstly, that the minimum conditions required for humans to thrive are met and, secondly, that there is a sufficient fit between opportunities and capacities (Veenhoven 2000b). In other words, quality of life means that individuals are able to value life's actual outcomes and usefulness, as well as enjoyment. Hence, self-reported quality of life is referred to as the ‘overall evaluation of life [which] involves all the criteria figuring in the mind of an individual’ (Veenhoven 2017, p. 7).2 Reported quality of life is measured by asking individuals to provide a global assessment of their life or domains of life, such as economic resources, health, employment, and social relationships, among others (Di Tella and MacCulloc 2006; Dolan et al. 2008; Helliwell and Huang 2014). Individuals are capable of making overall appraisals of their quality of life (Veenhoven 2000a) as they are not an academically constructed concept but one people use and understand (Rojas 2016). In contrast to other evaluative criteria (such as material wealth or good health), self-reported quality of life encompasses nonmaterial aspects of human well-being, such as the influence of social relationships (family and friends), comparisons with others, self-determination, and the absence of insecurity (Bárcena-Martín et al. 2017; Bartolini and Sarracino 2014; Dolan and Metcalfe 2012; Frey and Stutzer 2002; Stutzer and Frey 2010). An additional advantage to selfreported quality of life is that it takes into account individual judgements about aspects relating to outcome or actual quality of life, whereas other measures are indicators of potential quality of life (Frey and Stutzer 2002, 2017). In this regard, the study of self-reported quality of life in 2Following Veenhoven (2017), in this paper we use the terms ‘subjective well-being’, ‘happiness’, ‘life satisfaction’ and ‘reported quality of life’ as synonyms to refer to the degree to which an individual judges the overall quality of his or her life as favourable. 4 Latin American countries is very important given that the results could imply rethinking subsequent development strategies and implementing reforms (Rojas 2016). Most empirical works on subjective well-being have traditionally focused on the study of individual determinants, such as socio-demographic characteristics and other economic and social domains. However, several studies have shown that perceived well-being is conditioned not only by individual determinants (level 1), but also by the geographical contexts (level 2) in which people live. In this literature, multilevel (hierarchical or mixed) modelling is used to distinguish individual effects from contextual effects of subjective well-being. Contextual variables are usually generated in two different ways. For example, data can be collected directly at level 2 (region, country, municipality, etc.) using macroeconomic variables or through surveys at the neighbourhood or municipal level. The second way is to generate the variables at level 2 from the variables at level 1. In the review of the literature that follows, we group the studies according to how the contextual variables are generated. As regards the first option, Inglehart et al. (2008) used pooled data from the World Values Survey on subjective well-being for 52 countries over the period 1981 to 2007. The authors examined how contextual factors (country level) and individual factors shape subjective well-being. As contextual variables, they considered data on GDP per capita and economic growth rate from the World Bank database and a measure of a society's level of democracy from the Polity IV project (University of Maryland). They found that certain types of societies are more conducive to happiness than others. While economic factors have a strong impact on subjective well-being in low-income countries, at higher levels of development, societies that allow people relatively free choice in how to live their lives foster a higher level of subjective well-being. In the same vein, Novak and Pahor (2017) also used data on 40 countries from the sixth wave of the World Values Survey (2010-2014) to analyse the influence of economic development on life satisfaction. More specifically, they considered individuals' characteristics and macroeconomic variables at the country-level using World Bank data. As concerns contextual effects, the authors found that gross national income per capita had a significant and positive impact on life satisfaction, but that the effect of unemployment and inflation rate was not significant. Most studies that generate contextual variables (level 2) from individual variables (level 1) in a multilevel framework have focused on social capital since it is often considered a collective concept. Neira et al. (2018) studied how contextual effects (at regional level) of social capital affected subjective well-being in the European Union in 2012. The authors developed five indicators of social capital using principal components analysis where regional social capital variables were defined as the average values of individual indicators. They found a strong contextual effect of living in societies with a more developed civil society, that is, where people 5 use more formal networks or are more involved in social organizations. Nevertheless, given that the average of individual measures has some drawbacks (see Oshio 2017, p. 770), other studies have estimated the contextual variables of social capital using a multilevel framework. More specifically, they fit random intercept models with social capital as the dependent variable. The residuals, which indicate the degree to which social capital in an area (context) differs from the mean over the entire sample, have also been used as explanatory variables in multilevel models for subjective well-being. In this line, Oshio (2017) analysed the association between four kinds of social capital and perceived happiness in Japan in 2011, distinguishing between individuallevel and municipality-level social capital. He observed that both individual-level and municipality-level social capital had a positive and strong association with perceived happiness when they were used separately to predict perceived happiness. Furthermore, for all social capital measures, municipality-level social capital showed a much weaker association with perceived happiness than individual-level social capital. Following the same method for estimating contextual variables and using data from the Seoul Welfare Panel Study in 2008, Han (2015) considered social capital at three levels: individual, household and administrative areas of Seoul. He found that a relatively small percentage of happiness was attributed to the administrative-area level compared to the household level, which implies that a household context is more important for understanding variation in individual happiness. 2.2. Method of socio-economic stratification for residential housing in Colombia Unlike the studies reviewed in the previous section, the main goal of this paper is not to identify the (individual or contextual) determinants of quality of life in Medellin. Rather, we are interested in assessing the effect on the city of Colombia's public policy of geographical stratification from the perspective of self-reported quality of life as a more comprehensive concept of social progress. That is, we aim to determine whether the classification of households in socio-economic strata accurately reflects the level of quality of life of the households. To do so, it is necessary to first provide a brief review of the method used by the Colombian authorities for classifying residential housing into socio-economic strata. The socio-economic stratification of residential housing in Colombia was carried out from 2012 to 2014 by municipal governments throughout the country. The stratification methodology was designed by the National Administrative Department of Statistics (DANE, 2015). The objective of this stratified, socio-economic division of the city of Medellin was to group together dwellings with similar characteristics, as well as the streets and geographical areas where they are located. To this end, six socio-economic strata were established: 1 low- 6 low, 2 low, 3 medium-low, 4 medium, 5 medium-high and 6 high. On the basis of this classification, the municipal government charges households different rates for the residential services it provides,3 allocates subsidies, and collects municipal taxes. Prior to the stratification process, the dwellings of the most unprotected population, such as indigenous settlements in rural areas, housing for victims of forced displacement, and free housing (subsidized at 100%) were classified as stratum 1 without undergoing the stratification process. The rest of the dwellings were classified according to the following variables: (1) topography (sloped ground or not); (2) type of road (paved, unpaved, untracked); (3) public services available to the household (complete or incomplete); (4) land uses (institutional, residential, agricultural, mixed); and (5) housing characteristics, such as type of building (apartment or house), floor area, and number of rooms. Firstly, physically homogenous zones were established using the first four variables mentioned above as a reference. Secondly, geoeconomically homogenous zones were determined by grouping together dwellings of a similar price on the real estate market. To do so, the physically homogenous zones were taken into account and the characteristics of the dwellings were incorporated (variables 5). Based on these two classifications, a search was made of the spatial intersection in order to establish the spatial stratification units (SSU; UEE in Spanish). In these units, adjoining dwellings with similar physical and economic characteristics but which differ with respect to adjacent areas were grouped together. In the last step, the six strata were obtained from the SSU. For this purpose, each SSU was assigned a value that represents its quality, and each of the six strata were obtained using minimum variance methods (see DANE 2015, pp. 50–54). Therefore, the procedure designed by the DANE to obtain the strata only considers the characteristics of the dwellings, the streets and the surrounding areas, which in turn affect housing prices. 3. Data and variables 3.1. Data The empirical analysis in this study is based on data drawn from the Quality of Life Survey 2014 (Encuesta de Calidad de Vida de 2014, hereafter ECV2014) conducted by the Medellin Administrative Department of Planning using simple random sampling of households by the six socio-economic strata. Due to both sample constraints and missing data, the final number of 3Residential public utilities include water supply, sewerage, sanitation, electricity, and gas. 7 observations we used is 8,884 (heads of household). The ECV2014 was chosen because it includes data on private households related to several of the dimensions which are of interest to the study of quality of life. 3.2. Variables Appendix 1 lists the variables used in the study. Table 1 shows the descriptive statistics for all the variables. In what follows, we present the variables used in our models and justify their inclusion in the empirical analysis. Insert Table 1 here 3.2.1. Self-Reported Quality of Life The survey contains data about individuals' perceived quality of life. More specifically, we use the responses to the question: ‘On a scale from 1 to 5, rate the quality of life of the members of your household’. The response options were 1 Very bad, 2 Bad, 3 Acceptable, 4 Good and 5 Very good. As mentioned above, a question of this type refers to individuals' own criteria and overall evaluation of life (Veenhoven 2017, p. 7). As a result, we used the responses to this question as a proxy of self-reported quality of life. The Colombian authorities are interested in knowing whether the citizens of Medellin consider they have a good quality of life in order to focus their efforts on more disadvantaged citizens. In reference to this, we collapsed the ordinal variable into a binary that takes the value of 1 if the respondent perceives his or her quality of life as good or very good, and 0 otherwise. Some studies have concluded that when the ordinal scale is collapsed into a binary, the logistic regression yields similar results which implies only a slight reduction in power (Armstrong and Sloan 1989; Manor et al. 2000). In the happiness literature, several studies use the dependent variable in dichotomous form (see Medina et al. 2008; Pedersen and Schmidt 2011). We denote this variable as Quality of life. 3.2.2. Explanatory variables Socio-economic characteristics We control for the socio-economic characteristics that are common in the subjective well-being literature: Male (gender), Age, Race, Living partner, Illiteracy, Secondary, Tertiary, Good health, and Permanence in employment. With regard to the variable Permanence in employment, it must be highlighted that this is a continuous variable referring to the number of months the respondent has been working for a company or is self-employed, either in the formal or the informal sector. In our sample, the average number of months that individuals have been 8 working in the same company is 47, and ranges from 0 (unemployed) to 632 months of employment (Table 1). Economic resources Larger economic resources are expected to be associated with greater well-being due to the benefits of higher prosperity. However, the relationship between economic resources and selfreported quality of life is not as straightforward as initially thought (for a review, see Clark et al. 2008; Ferrer-i-Carbonell 2005; Inglehart et al. 2008). For the specific context of Latin America, several studies have shown that economic resources are positively associated with quality of life but are not the most important determinant (see Medina et al. 2008; Rojas 2011). We used monthly household consumption expenditure as a proxy of economic resources because the ECV2014 does not include a specific question about income. The question is: What are your total monthly household consumption expenses? (in dollars). Household expenses (or income) rather than personal expenses are normally used because they are a better indicator of an individual's real access to economic resources (Ferrer-i-Carbonell 2005; Oshio 2017). In order to control for differences in household size and economies of scale, we have applied an equivalence scale recommended by OECD in which we consider equivalent consumption expense as the household consumption expenses divided by the square root of the number of household members. Subjective safety The subjective evaluation of security has an impact on the evaluation of subjective well-being (Dolan et al. 2008; Wills-Herrera et al. 2011). It is convenient to distinguish two dimensions of perceived safety when the scope of study is a city: neighbourhood safety and personal safety. Thus, we consider two variables: Neighbourhood safety and Forced displacement. The former is a dummy variable that takes the value of 1 if citizens feel Very safe or Safe living in the neighbourhood, and 0 otherwise. A positive association between Neighbourhood safety and quality of life is expected (Powell and Sanguinetti 2010). When people perceive that they live in a safe neighbourhood free of crime and violence they tend to report a higher level of quality of life because the neighbourhood provides a stable living environment. In contrast, living in an insecure neighbourhood causes anxiety and feelings of unease, thus leading to lower perceived subjective well-being (Chong et al. 2017). The second variable within the subjective safety dimension is Forced displacement. This is also a dummy variable that takes the value of 1 if respondents have had to move from their former municipality of residence for any of the following public order causes: extortion, 9 kidnapping, pressure from armed groups, or threat of common delinquency. The rationale for including this variable is that in 2016, Colombians were the second largest group in the world (after Syrians) with 7.7 million people forcibly displaced by conflict and violence. Most displacements occurred within the country (7.2 million), generally from rural areas to larger urban areas.4 Medellin, along with Bogotá and Cartagena, became the main destinations for involuntary migration flows given that victims seek big cities in order to remain anonymous as a way to ensure greater security. Forced displacement has negative effects on quality of life because people's family and social ties break down, they lose their possessions, and they also have to re-enter the labour market. This implies that displaced people are more exposed to the risk of poverty (Sánchez Mojica 2013). Social and cultural capital Muffels and Headey (2013) distinguished between social capital, defined as the level of trust in other people and the capacity of people to build a social network, and cultural capital, defined as no materialistic values that influence people's achievements and outcomes. We use membership in associations and organizations as a proxy of social capital. We incorporate the dummy variable Social capital, which takes the value of 1 if the respondent is a member of at least one of the organizations in a list of 11, and 0 otherwise.5 As shown in Table 1, 11.1% of our sample is involved in such associations. Taking into account that social connections might enable individuals to access valuable resources, such as affective support, information on employment opportunities, or possibilities for association to develop productive projects, several studies have found positive effects of social capital on subjective well-being (Bárcena-Martín et al. 2017; Bartolini and Sarracino 2014; Han 2014; Neira et al. 2018; Oshio 2017) and also in Latin American countries (see Ateca-Amestoy et al. 2014; Wills-Herrera et al. 2011). Given that perceived freedom is a value that influences people's achievements and outcomes (Sen 1999), we consider perceived freedom to express thoughts and political ideas as a proxy of cultural capital. We use the dummy variable Freedom which takes the value of 1 if the respondent perceives that There is a lot of freedom, There is freedom and Acceptable, and 0 if the respondent perceives Little freedom and Very little freedom. The freedom to express thoughts and political ideas could encourage individuals to become involved in national politics and environmental protection, which constitute cultural capital. How much freedom or 4Estimates provided by the Internal Displacement Monitoring Centre (http://www.internaldisplacement.org/); the source used by the World Bank in the displacement statistic. 5These organizations include parents' associations, corporations, local administration boards, women's associations, youth groups, citizen oversight committees, community action boards, clubs for the elderly, neighbourhood assemblies, communal budget councils, and community health participation committees. 16 Model 1 and Model 0 in Figure 2 reflect the same successive strata ranking from 1 (lowest) to 6 (highest). Model 2 (Table 3) controls for both socio-economic characteristics and the variable Consumption. This new variable shows high quantitative significance and its sign is positive, thus, as in the literature reviewed for Latin America, an increase in household consumption expenditure increases the probability of reporting good or very good quality of life. In addition, it significantly improves the specification of Model 1, as shown by the statistical LR test. Both R2m and R2c have increased with respect to Model 1. However, in Figure 2 (Model 2) it can be observed that citizens in stratum 5 perceive a higher level of quality of life than those in stratum 6 (the intercept of stratum 5 is larger than the intercept of stratum 6). In addition, the perceived quality of life of citizens in strata 1 and 2 continues to be significantly below the overall average in contrast to those in stratum 5. The same behaviour was maintained in Models 2 to 5. Consequently, the inclusion of the variable Consumption as a proxy of economic resources changes the order of perceived quality of life of the citizens in strata 5 and 6. The successive incorporation of new variables related to subjective safety, social and cultural capital, and location improves the estimates: the Akaike information criterion (AIC) and the Bayesian information criterion (BIC) decrease, while R2m and R2c increase (see Table 3, Model 3, Model 4, and Model 5). In these models, Consumption remains significant and the estimated value of its parameter is high with odds ratio greater than one. The two variables related to subjective safety (Neighbourhood safety and Forced displacement) are also statistically significant, with high quantitative significance and the signs of their estimated parameters are as expected. The safer citizens feel, the more likely they are to report good or very good quality of life. In contrast, when individuals have had to change their place of residence due to problems of public order, they are less likely to report good or very good quality of life. Moreover, people who relate to others and are involved in associations (Social capital) and feel free to express political ideas (Freedom) are more likely to report good or very good quality of life. As regards location, it is worth noting that living all life in Medellin does not affect self-reported quality of life. However, the longer people remain in the same stratum, the less likely they are to report good or very good quality of life. In any case, the odds ratio of the variable Time in neighbourhood is very close to 1, indicating that the quantitative importance of its parameter is low. Consistent with previous studies, being a homeowner has a positive effect on self-reported quality of life. 5.3. Relationship between Quality of Life and Consumption by stratum 17 In order to check Hypothesis 3, Figure 3 shows the relationship between Quality of life and Consumption for each of the six strata. The logit models are shown in blue and represent the probability of being satisfied with life considering the level of monthly equivalent consumption expenditure per household (Consumption). The graphs in the figure indicate that the probability of being satisfied with life rises with an increase in Consumption. However, as can be observed, this behaviour is not the same for all six strata. In fact, the odds ratio of strata 1 and 2 are two times higher than the values of the rest of the strata, thus indicating that a change in Consumption does not have the same effect on Quality of life if a citizen belongs to a high or a low stratum. Therefore, if Consumption is used as a proxy for household economic resources, a change in this factor for the inhabitants in the lowest strata (1 or 2) would have a greater effect on their perceived quality of life than if this change occurred in the other strata. Hence, it would be interesting to analyse Quality of life taking into account not only the stratum to which an individual belongs (Specification 1), but also the interaction with the variable Consumption (Specification 2). Insert Figure 3 here In addition, as Figure 2 (model 6) indicates, the effect of Consumption on Quality of life is not the same if the individual belongs to a low or a high stratum. Therefore, to determine whether Consumption could affect each of the strata differently, we estimated a random slope model for each stratum (Table 3, Model 6). This model is more robust than Model 5, since the AIC value is lower and R2c and R2m are higher. Likewise, the LR test indicates that there are significant differences with respect to Model 5. In Model 6, the explanatory variables show the expected behaviour, which is similar to that of Model 5. Random effects or variability across strata explain approximately 10.26% of the variance of self-reported quality of life. As can be observed in Model 6-intercept of Figure 2, the perceived quality of life of citizens in strata 1 and 2 is significantly lower than the overall average, while it is above average for those in stratum 4. Furthermore, Model 6Consumption in Figure 2 shows that the effect of a variation in Consumption on the perceived quality of life of individuals in strata 1 and 2 is above the overall average, while the effect of this variation lowers the overall average for individuals in stratum 4. Nevertheless, these effects are not significantly different from the overall average for the individuals in strata 3, 5 and 6. These three strata show a higher dispersion in the 95% confidence intervals. In other words, in strata 1 and 2, where the likelihood of reporting good or very good quality of life is lower, an increase in household consumption expenditure would have a stronger effect on self-reported quality of life. Conversely, individuals in stratum 4 are more likely to report good or very good quality of life; however, an increase in household expenditure would produce the lowest increase in the level of self-reported quality of life. In addition, as 18 shown in Figure 2, the order of the strata has changed with regard to the previous order maintained in Model 2 to Model 5. 6. Conclusions and discussion The main objective of this paper was to analyse whether the Colombian government's classification of households in socio-economic strata accurately reflects the level of quality of life of households in Medellin. To this end, we formulated three hypotheses, which have been verified in the analysis. Thus, the answer to our initial research question is that the socioeconomic strata do not accurately reflect citizens' quality of life. This finding is particularly important given that the socio-economic stratification system of Colombia is used to guide public policies at the local level, namely, to differentially charge for residential public utility services such that households in the higher strata pay more to subsidize utility rates for households in the lower strata. In what follows, we provide an overview of the main conclusions arising from the three hypotheses. We tested for the existence of a stratum effect such that families living in the same stratum report more similar levels of quality of life (Hypothesis 1). That is, the factors taken into account by the Colombian authorities to carry out the stratification (characteristics of the dwellings and the environment, as well as housing prices) affect citizens' quality of life. However, when considering the individual factors reported in the literature on subjective well-being, we find a significant variation in citizens' perceived quality of life across strata (Hypothesis 2). The ranking of self-reported quality of life according to the strata established by the Colombian authorities ranges from 1 low-low to 6 high, whereas in our study the strata rank from low to high self-reported quality of life in the following order: 1, 2, 6, 3, 5, 4. In this regard, some studies have identified a cluster with high homicide rates in stratum 6 corresponding to the city centre of Medellin, as well as the highest rates of assault and motor vehicle and property theft in areas with the highest socio-economic status (Gaviria et al. 2010; Medina et al. 2008). Conversely, these studies have identified a cluster of low homicide rates in stratum 4, which occupies the highest position in our quality-of-life ranking. Likewise, in the case of the two most depressed strata (1 and 2), our results indicate that public policies targeted at increasing families' level of consumption expenditure would be very effective in improving citizens' quality of life (Hypothesis 3). It is important to recall that these two strata host people internally displaced by violence; a collective which is more exposed to the risk of poverty. Focusing on the determinants of quality of life in Medellin, our study identifies several non-economic factors, such as perceived freedom, subjective safety, and social capital, which are particularly significant in the context of a city in a country that has suffered armed conflict 19 for decades. Given that the conflict in Colombia is a political one where individuals fear expressing their political views (Wills-Herrera et al. 2011), it follows that citizens' perceived freedom to express political ideas is associated in a positive and very significant way with quality of life. Neighbourhood safety is positively correlated with self-reported quality of life, while personal insecurity (measured as forced displacement) is negatively correlated. Belonging to an association that fosters social contacts is also positively associated with perceived quality of life. Similarly, several studies have argued that these factors are complementary to each other in the sense that a safe neighbourhood provides a space of trust for people to interact with one another, thus leading to higher levels of social capital. In turn, these trusting relationships with neighbours could increase the perceived safety of the neighbourhood (see Chong et al. 2017; Wills-Herrera et al. 2011). In summary, our findings are highly consistent with the concept of quality of life presented in the previous section and lead us to argue that if the objective of public policy is to create an environment for citizens to lead satisfying lives and enhance their quality of life, then public policy measures should take a different direction. Firstly, given that there are striking differences between the current socio-economic stratification system and our ranking of strata in Medellin, it would seem that the system needs to be revised in such a way as to design municipal public policies that truly contribute to improving the situation of the most disadvantaged households. Secondly, in order to improve the quality of life in Medellin, public policies should focus on promoting the traditional determinants of quality of life (consumption, good health, and education), as well as other social resources (subjective safety, perceived freedom, and social capital), which will undoubtedly require more innovative measures. The empirical and graphical analysis method followed in this study could be extrapolated to other cities in different countries since the underlying idea is that the exchange of relationships and social support between people living in close proximity shapes quality of life. In an additional way, it would be key to identify the determinants of quality of life according to the history, socio-economic situation, cultural values, etcetera, of each country. In this vein, a limitation of our work is that due to the absence of statistical information, we have not included variables referring to psychological capital or personality traits of respondents. For future studies, we will focus more deeply on the analysis of the association between spatial relationships and quality of life with spatial econometrics techniques. We could study the existence of spatial dependence in quality of life, so that a portion of the quality of life of a respondent might be explained not only by his or her drivers but also by the quality of life of his or her neighbourhood. The presence of spatial clusters in high and low quality of life could be also studied. If spatial dependence on the quality of life were confirmed, public policies should 20 explicitly incorporate spatial information and be targeted to account for personal inequalities in quality of life. Table 1. Descriptive statistics of quality of life in Medellin, 2014 Mean SD Minimum Maximum Quality of Life 0.762 0.426 0 1 Male 0.517 0.500 0 1 Age 53.778 16.446 17 103 Race 0.036 0.185 0 1 Living p artner 0.531 0.499 0 1 Illiteracy 0.027 0.162 0 1 Seco ndary 0.460 0.498 0 1 Terti ary 0.110 0.312 0 1 Good health 0.768 0.422 0 1 Permanence in employment 47.067 92.831 0 632 Consumption 0.661 0.691 0.016 15 Neighbourhood s afety 0.887 0.317 0 1 Forc ed d isplacement 0.046 0.211 0 1 Social capital 0.111 0.314 0 1 Freedom 0.921 0.269 0 1 Time in neighbo u rhood 29.098 22.424 0 100 Long - term resident 0.730 0.444 0 1 Homeo wner 0.545 0.498 0 1 Note: N = 8,884. Adapted from Administrative Department of Planning of Medellin, Quality of Life Survey of 2014 (Encuesta de Calidad de Vida de 2014). Table 2. Cross-tabulation analysis of quality of life and socio-economic stratum in Medellin, 2014 Socio - economic stratum Quality of life 1 2 3 4 5 6 Row total 0 n X2 % 420 71.539 35.9 828 21.853 28.0 643 4.445 21.9 153 27.914 15.6 63 52.019 9.9 8 33.189 4.0 2,115 1 n X2 % 751 22.353 64.1 2129 6.828 72.0 2292 1.389 78.1 829 8.722 84.4 575 16.253 90.1 193 10.370 96.0 6,769 Column total 1,171 2,957 2,935 982 638 201 8,884 Note: Quality of life equal to 1 indicates that respondents perceive their quality of life as good or very good; Quality of life equal to 0 indicates that respondents perceive their quality of life as very bad, bad, or acceptable. Cell contents: numbers of surveys (n), chi-square contribution (X2) and n/column total *100 (%). Total observations: 8,884. 21 Table 3. Determinants of perceived quality of life and socio-economic stratum effect in Medellin, 2014 Model 0 Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Fixed effects Intercept 1.6105*** 0.2625 -0.1702 -0.6955* -0.9641** -0.9260** - 1.004** Socio-economic characteristics Male -- 0.1149 (1.122) 0.0911 (1.095) 0.0873 (1.091) 0.0970 (1.102) 0.0949 (1.099) 0.0853 (1.089) Age -- - 0.0056 (0.9944) - 0.0069 (0.993) - 0.0062 (0.994) - 0.0067 (0.993) - 0.0105 (0.990) - 0.0110 (0.989) Age2 -- 0.0001 (1.000) 0.0001 (1.000) 0.0001 (1.000) 0.0001 (1.000) 0.0001 (1.000) 0.0001 (1.000) Race -- - 0.3934** (0.675) - 0.3802** (0.684) - 0.3585** (0.699) - 0.3582** (0.699) - 0.3432** (0.709) - 0.3485** (0.706) Living partner -- 0.2188*** (1.245) 0.2264*** (1.254) 0.2275*** (0.699) 0.2292*** (1.258) 0.2247*** (1.252) 0.2309*** (1.260) Illiteracy -- - 0.4805*** (0.619) - 0.4658** (0.628) - 0.4567** (0.6334) - 0.4464** (0.640) - 0.4559** (0.634) - 0.4303** (0.650) Secondary -- 0.3305*** (1.392) 0.2954*** (1.344) 0.2794*** (1.322) 0.2749*** (1.316) 0.2774** (1.320) 0.2682*** (1.308) Tertiary -- 0.8557*** (2.3530) 0.7057*** (2.025) 0.7091*** (2.032) 0.6882*** (1.990) 0.6510*** (1.917) 0.6836*** (1.981) Good health -- 1.0280*** (2.796) 1.0190*** (2.770) 0.9798*** (2.664) 0.9770*** (2.656) 0.9651*** (2.625) 0.9665*** (2.628) Permanence in employment -- 0.0011*** (1.001) 0.0010*** (1.001) 0.0010** (1.001) 0.0011** (1.001) 0.0011** (1.001) 0.0011** (1.001) Economic resources Consumption -- -- 0.6061*** (1.833) 0.6079*** (1.837) 0.6081*** (1.837) 0.6279*** (1.874) 0.7913*** (2.206) Subjective safety Neighbourhood safety -- -- -- 0.6892*** (1.992) 0.5980*** (1.818) 0.6096*** (1.840) 0.6138*** (1.847) Forced displacement -- -- -- -0.4544*** (0.635) -0.4643*** (0.629) -0.4678*** (0.626) -0.4594*** (1.583) Social and cultural capital Social capital -- -- -- -- 0.2565** (1.292) 0.2429** (1.275) 0.2462** (1.279) Freedom -- -- -- -- 0.3931*** (1.482) 0.3823*** (1.466) 0.3849*** (1.469) Location Time in neighbourhood -- -- -- -- -- -0.0048** (0.995) -0.0049*** (0.995) Long-term resident -- -- -- -- -- 0.0421 (1.043) 0.0519 (1.053) Owner -- -- -- -- -- 0.3463*** (1.414) 0.3544*** (1.425) Random effects (variance) Intercept – Social stratum 0.661 0.246 0.055 0.059 0.060 0.057 0.160 Slope – Expenses -- -- -- -- -- -- 0.179 Model fit AIC 9486.9 8980.5 8929.0 8839.2 8817.7 8783.6 8772.0 BIC 9501.1 9065.6 9021.2 8945.6 8938.3 8925.4 8928.1 R2m -- 0.094 0.156 0.169 0.173 0.183 0.210 R2c -- 0.157 0.170 0.183 0.187 0.197 0.234 logLik -4741.4 -4478.3 -4451.5 -4404.6 -4391.9 -4371.8 -4364.0 LR test (X2) 268.0*** 526.3*** 53.54*** 93.80*** 25.46*** 40.11*** 15.56*** 22 Note: N = 8,884. Regression logit multilevel. Entries show parameter estimates with odds ratio in parentheses. *p < 0.1. **p < 0.05. ***p < 0.001. Figure 1. Mosaic chart of cross-tabulation between Quality of life and socio-economic stratum. Quality of life equal to 1 indicates that respondents perceive quality of life as good or very good. Quality of life equal to 0 indicates that respondents perceive quality of life as very bad, bad or acceptable. The Pearson's test was performed to determine independence between Quality of life and stratum. Residual Pearson's cells between (-2, 2) indicate independence. -7.2 -4.0 -2.0 0.0 2.0 4.0 8.5 Pearson residuals: p-value = < 2.22e-16 Stratum Quality of life 1 1 0 2 3 4 5 6 23 Figure 2. Conditional modes of the random effects. Model 0 to Model 5 are estimated random intercept models. Model 6 is an estimated random slope model for the variable Consumption. Horizontal lines represent the confidence interval (95%). The vertical line are the overall average for all the surveys or the intercept in the logit model. Intercept -1 0 1 2 1 2 3 4 5 6 Random effects Stratum Model 0 Intercept -0.5 0.0 0.5 1.0 1 2 3 4 5 6 Random effects Stratum Model 1 Intercept -0.3 0.0 0.3 1 2 3 4 6 5 Random effects Stratum Model 2 Intercept -0.3 0.0 0.3 1 2 3 4 6 5 Random effects Stratum Model 3 Intercept -0.3 0.0 0.3 1 2 3 4 6 5 Random effects Stratum Model 4 Intercept -0.3 0.0 0.3 1 2 3 4 6 5 Random effects Stratum Model 5 Intercept Consumption -1.0 -0.5 0.0 0.5 -1.0 -0.5 0.0 0.5 1 2 6 3 5 4 Random effects Stratum Model 6 24 Figure 3. Relationship between Quality of life and Consumption by stratum. The points in the figure represent the quality of life variable for each respondent (1 or 0) and the blue line represents the estimated logit model with Consumption as explanatory variable. *p < 0.1. **p < 0.05. ***p < 0.001. Appendix 1. Variables to analyse quality of life in Medellin, 2014 Variable Cases where dummy takes the value of 1 Quality of life R espondent perceived his/her quality of life as very good or good Male 1 = Male, 0 = Female Age Age in years Race R espondent is black, mulatto, Afro - Colombian or Afro - descendant Living partner R espondent lives with a partner Illiteracy R espondent is illiterat e Seco ndary T he last approved level of study is secondary Tertiary T he last approved level of study is tertiary Good health R espondent perceives his /her state of health as good or very good Permanence in employment Number of months respondent has been working for a company or self-employed (formal and informal sectors) Consumption Monthly equivalent expenditure on household consumption Neighbourhood s afety R espondent feels very safe or safe living in the neighbourhood Forced displacement R espondent has moved for any public order causes Social capital R espondent is involved in any organization on a list of 11 Freedo m R espondent considers that there is either a lot of freedom or that there is freedom to express political opinions Time in neighbo u rhood Number of years living in the neighbourhood Long - term resident R espondent has lived all his or her life in the same municipality Owner T he house is owned and fully paid Note: Adapted from Administrative Department of Planning of Medellin, Quality of Life Survey of 2014 (Encuesta de Calidad de Vida de 2014). odds-ratio = 4.818*** 0.00 0.25 0.50 0.75 1.00 0.0 0.5 1.0 Consumption Quality of life Stratum 1 odds-ratio = 4.645*** 0.00 0.25 0.50 0.75 1.00 0.0 0.5 1.0 1.5 2.0 Consumption Quality of life Stratum 2 odds-ratio = 1.869*** 0.00 0.25 0.50 0.75 1.00 0 2 4 6 Consumption Quality of life Stratum 3 odds-ratio = 1.313* 0.00 0.25 0.50 0.75 1.00 0.0 2.5 5.0 7.5 10.0 12.5 Consumption Quality of life Stratum 4 odds-ratio = 1.854** 0.00 0.25 0.50 0.75 1.00 0 5 10 15 Consumption Quality of life Stratum 5 odds-ratio = 2.072* 0.00 0.25 0.50 0.75 1.00 0 5 10 15 Consumption Quality of life Stratum 6 25 Funding acknowledgement This work was supported by the University of Medellin (Colombia), Project "Modelización Espacial de los Determinantes de la Calidad de Vida en los Hogares de Medellín", under the Grant code 881/2017. 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