Decentralizing the Chilean miracle: regional intergenerational mobility in a developing country

ABSTRACT We estimate spatially disaggregated measures of intergenerational mobility in Chile through an administrative dataset linking children’s and their parents’ earnings from the formal private labour sector. We report remarkable heterogeneity as we find higher and lower upward mobility in mining and agricultural regions, respectively, corroborating previous findings by Connolly et al. in 2019 with the distinction that Chile is a unitary state, implying that factors other than institutional differences shape mobility.


INTRODUCTION
Nobel laureate Milton Friedman famously described Chile as an 'economic miracle' because of the reorientation of the country's economy during the 1980s that led to steady economic growth over the subsequent decades (Friedman, 1982(Friedman, , 2000. This article questions this notion by studying the variation in intergenerational mobility (IGM) within Chile, that is, we examine how some regions of the country can be considered impressive 'economic miracles' while others exhibit high levels of intergenerational transmissions of both privileges and disadvantages.
Chile is an interesting case study to assess how IGM varies with geographical location not only because it has made significant progress in its development over the last three decades (achieving a 2018 gross domestic product (GDP) per capita of US$15,747; International Monetary Fund (IMF), 2022), but also because it is one of the countries with the most unequal income distribution (with a 2017 Gini index of 0.477 points; World Bank, 2022). Moreover, Chile is a novel case study due to its unitary form of government, with uniform laws across its heterogeneous territory and an undifferentiated income tax schedule to fund the national public budget that is defined by the central government and then assigned to local administrations for its execution.
Our contribution is to use a new and unique administrative data set to estimate different measures of IGM for each of Chile's regions. Specifically, we find that the least mobile region is Araucanía, an agricultural region where about a third of the population is ethnic Mapuche (an Indigenous population)the highest proportion of any region in Chile. This region contributes only 3% of Chile's GDP, with 17.2% of its population living in povertythe highest regional poverty rate in the country. Meanwhile, we find that the most mobile region is Antofagasta, a mining-intensive region located in the country's north. This result is in line with the findings of Deutscher and Mazumder (2020) for Australia and Connolly et al. (2019) for Canada and the United States, suggesting that commodity booms may be important drivers of intergenerational upward mobility. However, the fact that Chile is a unitary country with common laws across regions indicates that additional factors, such as labour market conditions, might shape differences in IGM.
The rest of the paper is organized as follows. Section 2 reviews conceptual and measurement issues that have been identified in the literature of IGM. Section 3 outlines relevant details about Chilean regions. Section 4 describes the administrative data and explains our main definition of earnings. Section 5 presents the methodology to estimate IGM and the construction of earnings rankings. Section 6 reports the empirical results. Section 7 concludes.

REVIEW ON INTERGENERATIONAL MOBILITY
2.1. Conceptual issues of IGM Becker and Tomes (1979) is the seminal work that formalizes the notion of IGM as the degree to which family endowments are transferred from parents to children. In their model, children's incomes are explained by the interaction between family endowments and maximizing behaviour. Becker and Tomes (1986) and Solon (1999) improve this model by adding the distinction between human capital and earnings from other wealth, and the role of family and community origins, respectively. Solon (2004) develops a theoretical model in which steady-state IGM depends on: the heritability of the endowment of privileges; 1 the productivity of human capital investment; the earnings return to human capital; and the progressiveness of public investment in children's human capital. The author concludes that higher income parents tend to invest more in their children's human capital, reducing social mobility. Becker et al. (2018) extend these results by explaining the high persistence at the top of the distribution. They argue that successive generations of 'high economic class families' may not need to regress toward the population mean, developing a 'human capital elite'. 2 Finally, Conlisk (1974) develops a simultaneous equation model and Nybom and Stuhler (2013) extend it by allowing income to depend on human capital through a vector of productive characteristics instead of a single factor, including non-cognitive skills. Nybom and Stuhler (2013) find that IGM relies not only on contemporary transmission mechanisms but also on the distribution of income and skills of the parent generation. 3 2.2. Measurement issues of IGM IGM is measured by running an ordinary least squares (OLS) regression of children's log permanent income (or ranking) on their parents' log permanent income (or ranking). The regression coefficient provides a measure of the intergenerational association between the log permanent income (or ranking) of children and their parents.
Regardless of the used IGM measure, the econometrician requires good proxies of permanent income or earnings for children and their parents, relies on the assumption of a linear relationship between variables, and has access to link parent-child information. However, there are at least five problems that appear in practice. First, the life cycle bias that appears when the observed measure of earnings for parents and children is not a good proxy of their actual permanent earnings. 4 Second, the attenuation bias that arises when there is an increasing transitory earnings variance over time that may affect children's earnings and might present downward biased estimates. Third, information from peculiarly homogeneous samples that appears when data are not drawn from random samples. Fourth, non-linearity in the intergenerational transmission of earnings that appears when the relationship between parents' and children's earnings exhibits a concave or convex pattern. Fifth, there is no link between parents and children, which means that the data have income information for only children or parents but not both, implying that some imputation of the missing earnings is needed to measure IGM. These problems that may arise in practice are summarized by Solon (1989), Solon (1992), Corak (2020a) and Chen et al. (2017).
An ideal sample to assess IGM should include income for both generations throughout the entire working life cycle, between the ages of 25 and 55, and be chosen at random (Mazumder, 2016(Mazumder, , 2005Deutscher & Mazumder, 2022). Since the data used in practice differ from this ideal (Chetty et al., 2014b;Bloise et al., 2021), IGM estimates could suffer intensely from life cycle effects (Nybom & Stuhler, 2017). Although the Spearman's rank correlation is much less sensitive to the life cycle effect, the number of years that income is observed and the treatment of zeros (Mazumder, 2016;Nybom & Stuhler, 2017), it may be influenced by child age and the definition of income. Indeed, the child's age should be greater than 25, otherwise intergenerational correlations might be close to zero or negative (Engzell & Mood, 2021;Deutscher & Mazumder, 2022). 5 To correct for attenuation bias, it is necessary to use a multi-year earnings averaging approach as a proxy for lifetime earnings (Chen et al., 2017). Corak and Heisz (1999) and Chetty et al. (2014b) find, for Canada and the United States, respectively, that treatment of observations with zero income can change the intergenerational income elasticity (IGE) dramatically. In addition, Chetty et al. (2014b) show that life cycle bias is small for rank-rank correlations when child income is measured after age 30. Regarding attenuation bias, they find that the rank-rank slope is unchanged when adding more years of data beyond five years when estimating permanent income. When the life cycle and attenuation biases are not adequately addressed, the patterns of non-linearity can be significantly misread, especially over the upper part of the distribution (Chen et al., 2017).
To account for a non-linear transmission of earnings from a parent to a child, researchers can measure IGM on the basis of rank-based transition probabilities, that is, the conditional probability that a child belongs to a percentile of the income distribution given that their parents belong to some percentile of the income distribution (Nybom & Stuhler, 2017;Deutscher & Mazumder, 2022). In the case where the income information for parents and their children is not linked, the literature has used the two-sample two-stage least square (TSTSLS) procedure to impute the missing income information.
However, this procedure leads to biased estimates (Klevmarken, 1982;Angrist & Krueger, 1992;Björklund & Jäntti, 1997;Jerrim et al., 2016). 6 2.3. Geographical variation of IGM Based on administrative data, Chetty et al. (2014b) estimate IGM measures for different commuting zones (CZs) in the United States. 7 They find a considerable variation in IGM across CZs where some areas are 'lands of opportunity' with high rates of mobility across generations, while others are 'circles of poverty' where few children escape poverty. They also find that high mobility areas are correlated with less residential segregation, less income inequality, better primary schools, more significant social capital and greater family stability. 8 Connolly et al. (2019) compute IGM at regional levels in the United States and Canada, concluding that Canada exhibits higher mobility than the United States. Furthermore, the cluster with the highest mobility level is composed of cities that go through Alberta and Saskatchewan into the Mid-western US states. These regions experienced robust labour markets due to a boom in oil, potash and other commodity prices. Meanwhile, Corak (2020b) estimates intergenerational income mobility within each of hundreds of subnational Canadian regions, finding that low-income parents face a relatively high probability of remaining in poverty and with a limited opportunity of rising to the top of the income distribution. 9 Heidrich (2017) performs a similar analysis for Sweden, and contrary to Chetty's findings, her results suggest that IGM is relatively homogeneous across different regions of Sweden, a unitary country. Eriksen and Munk (2020) study the case of Denmark, finding that municipalities with the four largest cities have the lowest IGM together with poor rural and peripheral municipalities. Deutscher and Mazumder (2020) produce estimates of IGM in Australia, finding a notable dispersion in the Australian estimates, but much less than the United States. 10 However, they find that regions with a higher fraction of Indigenous and lower school attendance have greater intergenerational persistence. Acciari et al. (2022) study the case of Italy, concluding that there is substantial heterogeneity in upward mobility across provinces. The variation in mobility can be explained through significant correlations between IGM and several demographic indicators computed at the provincial level. 11 Furthermore, Güell et al. (2018) find high levels of geographical heterogeneity in Italy. Their research suggests that differences in mobility cannot be uniquely credited to institutional variations within a country. Instead, they propose that differences in mobility between regions are driven by the accumulation of human capital and the conditions of the labour market. 12 2.4. The relevance of different spatial scales There are challenges to using a smaller spatial scale to measure geographical IGM. For example, if the spatial scale is too small, the measurements of structural factors that affect IGM could be biased. Indeed, following Solon (2004), these factors are related to returns in the labour market, the productivity of investment in human capital or the progressivity of the tax system. In addition, an estimation of IGM at a lower geographical scale might also be affected by sorting and other potential sources of confounders. This issue does not appear in the national-level data, since the sorting across cities is aggregated away when adding up all towns in the country.
For example, Chetty et al. (2014b) use CZs as a spatial scale because a lower geographical scale, such as the neighborhood, can present sorting bias. Concretely, property prices are typically homogeneous within narrow areas and home values are highly correlated with parent income; that is, comparisons within a small neighborhood effectively condition on a proxy for parent income. As a result, the variation in parent income across individuals in a small area (such as a city block) must be correlated with other latent factors that could affect children's outcomes directly, making it difficult to interpret the resulting mobility estimates. In addition, in small geographical areas, parental earnings could be homogeneous, implying a low variance on the regressor (parental earnings). This means that the estimated coefficient in an OLS regression could not be precisely estimated. 13 In this article, we estimate IGM using Chilean regions, which we describe in detail in the next section. This geographical unit is comparable with CZs in terms of square miles, population and geographical heterogeneity. By having regions, we reduce the likelihood of sorting bias and ensure that the variance in parental earnings is enough to estimate IGM indicators with precision.

Literature on IGM and inequality in Chile
Concerning Chile, our work does not materialize in a vacuum. Researchers have studied IGM in Chile ever since the work of Núñez and Risco (2004) who analyse the IGM of income of the country through TSTSLS. Each subsequent piece of research has computed countrywide estimates via survey data and/or TSTSLS (Núñez & Miranda, 2010Sapelli, 2013;Torche, 2005;Celhay et al., 2010;Núñez & Risco, 2004), except for Cortés et al. (2022), which is the first work to estimate intergenerational earnings mobility at the national level using linked administrative data. Cortés et al. (2022) find that earnings mobility is highly non-linear, as mobility is remarkably high for the bottom 80% while the upper deciles of the earnings distribution exhibit high levels of persistence in privilege. The only three papers that study IGM of education at regional levels in Chile are Muñoz (2021Muñoz ( , 2020 and Celhay et al. (2010). Our paper expands on the previous literature by being the first to use administrative records to study how geographical location is associated with differences in intergenerational earnings mobility in Chile, a developing country.
Chile is recognized for its massive poverty reduction and increase in GDP per capita over the last three decades. However, it is one of the countries with the highest levels of income inequality around the world (Díaz et al., 2021; Decentralizing the Chilean miracle: regional intergenerational mobility in a developing country 787 Gutiérrez et al., 2015;Fairfield & Jorratt, 2016;Flores et al., 2020;Gutiérrez Cubillos, 2022). On this front, our work connects with an incipient literature that examines the spatial decomposition of socio-economic inequality in Chile. The potential effects of geography are particularly interesting for a country such as Chile, where climate and economic conditions are significantly heterogeneous across its geography. Concretely, Paredes et al. (2016) find that 21% of the income inequality in Chile is attributable to geography. 14 Similarly, Paredes (2013) contends that natural resources are the primary cause of spatial wage variability in Chile. Furthermore, the literature reveals that Chilean mining municipalities, which collect mineral taxes, show greater spending on public goods such as social activities and community services (Paredes & Rivera, 2017), but not necessarily on education (Oyarzo & Paredes, 2021). This result might suggest that differences in socio-economic indicators might be driven by labour market conditions, rather than by heterogeneous fiscal spending.

CHILEAN REGIONAL CONTEXT
Chile is divided into 16 regions, the first-level administrative division of the country. Each region is designated by a name and an abbreviation. Figure 1 maps Chile with its regions and their abbreviations. For example, the Región de Antofagasta (ANTOF) is a mining region located in the northern area of the country. The Región Metropolitana (RM) is located roughly in the middle of the country and contains the capital of Chile, the city of Santiago, which has been recognized as one of the cities with the best quality of life in South America. The Región de La Araucanía (ARAUC) is located in the southern part of Chile and a third of the region's population is of Indigenous Mapuche ethnicity, which represents the highest concentration of this community (or, indeed, of any other national Indigenous peoples) of any Chilean region. 15 Table A1 in Appendix A in the supplemental data online presents current information of each region. Among the 16 regions, the Región Metropolitana stands out as the most populated with over 7.5 million inhabitants in 2017 (41% of Chile's population) according to the National Institute of Statistics of Chile (INE). Based on estimates from the Central Bank of Chile (BCCh) (2020) for 2018, the Región Metropolitana produces 46% of Chile's GDP, with manufacturing, services, retail and financial services as principal economic activities (see Table A2 in Appendix A in the supplemental data online). According to official estimates by the Chilean government, 9.0% of the population of this region lived in poverty in 2020, and this region has a Gini coefficient of 0.43 in 2017 (Ministry of Social Development, 2017. 16 The Región de Antofagasta (ANTOF) stands out with a production of 10% of Chile's GDP. The mining industry led by copperis its main economic activity (see Table  A2 in Appendix A in the supplemental data online). In fact, according to estimates of the Central Bank of Chile, mining output represents 52.64% of regional production (BCCh, 2020). This region had a population of 623,851 inhabitants in 2017 according to the INE. This region has the highest GDP per capita in the country (over US$25,000), 9.3% of its population lives in poverty  in 2020 and its Gini coefficient is 0.41. At the other end of the income scale in Chile, the Región de La Araucanía (ARAUC) is the country's poorest region in terms of GDP per capita, with US$6000 per inhabitant, on average. This region contributes with 3% of Chile's GDP and 17.4% of its population living in poverty in 2020the highest regional poverty rate. Unlike the United States and Canada, Chile has a unitary form of government. As such, regional governments are subject to the legislative and constitutional powers vested in the central government. Importantly, the Chilean central government defines the national public budget, which is then distributed among the regions of the country for its execution. According to official estimates from the Chilean government for 2018, national public expenditure was approximately 25% of GDP. Specifically, 58% of this public expenditure was executed in the Región Metropolitana, where 33% corresponded to public expenditure in education. Meanwhile, only 2% and 5% of the national public expenditure was executed in the Región de Antofagasta and the Región de La Araucanía, respectively, where 35% and 31% of these amounts were earmarked for education in the Región de Antofagasta and the Región de La Araucanía, respectively (DIPRES, 2019).

Parent-child linkage
We create a new and unique dataset that associates children and their parents using the linkage keys provided by Chile's Civil Registry Office (CRO). The CRO keeps track of all births, marriages and deaths that occur in the country. Births are supported by a birth certificate that includes the unique identification numbers RUN (Rol Unico Nacional) of the parents and child at the moment of birth. For individuals, the RUN number is the same as the individual tax ID number that appears in the earnings and residential data.
Our linkage procedure associates children with their legal parents, unlike the case of Chetty et al. (2014b) where the linkage relies on cohabitation between children and their parents during the children's childhoods. This might raise doubts about our estimates, as the literature of IGM attempts to capture how the economic resources of parents (legal or not) affect their dependent children while they are growing. Nevertheless, Chilean law requires legal parents to provide their children with an alimony that increases proportionally with the economic capacities of the parents. Concretely, the lowest amount allowed by law is 40% of the minimum wage in the case of only one child and 30% of the minimum wage per child in the case of siblings, while the maximum amount cannot exceed 50% of the total income of the financial supporter (Diario Oficial de la República de Chile, 2001). Owing to this, we contend that our linkage procedure captures to a great extent the economic resources that are transmitted across generations. 17

Earnings data
As mentioned, IGM research in Chile has been characterized by the use of survey data and self-reported information. On the contrary, we use the administrative database of the Chilean government's unemployment insurance programme (UIP) to gather information on the monthly labour earnings of children and their parents from September 2002 to December 2018. The UIP is a benefit that covers all over 18-year-old employees working formally in the private sector. Participation in this benefit is mandatory for all contracts that started after September 2002, and voluntary for contracts that began before that date.
For our baseline analysis, we consider a sample of children composed of individuals aged between 28 and 33 years old in 2018. We use the linkage keys provided by the CRO to merge these observations to a sample of parents composed of individuals between 42 and 87 years old in that same year. Owing to the difference in age between children and parents, our baseline sample might be affected by life cycle bias (Engzell & Mood, 2021). To account for this, we perform several robustness checks in which we control for cohort, parental age and children's age, finding that our main conclusions remain valid. 18 We measure parental earnings as the five-year average of monthly gross formal labour earnings between 2003 and 2007 to account for attenuation bias. 19 For example, if a parent worked 50 months between 2003 and 2007, we compute our permanent earnings measure as total gross formal labour earnings earned during the period divided by 50. Moreover, we only consider parents who worked at least six months over the period of interest. If the two parents worked for at least six months during the period, we first compute the five-year average of monthly gross earnings for each parent and then measure parental earnings as the arithmetic mean of their five-year individual averages. 20 Also, in our baseline sample, we pool fathers and mothers.
Similarly for children, we measure permanent earnings as the five-year average of monthly gross earnings in the 2014-18 period to reduce attenuation bias. Also, in our baseline sample, we pool male and female children. As with parents, we only consider individuals with at least six months of positive earnings.
In addition, we account for the effects of inflation by deflating monthly earnings by the monthly consumer price index reported by the National Institute of Statistics. Unlike , who use a differentiated price index by CZ, we use a general price index that reflects overall inflation at the aggregate national level. 21 The use of a homogeneous price index might be problematic when estimating IGM at regional level, as Paredes (2011) has documented the presence of price differentials for homogeneous houses across regions in Chile. That is, changes in price differentials across regions over time might lead to a biased estimation of regional IGM.
Decentralizing the Chilean miracle: regional intergenerational mobility in a developing country However, no official regional price index available reflects the heterogeneity of prices across regions in Chile. Moreover, unofficial spatio-temporal indexes such as that proposed by Lopez and Aroca (2012) rely on a fixed basket of goods, an approach that might lead to a biased estimation of the true cost of living (Paredes & Iturra, 2011). Taking into consideration the uncertainty behind unofficial price indexes and the lack of available data for their estimation in a sufficiently disaggregated temporal scale, we decide to rely on the official national price index to deflate monthly earnings. 22 Finally, the voluntary nature of the UIP scheme for contracts that began before September 2002 might raise doubts regarding the coverage of our sample. Table A3 in Appendix A in the supplemental data online presents the percentage of workers covered by this programme in comparison with the National Employment Survey (Encuesta Nacional de Empleo -ENE), which is a representative survey including private formal employees, public sector employees, informal workers, training contracts and domestic workers. It can be seen in the last column of Table A3 that during 2003 and 2004, the coverage of our dataset for formal private contract workers is below 50% due to the optionality of the programme for contracts that started before September 2002. This number has increased steadily over the years, reaching 86.8% coverage in 2012. In recent years, the sample is highly representative of formal private workers with a coverage rate greater than 90% since 2015. Furthermore, it can be observed in the second-to-last column of Table A3 that the coverage of our data in relation to the total of formal workers reaches 80% in 2018. The remaining 20% are mainly public sector employees who are covered under a similar but separate scheme.
To see how different the earnings in our database are from those of ENE, we compare the earnings percentiles generated by both the UIP data set and the ENE database for 2018. Table 1 reports the percentiles. We can see that the earnings generated by both databases are alike, and as such, this suggests that the earnings from the formal private sector and other sectors of the economy are similar.

Residential data and regional assignment
We link our baseline sample of parent-child associations with residential data in order to assess how IGM varies with the region in which children grow up.
We assign children to regions by linking the pairs of children' and parents' earnings to the child's residential address while attending 12th grade in school. In this case, the child age is between 17 and 18 years old, depending on the month in which the child was born. 23 We obtain this information from administrative records provided by the Ministry of Education of Chile. If the child's residential address while attending 12th grade is not available, we use the most recently available residential address while enrolled from 7th to 11th grades in school (when the child is 13-17 years old). We end up with 93.17% (575,633 linkages) of the children's sample linked to their residential address.
Naturally, the region where a child grew up does not necessarily correspond to the region where she lives in as an adult at age 28-33 in 2018. However, in addition to the fact that our data set does not allow us to identify the residence of children after 12th grade, the analysis of the geography of IGM focuses on how the available resources and opportunities in neighbourhoods in which children grow up shape their earnings during adulthood (Chetty et al., 2014b;Chetty & Hendren, 2018).
As mentioned, in our baseline sample we use the child's residence in 12th grade to perform the regional assignment. With this, we might wrongly attribute exposure effects from earlier childhood years to 12th grade. We address this concern in Section A1 in Appendix A in the supplemental data online through a robustness check in which we estimate our results using a proportional geographical link that relies on the number of years a child lived in each region between 7th and 12th grades. As we discuss below, the results are similar. Nonetheless, we prefer using children's residence during 12th grade for our baseline results as we have higher quality data in later years. Concretely, the proportion of missing data is remarkably lower in 12th grade than in early childhood years. 24

METHODOLOGY
We begin our analysis by ranking parental earnings on the basis of their position in the national earnings distribution. Concretely, we pool both dual-and single-earnings parents into one unique cohort. In the case of children's ranks, we construct a single national pool composed of females' and males' individual earnings. In this, we follow  (2020) and Corak (2020b) who use national ranks. The particular advantage of ranking earnings with respect to their position in the national distribution is that it allows for the comparison between subgroups in a consistent manner. For our research purposes, we can directly compare regions with the knowledge that the estimated indicators reflect changes in outcomes in a comparable way. To construct the rankings, we consider all children with sufficient earnings data, regardless of whether they present a parentchild linkage. We employ the same procedure for parents. 25

Rank-rank correlation
The rank-rank correlation is a statistical measure of the intergenerational association between the income rank of children and their parents that has gained popularity over the past years (Mazumder, 2016;Chetty et al., 2014aChetty et al., , 2017aChetty et al., , 2017b. Since rankings on the earnings distribution are determined at earlier ages and are difficult to change throughout the age distribution, it is argued that this indicator is robust to the life cycle bias (Corak, 2020b). 26 This correlation can be estimated through the following OLS regression: where r c i is the ranking of the ith child in the national distribution of child earnings, r p i is the ranking of ith child's parent on the national distribution of parental earnings, e i is the error term, and b is the rank-rank correlation. This correlation is an indicator of relative mobility that compares the influence of parental ranking on expected child ranking, where a small number reflects a society with a high degree of IGM. We rely on this estimator to compute the main measure of relative mobility for each region of the country, that is, we fit equation (1) for each region of Chile, thus obtaining estimates of a and b for each region.

Transition probabilities
We also estimate quintile transition probabilities. These probabilities are defined by the conditional probability that a child is in quintile m (with m ¼ 1-5) of the child earnings distribution given that her parent is in quintile n (with n ¼ 1-5) of the parental earnings distribution. These alternative indicators complement the rank-rank correlation in the sense that linearity is not assumed, in addition to being informative on the magnitude of the intergenerational earnings transitions.
Thus, we complement the previous measures by estimating for each region three quintile transition probabilities widely studied in the literature: (1) the circle of poverty, defined as the probability that the child will belong to the bottom quintile given that their parents also belong to the bottom quintile; (2) the circle of privilege, defined as the probability that the child will belong to the top quintile given that their parents belong to the top quintile; and (3) the rags to riches, defined by the probability that the child will belong to the top quintile given that their parents belong to bottom quintile. We call these probabilities p 11 , p 55 , and p15, respectively, and we formally define them as in Corak (2020b): where y c represents the earnings of the child, y p are parental earnings, Q c j is the set of children's earnings belonging to the jth quintile, and Q p j is the set of parental earnings that belong to the jth quintile. Following Chetty et al. (2014b), we interpret p 11 as a measure of bottom persistence, p 55 as a measure of top persistence and p 15 as a measure of upward mobility. We compute these transition probabilities for each region of Chile.

RESULTS
In this section we present the main results. Furthermore, in section A1 in Appendix A in the supplemental data online we perform a series of robustness checks that consider alternative definitions of earnings, different procedures to construct the rankings and more restrictive samples.
First, for each region, we plot a binned scatterplot of the mean child rank conditional on the parental rank.
As can be observed in Figure 2, the relationship between parental rank and child rank is relatively linear up the ninth parental decile for several regions, which implies that rank-rank correlations are valid for a high proportion of the joint distribution between parent and children. The non-linearity of the 10th parental decile is particularly pronounced in Tarapacá  For instance, the authors show that the rank-rank correlation is practically linear for Chicago, while for San Francisco, the top percentiles are above the linear trend. Heidrich (2017) also finds that the top percentiles are not well approximated by the linear trend for Stockholm. The non-linearities presented in the 10th parental decile are captured by the transition probabilities that are shown below. Table A4 in Appendix A in the supplemental data online presents the baseline indicators for each region, while Figure 3 displays the 95% error bars for the parameters. Finally, Figure 4 shows the geographical variation of mobility through choropleth maps. As can be seen in Table A4 and Figure 3, there is substantial heterogeneity across regions. For instance, in Figure 3c, the region with the highest rags-to-riches probability, p 15 , is Antofagasta (ANTOF), where a child whose parents belong to Decentralizing the Chilean miracle: regional intergenerational mobility in a developing country the bottom quintile of the national earnings level has a 29.8% probability of belonging to the top quintile; whereas for a child from La Araucanía (ARAUC), the probability of placing in the top quintile of the child earnings distribution provided that their parent belongs to the bottom quintile is 8.5%, the lowest probability among all regions. Thus, a child who grew up in Antofagasta with a parent that belongs to the bottom quintile is about 3.5 times more likely to arrive to the top quintile than a child under the same conditions who grew up in Araucanía. Nonetheless, Araucanía's p 15 confidence interval exhibits substantial overlap with El Maule's (MAULE), Los Lagos' (LAGOS) and Aysen's (AYSEN) confidence intervals, which might suggest that the differences in upward mobility between these regions might not be statistically significant. 27 On the other hand, Antofagasta exhibits a rags-to-riches probability that is statistically greater than all other regions. Chetty et al. (2014b) find that the city with the highest rags-to-riches probability is San Jose in California with a probability of 12.9%. Boserup et al. (2013) and Corak and Heisz (1999) estimate a rags-to-riches probability equal to 11.7% and 13.4% for Denmark and Canada, respectively. As can be seen, these probabilities are less than 50% of what we find for Antofagasta. The low p 15 that we find for Araucanía is comparable with Siracusa, Minneapolis in Minnesota and southern Ontario for Italy, the United States and Canada, respectively (Chetty et al, 2014b;Acciari et al., 2022;Connolly et al., 2019).
Similarly in Figure 3b, for circle of poverty probabilities ( p 11 ), we find a 12.5% probability for Antofagasta and a 32.6% probability for Araucanía, the lowest and highest point-estimates, respectively. As Antofagasta's confidence interval does not overlap with others, this suggests that the region has the lowest persistence in poverty across regions. In contrast, Araucanía's confidence interval intersects substantially with O'Higgins' (LGBO), El Maule's and Ñuble's (NUBLE) confidence intervals, which might suggest non-significant differences in bottom-persistence among these regions.
As mentioned, Araucanía presents a large population of Indigenous people and has the highest rate of poverty across Chilean regions. Similarly, Chetty et al. (2014b) find low levels of upward mobility for CZs in areas where there is one of the largest Native American reservations in the United States that suffer from very high rates of persistent poverty, especially in the Southwest of South Dakota. Connolly et al. (2019) conclude that northern parts of Canada (eastern parts of Alberta and southern parts of Saskatchewan) present high levels of p 11 where there exists a significant Indigenous population.
Correspondingly, Antofagasta also exhibits the highest degrees of top persistence in Figure 3d, as children with parents in the top earnings quintile have a 44.5% probability of belonging to the top quintile. Once again, Antofagasta's non-overlapping confidence interval suggests significant differences between Antofagasta and other regions. By contrast, the region with the lowest p 55 transition probability is Aysen.
Finally, in terms of relative mobility in Figure 3a, our results indicate that the least mobile region is the Región Metropolitana with a 0.25 rank-rank correlation. Meanwhile, Arica y Parinacota (AyP) exhibits the highest degrees of independence between parents' and children's income as suggested by its 0.118 rank-rank correlation. However, the former region might be statistically indistinguishable to O'Higgins (LGBO) in terms of relative mobility, while the latter might not be statistically different from Aysen (AYSEN), Atacama (ATCMA), Antofagasta (ANTOF) and Los Rios (RIOS). Comparing with international estimates, the Región Metropolitana (RM) presents similar relative mobility to Las Vegas in Nevada and Trapani in Italy, while Arica y Parinacota (AyP) has a comparable level with Trento in Italy and as much as twice relative mobility than Los Angeles in California (Chetty et al, 2014b;Acciari et al., 2022). Figure 4 presents choropleth maps for all indicators. We can see that the most upwardly mobile regions are those located in the north of the country. As stated above, Antofagasta is the most upwardly mobile region, while the least mobile region in relative terms is the Región Metropolitana (RM). In addition, the regions most persistent in poverty are those located in the upper south area of the country, particularly El Maule (MAULE) and Araucanía (ARAUC). In contrast, the regions most persistent in privilege are those located in the north and the Región Metropolitana.
In general, these figures illustrate that mining regions exhibit the highest degree of upward mobility. 28 The case of Antofagasta is particularly illustrative, since it stands as the most upwardly mobile region but also as the most productive region in terms of its mining industry, with 52.65% of its regional GDP stemming from this sector. These findings are relevant for Chile, as the country is the leading producer of copper in the worldwith approximately 28% of the total world production in 2018. These results corroborate Connolly et al. (2019) who find that commodity booms may be important drivers of intergenerational upward mobility. In particular, they find that commodity-producing provinces such as Alberta and Saskatchewan in Canada, and US Midwest states present the highest upward mobility indicators.
Similarly, our estimates fall in line with Deutscher and Mazumder (2020) who find that mining booms in Australia raised the expected rank of children who grew up in Figure 3. Error bars representing 95% confidence intervals for (a) relative mobility β, (b) circle of poverty p 11 , (c) rags to riches p 15 and (d) circle of privilege p 55 transition probabilities for Chilean regions. Note: Heteroskedasticity-consistent standard errors are used to compute the confidence intervals for rank-rank correlations. For transition probabilities, the normal approximation:p ij + z * p ij (1−p ij ) n i is used, where n i is the number of links in which the parent belongs to the ith quintile.
Decentralizing the Chilean miracle: regional intergenerational mobility in a developing country 793 Figure 4. Geography of intergenerational mobility in Chile. Note: A darker shade means a higher value for the indicator. affected regions. Thus, a positive shock to the price of copper can directly impact wages and the labour market in geographies that are intensive in copper production. However, Chile is a unitary country with uniform laws across its territory, unlike the United States, Canada and Australia, which are federal states with differential earnings tax schedules across geographical units. Specifically, given that the earnings tax schedule is uniform across Chilean regions, our estimates suggest that factors other than institutions or fiscal policy are important drivers of IGM. We conjecture that labour market conditions might be a significant force behind the observed heterogeneity in regional IGM. For example, related sectors of Antofagasta's (ANTOF) economy, such as construction and services, might be positively impacted by the growth of the mining industry. Regarding the low mobility experienced by Araucanía (ARAUC), we suspect that the results can be explained by the region's ethnic conflict which might disincentivize the development of entrepreneurial activities, leading to the absence of high-productivity jobs. This idea is supported by the fact that Araucanía is the region with the lowest average labour income and a significant education gap, especially in secondary levels (Ministry of Social Development, 2020).

CONCLUSIONS AND POLICY DISCUSSION
Chile is internationally recognized for its impressive economic expansion during the last three decades, which led it to become the regional leader in 2016 in terms of GDP purchasing power parity (PPP) per capita (Bolt & van Zanden, 2020). Our research provides robust evidence that this nationwide progress hides outstanding geographical variation in the degrees of economic success achieved, where some regions of the country have attained remarkable upward economic mobility, while others have experienced relevant persistence through circles of poverty and circles of privilege.
Specifically, we find that a child in Antofagasta whose parents belong to the bottom quintile of the national earnings distribution has a 30% probability of belonging to the top quintile. This finding might be in part due to the positive direct or indirect effects of the mining industry on the growth of labour markets of related sectors of the regional economy (e.g., construction and services). Meanwhile, we encounter that a child in Araucanía whose parents belong to the bottom quintile of the national earnings distribution has a 33% probability of remaining in the same quintile. This result can be partially explained by the fact that the Araucanía is the poorest region in the country, with high rates of poverty and socio-economic inequality. Additionally, it is the region with the lowest average labour income in the country.
Our analysis suggests that effective national transformation strategies to progress in social mobility require governance mechanisms that take into account territorial perspectives, especially for Chile that has uniform laws across its diverse territory. According to the Organisation for Economic Co-operation and Development (OECD) (2017), the central government should make an effort to advance the implementation of a significant decentralization agenda by developing capable local public administrations that allow it to improve the regional progressiveness of public investment in children's human capital; promote labour market development strategies related to improvements of both the productivity of the human capital investment and the earnings return to human capital in each Chilean region; and equalize the level of amenities across regions to attract high-productivity human capital to work and live in the regions with less social mobility.
Our results also reveal that Antofagasta and the Región Metropolitana exhibit the highest degrees of top persistence, as children with parents in the top earnings quintile have a 44.5% and 39.0% probability of belonging to the top quintile, respectively. These findings can be due to at least three factors: the predominance of high-productivity economic sectors in these regions, such as mining, construction and financial services, which pay the highest earnings (OECD, 2017); the concentration of high-quality human capital institutions in the Región Metropolitana, which generates outmigration of high-productivity human capital towards the centre (Paredes et al., 2016); and the possibility in these regions of transferring privileges from parents to children through social capital (Otero et al., 2019) or a private education system (Zimmerman, 2019) that preserve a small elite. These results invite the central government to promote policies to avoid the heritability of the endowment of privileges through, for example, a more progressive national tax system, where the public expenditure is focused on regions with less social mobility and is invested in the development of children's human capital as well as the equalizing of the level of amenities and high-quality human capital institutions. In this context, strong local public administrations are also needed to translate interactions among businesses, academia and civil society into actionable strategies and policy tools to improve social mobility.
Finally, as our work is descriptive in nature, we believe that future research should focus on understanding the channels that drive differences in IGM between geographical zones. Given our results, we conjecture that the conditions of the labour market and the heritability of the endowment of privileges might be important drivers of regional IGM. Nevertheless, to assess these mechanisms empirically, there are at least three approaches that future researchers could follow. First, scholars might perform descriptive analysis by subgroups of interest, for example, Indigenous people, by gender or by groups of last names. Second, they could implement a decomposition of the rank-rank correlation to quantify the relative importance of factors related to these mechanismssuch as high-school attended, last name, municipality, university attended and college degree obtained in shaping IGM (Güell et al., 2015;Chetty et al., 2017). Lastly, social scientists could exploit some policy Decentralizing the Chilean miracle: regional intergenerational mobility in a developing country 795 variation related to these mechanisms, for example, the tuition-free college policy implemented in Chile in 2015 (Bucarey, 2018) or the reduction in the number of higher education openings for new students during the military dictatorship in Chile (Bautista et al., 2022), which would allow for the estimation of the causal effect of policy changes on IGM.

DISCLOSURE STATEMENT
No potential conflict of interest was reported by the authors.

NOTES
1. Endowment represents the combined effect of many children's attributes influenced by nature or nurture. For example, sociocultural skills, cognitive abilities or access to networking. 2. Another finding from Becker et al. (2018) is that the relationship between inequality and mobility is ambiguous. It depends on the human capital transmission function and complementarities in the human capital production function of children.
3. This implies that changes in policies and institutions can affect long-run mobility trends. In addition, changes in mobility today can be caused by events of the far-reaching past. Thus, differences in mobility between geographical regions reflect the consequences of current and past policies, institutions and conditions. 4. For instance, when child earnings are observed at younger ages (before 25), or parental earnings are observed at older ages (in their 50s and 60s). 5. Recent studies have suggested additional reasons for concern if outcomes are not observed at a comparable time (e.g., see Engzell & Mood, 2021, for more details). 6. Despite this, several papers use this method to estimate IGM in developing countries (Dunn, 2007;Narayan et al., 2018;Núñez & Risco, 2004;Núñez & Miranda, 2010;Sapelli, 2013;Ferreira & Veloso, 2006;Jiménez, 2011;Torche, 2005). 7. CZs are geographical aggregations of counties that cover urban and rural areas in the United States. 8. Chetty et al. (2016) and Chetty and Hendren (2018) also estimate the impact of communities to determine IGM in the United States. The latter find that most of the variation in IGM between CZs and counties is driven by causal effects of place rather than differences in the types of people living in those places.
9. Corak (2020b) shows that inequality in the bottom half of the distribution may be vital to understanding social mobility, negatively correlating with a series of mobility indicators. 10. A possible explanation of this result would be that Australia is a more centralized federation than the United States, with less geographical variation in policies that might influence mobility. 11. They conclude that around half of the province effect is due to a selection of the resident population, and the other half is the result of local socio-economic conditions. 12. There is also a literature that studies IGM using education as a proxy for privileges. For instance, Alesina et al. (2021) find for Africa that geographical and locationspecific features, including distance to the coast and capital and favourable ecology to malaria, correlate negatively with upward IGM. Muñoz (2021) documents wide cross-and within-country heterogeneity in Latin America and the Caribbean, whereas Asher et al. (2021) conclude that upward educational mobility is on average five points higher in urban areas from India. 13. However, a more desegregated geographical scale can better estimate neighborhood effects. These effects explain spillovers within distinct social environments that can generate persistent poverty, resulting in low IGM, giving a better estimate for IGM (Durlauf, 2006;Durlauf & Shaorshadze, 2015;Durlauf & Seshadri, 2017). 14. Andrews et al. (2004) and Hortas-Rico and Rios (2019) find similar results for Australia and Spain, respectively. 15. In the period 2007-18, the Región de Los Ríos (RIOS), de Arica y Parinacota (AyP) and de Ñuble (NUBLE) were created after dividing into two areas the Región de Los Lagos (LAGOS), de Tarapacá (TPCA) and del Biobío (BBIO), respectively. Ñuble was created in 2018 and there are no official GDP estimates for the region (BCCh, 2020). 16. There are no official Gini coefficients for each region in 2020. 17. Our linkage procedure is not exempt from further criticism. For example, in the case of legal parents absent from their child's life, we are not taking into account how the economic resources of non-legal parents impact their dependent children while they are growing. However, a similar problem is also present when the linkage relies on cohabitation between parents and children, because we would be omitting all the economic resources coming from legal parents who are present in their children's life but do not live with them. Unfortunately, we do not have information on earnings for non-legal parents. Nevertheless, according to the assortative mating literature, there exists a positive correlation between spouses' educational attainment and income (Schwartz & Mare, 2005;Western et al., 2008;Eika et al., 2019;Alonzo, 2022). Thus, even in the case where the child lives with the non-legal parent, our linkage procedure would be partially considering the economic resources of the non-legal parent due to the fact that the correlation between 796 Javier Cortés Orihuela et al.
earnings (economic resources) of the legal parent and the non-legal parent is probably relatively high (Gelissen, 2004). 18. Since we observe daughters around the time they are likely to become mothers, gender differences in part/fulltime work could have implications for our analysis. Unfortunately, the data do not contain information on hours worked. Thus, we cannot differentiate between full-and part-time workers. Although this is a limitation of our data, our proxy of lifetime earnings (five-year average) and the robustness of our results suggest that this is not a major source of concern. 19. Our sample can potentially contain missing at nonrandom because we are working with the formal private sector. To reduce this phenomenon, we do not use data before 2003 to avoid potential bias stemming from the self-selection of workers into the programme. 20. This is similar to Chetty et al. (2014b) and Corak (2020b) with the difference that they impute missing earnings as zero. In Section A1 in the supplemental data online we perform a robustness check in which we impute these missing earnings as zero. 21. Before 2010, the official consumer price index only reflected price changes from the Región Metropolitana. From 2010 onwards, the index incorporates price changes in other regions. 22. Additionally, unofficial price indexes rely on the Chilean Socioeconomic Characterization Survey (CASEN), which is released every two or three years. Thus, the production of a complete regional price index would require the imputation of all monthly data points between survey waves, which could introduce further biases. 23. Children who did not repeat any grade and were born before 30 June should be 17 years old in 12th grade.
Children born after 30 June should be 18 years old in 12th grade. 24. Additionally, neighbourhood effects seem to be of a larger magnitude during adolescence than in the earliest years of childhood (Chetty et al., 2014b). This is relevant to the Chilean context as 12th grade is the year in which students are tested in the national university selection test. 25. Section A1 in the supplemental data online explores a different ranking scheme in which parents and children are ranked in relation to their respective birth cohort. 26. Engzell and Mood (2021) suggest that while the rank-rank correlation might also be sensitive to the age of observation or the definition of income used, it is still more stable than log-based measures. 27. Overlapping error bars do not ensure that differences are necessarily insignificant. 28. Table A2 in Appendix A in the supplemental data online outlines regions with a prominent mining industry.