Educational Inequality and the Poverty Trap in Teacher Recruitment

Abstract The regional concentration of poverty and the resulting disparities in living conditions create conditions where educational inequalities are intensified. These adverse conditions could lead teachers to refuse to work in disadvantaged locations that are characterised by high incidences of poverty and low-performing students. In this paper, we estimate how poverty in the districts where the schools are situated influences the probability that teachers accept a job offer in Costa Rica. Working with data on contract offers acceptance or rejection is a methodological novelty that makes it possible to dissociate students’ poverty from the poverty of the schools’ location. The estimation of a three‐level hierarchical model allows us to deal with aggregation bias and unobserved heterogeneity. The results show evidence that district poverty is a key determinant of teachers’ rejection of offers. Although the study uses data from Costa Rica, the results indicate more generally, how educational inequity can perpetuate poverty.


Introduction
Poverty traps are self-reinforcing mechanisms that can arise both from market and institution failures and makes poverty persist over time (Azariadis & Stachurski, 2005). As Thorbecke (2019) points out, there are many different types and causes of poverty traps such as (1) undernutrition resulting in low physical activity and productivity; (2) under-investment in education and skill acquisition; (3) geographical remoteness; (4) social exclusion and marginalisation; and (5) lack of assets sealing some household out of the capital market. Teacher recruitment is a good example of poverty trap. Working conditions affect teachers' decisions to work in schools and thus how teaching staff is distributed among schools. In this regard, the literature indicates that novice teachers and those less qualified tend to work to a greater extent with students of the objective of this work: high-quality administrative statistics on acceptance and rejection of teaching contract offers. Such data have not previously been used in the literature and has the advantage of reducing potential problems of unobserved heterogeneity. Thus, it allows for drawing robust conclusions to evaluate the relationship between the characteristics of the school location and the probability of teachers deciding to accept a position.
The results showed that poverty in the districts where the schools are located were the most prominent explanatory factor associated with teachers' rejection to positions offered, even more relevant than the students' performance, the main determinant highlighted by the previous literature (Berlinski & Ramos, 2018;Luschei & Chudgar, 2017). Moreover, our results showed that the probability of acceptance further decreased at higher-poverty levels, particularly affecting districts with the worst socioeconomic conditions, causing poverty to persist.
The work is organised as follows. Section 2 presents the theoretical framework and the background in the literature. Section 3 explains the teachers' hiring system in Costa Rica. Section 4 describes the data. Section 5, is the model. Section 6 presents the results. Section 7 discusses the findings. Section 8 concludes.

Theoretical framework and literature review
The conceptual framework for analysing the teachers' decisions about the job offers they accept derives directly from the economic theory on the functioning of the labour market. The demand for teachers is defined as the number of teaching positions that are offered at a given time in exchange for compensation. On the other hand, the supply consists of the number of teachers who are willing to teach for that compensation. In a broad concept of compensation, we refer to more elements than economic income, also including other types of rewards, such as nonmonetary working conditions (amenities). The imbalances between supply and demand for teachers occur in two circumstances: the oversupply of professionals in positions that are very attractive and the lack of teachers for vacancies that are difficult to fulfil (Guarino, Santibanez, & Daley, 2006;Jacob, 2007).
The theory of compensating differentials contributes to understanding the balances of supply and demand, recognising that workers (in our case, teachers) differ in their preferences about the characteristics of the jobs and that jobs differ in the conditions they offer (Rosen, 1986). This theory explains that teachers receive different salaries that equalise the advantages and disadvantages between positions. Differences in salaries are called compensating differentials.
Positions in the teachers' labour market present characteristics that vary according to the students, the school, and the school's location. For their part, teachers also have different characteristics that are not always easily observable, for example, quality. If low-quality teachers accept less attractive positions, the market reaches equilibrium without the need to compensate them for those positions (Borjas, 2008). This lower-quality teacher selection bias causes market equilibrium to be achieved at the expense of students who attend unattractive schools, which are generally those with educational and socioeconomic disadvantages (Rosen, 1986). Unattractive schools can have chronic staff recruitment problems and be forced to hire teachers with minimal qualification requirements (OECD, 2019). This situation could end up affecting the quality of the students' education.
In the teachers' labour market, as in other labour markets, both employers and teachers seek to maximise their utility. Teachers try to get the best possible position in the system. To do this, they invest in human capital to make themselves desirable to employers and expand their job options (Guarino, Brown, & Wyse, 2011). The attractiveness of the positions depends both on the remuneration (such as salaries, bonuses, and other forms of monetary compensation), and on non-monetary elements such as the characteristics of the students (discipline and results), the working conditions (schedules, training courses or in-kind compensations) and the school's location (accessibility of services or safety).
The two main strategies followed in the literature to analyse the characteristics that discourage teachers from accepting and staying in jobs have been, first, to follow-up historical information from schools on the departure and retention of teachers' panels (Boyd, Lankford, Loeb, & Wyckoff, 2005) and, second, to analyse the voluntary teachers' request to transfer from the school they are working, as in Boyd, Lankford, Loeb, Ronfeldt, & Wyckoff (2011), and Barbieri, Rossetti, & Sestito (2011).
The first strategy has the drawback that it cannot distinguish to what extent teacher mobility is driven solely by the teacher's preference or also by the employers. The second strategy can isolate the effect of the employer, but the groups of teachers that are analysed through their transfer requests can present selection biases if they have to meet a particular condition that allows them to request it. 3 Therefore, the results may not be generalisable (Engel, Jacob, & Curran, 2014). Strategies analysing applications to transfers provide relevant information about teachers' preferences based on their experience with districts, schools and students, that provide insights for teachers' retention policies. Yet these characteristics may be linked to those of the neighbourhoods, which makes it difficult to distinguish between a preference for advantaged neighbourhoods or advantaged schools (Prost, 2013). On the other hand, by using administrative mobility data, we know if a teacher was hired, but do not know who else may have received a job offer for the same position, neither the characteristics of offers rejected to estimate school preferences for teachers (Boyd et al., 2011). Neither of the two strategies allows for distinguishing between the relationship of the sociocultural characteristics of the students and the characteristics of the school location. This shortcoming has a special significance in the case of student's poverty compared to that of the location's poverty conditions key to design policies to attract teachers. A third method to understand characteristics that discourage teachers from accepting and staying in jobs is asking teachers directly. This is a more qualitative approach that provides insights into mechanisms of the decision-making process (for low-and middleincome countries examples see Luschei & Chudgar, 2017;Lentini, 2019).
The corresponding empirical literature highlights the fact that the adequate strategy to analyse the link between the characteristics of the school location and the teachers' decision to undertake a position would be to use information on the acceptance or rejection of job offers (Boyd et al., 2011;Prost, 2013). In this research, we exploit data that includes this information, and the characteristics of the offers (related to the district and the school), as well as the characteristics of the teachers who expressed their preferences. As far as we know, it has not been used in the previous literature.
Despite offering incentives, there are schools that are not attractive to teachers, even if the location is close to their place of birth (for main attraction factor, see Scafidi, Sjoquist, & Stinebrickner, 2007;Engel et al., 2014). A factor that is emerging as fundamental in teachers' decisions and that has received little attention in the literature is the poverty in the area around the school. Poverty in surrounding neighbourhoods has consequences in terms of crime, access to infrastructure, the socioeconomic level of its population, and student outcomes, while it generates negative externalities for the teacher and his/her family. The effect of poverty on the distribution of teachers is particularly important in countries with large concentrations of vulnerable populations and internal asymmetries in the provision of services, such as Latin American and other developing countries (OECD, 2018).
Literature on teacher recruitment and distribution in low-and middle-income countries identifies rural-urban location as a key determinant of teacher sorting patterns (Crawfurd & Pugatch, 2020;McEwan, 1999). But there are also certain nuances when differentiating urban centres from well-located rural localities or from isolated and dispersed rural areas. In the case of Costa Rica, well-located rural districts are mainly in tourists' clusters areas, and the less attractive are in districts located in the borders of the country. Local studies on the distribution of teaching resources have indicated that there are serious geographical imbalances in the country but not directly related to rurality (as defined by the Costa Rican Census). 4 High schools The poverty trap in teacher recruitment 719 are mainly located, even in rural areas, in more populated areas within the districts. Teachers with lower qualifications and with non-permanent contracts are concentrated in the poorest (urban-rural) and with fewer social development districts. Current incentives to attract teachers to the latter areas have been ineffective in promoting equity in teachers' distribution (PEN, 2017;Lentini & Rom an, 2018).

The hiring system for teachers in Costa Rica
The hiring and allocation of teachers in the Costa Rican public schools (managed by the central government) are defined through a centralised system like in the majority of low-middle-income countries. A single non-market employer (government) determines the quantity, wages, skills, and spatial distribution of teachers. This is the main difference between a more competitive labour market, like the one in the United States, where many states and school districts use pay-related methods to recruit and retain teachers (Loeb & Beteille, 2008). In Costa Rica, academic level attained and seniority provide teachers with a score to compete for vacant positions in the schools. For each vacant, applicants to positions in the region are ranked according to their score. The applicant with the higher score is offered the contract by the centralised system. The educational level also determines the professional category that the teacher reaches if he/she is hired. Positions can be offered through permanent (owned) or nonpermanent (interim) contracts. The mechanism by which teachers can compete for the positions is to register on a candidate's list, declaring the geographical regions where they would be willing to work, and describing their academic degrees and experience. Teachers who register to compete do not choose either the district or the school, just the region. They are not aware of the vacancies that will open when they register as candidates.
Once the system selects the candidate and makes an offer, the teacher decides if he/she accepts it or not. Teachers who reject a contract offer can remain on the candidates' list and may reject new position offers the same year or any time in the future. 5 The flexibility of the mechanism to reject contract offers without repercussions for the teacher makes it a common practice. 6 In 2018, each school experienced an average of 4.12 rejections of a contract offer (Lentini & Rom an, 2018;MEP, 2018). 7 The record of these rejections, which is the information we use in this work, is a source of data of singular interest to study the preferences of teachers on the characteristics of the schools' locations.
Centralised contract systems can influence teacher recruitment. One might expect that a centralised system should pursue equality among schools and teachers; contrary to decentralised systems in which schools may compete to have the best teachers. In low-income and middleincome countries, like Costa Rica, it is expected that difficult living (or teaching) conditions in high-poverty regions can influence teachers' decisions more than they do in high-income countries. However, because our analysis is based on revealed preferences, our data are not restricted to the case of a centralised allocation system, and our results can be, to a large extent, generalised to cases when the allocation of teachers across schools is not centralised.

Data and descriptive statistics
For this research, we used a database that we created from two main sources. The first source, provided by the Ministry of Public Education, contained the administrative records of all contract offers accepted and rejected by public secondary education teachers in 2018. 8 The second contained information on the population (projected to 2017) in the districts where the schools are located, from the 2011 Population and Housing Census of the National Institute of Statistics and Censuses (INEC).
The database included the 6,070 contract offers to secondary education teachers in 2018, both interns and novice staff. In total, we have information on the characteristics of 4,484 teachers (each teacher received an average of 1.35 offers) who were offered positions in 650 public schools (93per cent of all schools in the country), located in 339 districts (99per cent of the districts where there are schools). 9 The supplementary material presents details on the construction of the database, as well as the descriptive statistics of the universe of contracts offered by the Ministry of Education (Table A.1 of the supplementary material). Table 1 presents the mean, standard deviation, and number of missing values of each variable of the three dimensions of analysis (teachers, schools and districts), as well as their definition and source. In the sample 54% of the contracts were offered in the same province where the teacher was born. Teachers in higher professional categories had contracts in their provinces of birth in a higher proportion than the rest. The Ministry of Public Education is responsible for assigning the professional category to each hired teacher, and this category is associated with his/her academic level. Those in the highest level must have graduate or undergraduate degrees and those who have the previous level to the maximum must have reached an undergraduate degree. The category and the experience define the final salary that the teacher receives for the lessons that he/she is hired. 10 The proportion of repeaters in the sample reached 17 per cent and the average ratio of students to teachers was 11.40. We used the repeaters variable as a proxy for students' abilities and to differentiate schools whose population required a greater teaching effort. In the sample, 93 per cent of the public schools and 99 per cent of the districts where there is a public school are represented.
Poverty is the key variable in the study. The poverty measure that we use was created by INEC through the methodology of Unsatisfied Basic Needs (UBN) proposed by the Economic Commission for Latin America and the Caribbean (Feres & Mancero, 2001a). Its construction includes four components: (1) housing (quality of the property, access to electricity, and degree of overcrowding); (2) health (variables related to access to physical health infrastructure); (3) education (access to and educational attainment of the youths of the household); and (4) consumption (possibility of acquiring goods and services, according to the number of income earners -employed, pensioners or rentiers-, their educational level and the number of in-home dependents). The indicator is built based on 17 questions that identify deficiencies in any of the 4 components (each component has the same weight). The INEC classifies as poor those households with deficiencies in all the components of the indicator (INEC, 2013, p. 7). Figure 1 shows the distribution of poverty by districts. Those that concentrate the country's poverty are the rural districts and the districts far from the central region (where the capital is located). There is a positive correlation (.64) between the percentage of the rural population and the percentage of the population living in poverty (significance at the 1% level). Figure 2 shows that the percentage of the population living in poverty is higher in rural districts. In the 20% of the districts with the highest concentration of rural population, 40.3% of their inhabitants live in poverty; compared to the 20% of the districts with the lowest concentration of rural population, where 17.2% of their population lives in poverty.
The multiple components that are integrated into the construction of the poverty variable that we incorporate in the model allow us to reflect the structural situation of the households in the districts where the schools are located. 11 Methods that measure poverty by focusing solely on the economic dimension explain little about what people do with disposable income. Faced with these methods, the measurement of poverty through unsatisfied basic needs measures both, the consumption made and the possibility of doing so, and it also reflects the deficiencies in the geographical context (Bourguignon & Chakravarty, 2003;Feres & Mancero, 2001b). On the contrary, in districts with low proportion of poverty (low unsatisfied basic needs) population enjoy a healthy life, its citizens achieve a decent standard of living, students have access to education services that favour the development of their human capital and inhabitants have the possibility of acquiring goods and services they need. Teachers that accept a job in these districts become members of a community that offers good conditions for them and their families.
The poverty trap in teacher recruitment 721 The poverty trap in teacher recruitment 723 On average, 28 per cent of the population in the sampled districts lived in poverty. This variable was widely scattered according to the school location where the contract was offered (13 percentage points of standard deviation). The dispersion in the percentage of  poverty in the districts of the sample reached between 7 per cent and 91 per cent of the population, which was comparable to that of all the districts of Costa Rica (between 6% and 91%) (PESH, 2018).
In the districts of the poorest decile of the sample, the population that did not meet basic needs was over 45 per cent, more than 3.5 times the proportion in the districts of the richest decile.

The model
We estimated a three-tiered Hierarchical Linear Model (HLM). The methodology is suitable due to the nested structure of our data: 5,943 contracts were offered in 633 schools that were distributed in 333 districts. In this case, the method improves estimations' efficiency compared to conventional methods. The HLM incorporates specific intercepts for every school and district, allowing us to control for the presence of spatial unobserved heterogeneity of unknown origin. In this way, it is possible to mitigate the correlation between the unobserved part of the model and the predictors and obtain robust standard errors using the clusters information. 12 The three-level model that we used can be expressed as: In Equation (1), Y ijk was the expected probability of acceptance of the contract i, offered in school j, in district k; C ijk , S jk and D k were vectors of predictors at three levels: (1) the contract being evaluated by the teacher, (2) school, and (3) district. In vector D k we incorporated our variable under study: the poverty of the district where the contract is offered. e ijk was the unexplained component.
Equation (2) was estimated simultaneously with Eq. (1) and allowed us to model the schools and districts random intercepts and the associated complex error structure. v 0k and u 0jk were the respective deviation of the schools' and the districts' means from the overall mean c 00 that allow us to control for unobserved heterogeneity at the school and county levels. They were assumed to be normally distributed, with mean 0, and uncorrelated with e ijk : The explanatory variables included in each vector of the model were proposed by Barbieri et al. (2011), and were expanded to incorporate the poverty dimension associated to the school district. The variables were the following: 1. Characteristics of the teachers to whom the contract was offered: gender, age, age squared, province of birth of the teacher, contract in a province that matched with the teacher's province of birth, professional teaching category, if the subject to be taught was basic (mathematics, social studies, Spanish, English, and science) and if the subject to be taught was scientific (mathematics, biology, chemistry, physics, and computer science). 2. Characteristics of the schools of destination: the annual proportion of repeaters, studentteacher ratio, type of school (academic or technical), and the number of lessons offered by the contract. 3. Characteristics of the destination districts: poverty, the proportion of the foreign population, participation rate in the labor market, number of schools in the district, and size of the canton to which the district belonged (by number of inhabitants).
We used a multilevel logit estimation method to determine how poverty in the district where a school was located increased or decreased the probability of acceptance of teachers' contracts. The results were presented using the coefficients and odd-ratios (or probability ratios) of the The poverty trap in teacher recruitment 725 estimators. The sign of the coefficients indicated the direction of the effect of the independent variable on the probability of acceptance of the contract offer, and the t tests allowed to confirm or reject the hypotheses about the logit coefficients.
Equation (3) shows the way in which the odd-ratio of an estimator is defined, which is the quotient between the odds that the contract offer is accepted and the odds that it is not: where Pr is the probability of acceptance of the contract. The odd-ratio can take a value from 0 to infinity. We interpret that the variable increases the possibility of the event occurring if the odd-ratio is greater than 1, and that it reduces it if it is less. An odd-ratio equal to 1 indicates that the possibility of the event occurring is independent of the explanatory variable.
The contracts shared similar characteristics when they were offered in the same districts. This entailed that the disturbances could be correlated and that the estimates of the standard deviations might be biased (Moulton, 1986). To control for this situation, we corrected the standard errors clustering within-districts.

Results
Table 2 presents the maximum likelihood coefficients and odd-ratios of the multilevel logit model that estimate the probability of accepting a contract with robust standard errors. The estimations include the fixed-and-random effects. 13 The latter, at the bottom of the table, show the variance from the overall mean, with origin in the school-and-district-level variance unaccounted for in the model. The fixed effects account for the overall expected effects of the teachers', schools', and districts' characteristics on the probability of acceptance of the contract, such as teachers' socioeconomic background, schools' infrastructure, or districts' public services quality; the random effects give information on whether this effect differs between schools or districts.
The estimated coefficients revealed that increases in the poverty rate in the school district were the major determinant associated with the possibility of the contract being rejected. Moreover, contract rejection probability increased in schools with students' higher repetition rates, and when candidate teachers were higher profile.
Additional results showed that the possibility that the contract would be accepted increased if it was offered in a province that matched the teacher's province of birth, if the subject to be taught was basic or scientific, if the number of lessons in the contract increased and if the ratio of students per teacher was higher. The variables that were not statistically significant were: gender, age, age squared, the teacher's province of birth, the type of school (technical or academic), the proportion of foreign population, the number of schools in the district, the participation rate in in the district's labour market, and the size of the canton where the school was located.
The results showed that poverty in the school district reduced the probability of teachers' acceptance of contract offers. A higher percentage of poverty in the district was associated with a lower chance of teachers taking up a position as he probability of accepting a contract goes down by 85 per cent in poorer districts (odd ratio of 0.154). Poverty was the variable that most predicted the reduction in the probability of acceptance, even to a greater extent than student performance, quantified through the proportion of repeaters (odd ratio of 0.190, see column 2 of Table 2). Another way to analyse the result is by observing the coefficient of the variable. According to Studenmund (2016), an interpretation roughly equivalent to a linear probability model coefficient for continuous variables can be calculated by multiplying it by 0.25. In our The poverty trap in teacher recruitment 727 Dependent variable: acceptance of the contract. The value 0 denotes that the contract is rejected, and 1 that it is accepted.

Note:
The calculated standard errors were robust in 333 clusters by district (within-district clustering). Ã case, the maximum possible changes in the probability of accepting a contract offer when poverty in the school district increases is -47 per cent (-1. 870 Ã 0.25 ¼ 0.468). 14 The average probability of accepting contract offers, keeping the rest of the variables at their observed level, reached 88 per cent. The probability of acceptance decreased 18 percentage points when contracts were offered in schools located in districts with the highest levels of poverty.
The estimates made it possible to size the predicted probability of accepting the contracts associated to each regressor. The main contribution of the results was the confirmation of the hypothesis that poverty in the districts reduced their probability of attracting teaching staff. Poverty was higher than the national average in districts where 46 per cent of the contracts were offered, and schools where 33 per cent of the students attended.
The two variables on teacher characteristics that had predicted the larger probability of accepting the contracts were: (1) the concurrence of the location of the school with the teacher's province of birth, which almost doubled the probability of acceptance (88%, in column 2); and (2) the increases in the teaching professional category, which reduced it (35%).

Further analysis
The contract sample was restricted from part-time to full-time contracts (i.e. no less than 20 up the total of 40 lessons). 15 Restricting the sample could have introduced selection biases. Yet, Table 3 presents the results of replicating the multilevel logit regression of Equation (1) using the data from the universe of contracts that prove that the sample did not face this drawback to affect the findings. Table 4 also presents the results of the model transforming the poverty variable, of a continuous nature, into a categorical one, with four levels for classifying the districts. The rationale of this transformation relies on the interest of analysing whether the effect of poverty is heterogeneous using certain specific thresholds (i.e. levels of poverty associated with different districts as it is explained in the main text) to observe and compare these effects in relation to the poorest district. The analysis of the results with the poverty variable as categorical shows that the probability in the acceptance of contract offers was heterogeneous, with a greater impact in the poorest districts. The lowest level, with 19 per cent or less of the population living in poverty in the district, was the base. This level was the average observed in the districts located in the central region of the country. This region (where the capital is located) with 62 per cent of the country's population, concentrates the economic activity of Costa Rica (66% of the economically active population), the residents with the highest educational qualifications (78% of graduates) and socioeconomic levels (78% of households in the highest-income quintile), as well as the most highly qualified teachers (ENAHO, 2019). The second level was the percentage of poverty observed mainly in districts that surround the central region. The third level, the percentage in districts where tourism economic activity is developed. Finally, the fourth level of poverty was common in the border, coastal and rural districts mainly dependent on primary economic activities (see Figure 1). The results suggested that districts with poverty levels above those in the central region of the country were less attractive to teachers.

Robustness analysis using other indicators
The two main indicators of social development in Costa Rica at district level are the measurement of poverty through unsatisfied basic needs that we used, and the composite district-level index of social development (SDI) that has five components (weights in brackets): health (0.216), economy (0.279), education (0.266), security (0.123) and electoral participation (0.116). The SDI shows values between 0 and 100. Values close to 100 indicate a better situation. The average in our sample is 65 .35 per cent (s.d. 15.15). The SDI presents a -0.909 significant inverse The poverty trap in teacher recruitment 729  Dependent variable: acceptance of the contract. The value 0 denotes that the contract is rejected, and 1 that it is accepted.

Note:
The calculated standard errors were robust within district clustering. Ã The poverty trap in teacher recruitment 731 correlation with poverty. As a robustness check we run the analysis with the SDI measure as well as with separate variables for each of its dimensions. As expected, the SDI has a significant positive effect on the teachers accepting the contract offer (Table A.2 of the supplementary material). The higher the social development of the school district, the higher the probability of acceptance. The disaggregation of the SDI shows mixed results. While the dimensions of Economy, Electoral participation and Education have a significant and positive correlation with the job offers acceptance, the same cannot be said for Health and Security dimensions, with no statistical significance in the regression. In sum, the results confirm a virtuous nexus between education, civic participation, economic and social development, and talent attraction. As Gimenez and Vargas-Montoya (2021) state, like other employees, teachers seek a better quality of life by moving to areas with high human capital and, therefore, that have faster population and employment growth. Their well-being and productivity can increase by interacting with and learning from high-skilled teachers (Berlinski & Ramos, 2018;Correa, Parro, & Reyes, 2015). Additionally, we considered whether our results differ when we account for specific monetary incentives associated to less developed regions (MEP-1806-2019). As we have previously explained, teachers' salaries are fully defined by category and experience, only with the exception of these incentives that aim to compensate for particular disadvantaged conditions. Therefore, we proceeded by including in our regressions associated to Tables 2 and 3 these monetary incentives. The results (Table A.3 of the supplementary material) indicate that incentives do not increase the probability of teachers accepting a contract.

Discussion
The main result of our research was that poverty in the district where the school is situated was the highest predictor of the probability of teachers accepting the position. To the best of our knowledge, there are no other studies that use similar strategy that allows us to compare the results. Other studies have not used poverty variables related to the school's district, but have based their analysis on the students' socioeconomic characteristics.
High poverty levels in the districts embody a series of negative externalities for teachers. These include family and professional sacrifices such as fewer cultural options, higher exposure Table 4. Multilevel mixed-effects logistic regression odds ratios estimates of the poverty variables by levels, using the same covariates than in Tables 2 and 3 Odd-ratio Standard Error The acceptance of the contract can take a single value of 1 or 0. The value 0 denotes that the contract is rejected, and 1 that it is accepted. Note: The calculated standard errors were robust within district clustering. Ã p < 0.1; ÃÃ p < 0.05; ÃÃÃ p < 0.01.
to crime events, fewer job options for the teacher's partner, less culture and entertainment offers, worse transport, telecommunications, and supply infrastructure, worse housing, and worse health services than in districts with low levels of poverty (Gimenez et al., 2018;Luschei & Jeong, 2018). Teachers refuse to work in poor districts because differences in salaries to make them attractive are not enough to compensate for the externalities (Crawfurd & Pugatch, 2020;Santibañez, 2010). In Costa Rica, teachers' salaries are identical, in respect to their qualifications and years of experience, except for specific incentives in some less-developed regions aimed to compensate for disadvantaged conditions (MEP-1806-2019). The same teacher working in a poorer district has a higher wage than in other districts. However, incentives aimed to compensate for disadvantaged conditions have been criticised because they present discrepancies between the conditions of some schools and districts where they are located, and the score assigned to the educational centre in order to obtain the incentive (PEN, 2015;S anchez & Zamora, 2017). We tested this hypothesis by running the model including the incentives, and the results showed that they did not play any role in the teachers' decision regarding whether to accept a contract offer (see Table A.3 in the supplementary material). Thus, confirming critics present in previous literature concerning the efficacy of this policy (Pugatch & Schroeder, 2018;Wei & Zhou, 2019). The greater difficulty for poor districts to recruit teachers means that the opportunity to close gaps between students of different socioeconomic levels is missed. The situation exposes students in these districts to falling into a 'poverty trap or persistent poverty' (Mihai, Ţiţan, & Manea, 2015;Rivkin, Hanushek, & Kain, 2005).
In line with Luschei and Jeong (2018), our results do suggest contextual differences between lower-middle-and higher-income countries. Difficulties of living in poor areas in lower-middle countries might create greater cross-district sorting than in industrialised countries, where even the most disadvantaged areas have higher standards than those in poor countries.
Three additional results that we have obtained are in line with the literature that studies the determinants of teacher mobility. First, teachers of lower professional category levels were more open to working in any district, including the most vulnerable. Those of higher categories were more selective with their jobs (as in Cowan & Goldhaber, 2018;Wei & Zhou, 2019). In Chile, studies by Correa et al. (2015) and Berlinski & Ramos (2018) found that teachers with higher abilities self-selected to work in schools with better socioeconomic conditions (see column 2 in Table A.4 in the supplementary material where the results are shown by teaching category according to the academic grade of the teaching staff). The selection bias of low-qualified teachers in disadvantaged schools was also confirmed in an analysis that included all countries that participated in international standardised tests for students (in PISA 2015). This analysis pointed out that teachers from more disadvantaged schools had lower qualifications and experience, and that ignoring this bias in hiring teachers has consequences for educational equity (OECD, 2019).
Second, our results showed that teachers preferred to work in places close to their place of birth. According to Reininger (2006), who analysed information from the United States labour market, the propensity of teachers towards preferring to work near their place of origin is particularly high compared to other occupations. This trend is similar in Costa Rica: 57 per cent of secondary education teachers, 59 per cent of primary and 62 per cent of preschool teachers work in the same province where they were born; compared to 48 per cent in the case of nonteaching professionals (INEC, 2011). The proximity of schools to the place of birth, where they grew up or studied in their youth, encourages teachers to prefer these workplaces. This situation harms the districts with the fewest graduates, which are generally those with the greatest levels of poverty (PEN, 2017;Reininger, 2012). In the case of Peru, Jaramillo (2012) finds that being born in a certain province substantially increases the probability of having a first teaching position in that same province. The author suggests that, given that geographic mobility of teachers is quite limited, policies that seek to strengthen teacher educational systems and reduce inequities should focus on the local level.
The poverty trap in teacher recruitment 733 Third, our finding related to the inverse relationship between the proportion of repeaters and the probability of acceptance of contract offers is in line with Bruns & Luque (2015), that point out that, with complex academic situations that require more teaching efforts, teachers may not accept jobs.
The positive relationship with the contract acceptance was also observed when they were to teach basic subjects and with those that were offered for a greater number of lessons. This makes sense because contracts for basic subjects, being mandatory, are more likely to be offered for more lessons. In Costa Rica, schools with few students have difficulty hiring full-time teachers of complementary subjects (not mandatory) (Lentini & Rom an, 2018).
This situation could also explain that a higher ratio of students per teacher had a positive relationship with the acceptance of contracts. The variable could be capturing the size of the school rather than the workload of the teachers. 16 Barbieri et al. (2011) andProst (2013), who find that the student-teacher ratio increases the probability that teachers would remain in their positions reach the same conclusion.

Conclusions
In this work we analyse how the poverty levels in the districts where the schools are situated affect the probability of teachers accepting positions. The use of a single database of 6,070 contract offers to teachers in Costa Rica in 2018 made it possible to overcome the main limitation present in the previous studies, to dissociate students' poverty from the poverty of the schools' location.
We found that poverty in the school district turned out to be the most predictive variable on the probability of job rejection, even to a greater extent than student performance, quantified through the proportion of repeaters. Moreover, this probability of rejection was greater in the poorest districts.
Moreover, the link between poverty and the rejection of teachers has implications for the distribution of teachers in schools. The variability in the attractiveness of schools for teachers causes disadvantaged and geographically segregated schools to perpetuate their situation (Owens, Reardon, & Jencks, 2016).
The problems faced by unattractive schools in recruiting staff can compromise their students' quality of education. In the first instance, because teachers with lower qualifications are more open to accepting contracts than those with higher qualifications. Second, because the absence of adequate compensatory differences makes teachers who accept these positions unmotivated and deteriorate their performance, even when they are highly qualified.
The results suggest the need to intervene on the demand side to reinforce the hiring of teaching staff in disadvantaged schools. Conditions in the poorest districts are difficult to change in the short term, but positions can be made more desirable through incentives that motivate teachers to work there. To combat the unequal distribution of teacher quality, it is necessary to develop a strategy based on the effective design of incentives that can stimulate the geographical mobility of teachers. Among the possible incentives, the literature identifies monetary incentives as the most attractive to teachers (Cowan & Goldhaber, 2018). However, these incentives have limitations in countries such as those in Latin America, where there are major budgetary restrictions to address internal inequalities. Thus, in the short and medium term, complementing pecuniary incentives with non-pecuniary ones is a good strategy since it adds versatility to the design of incentives and reduces budgetary problems. Among these non-pecuniary incentives, we could mention the presence of highly qualified teachers in the school, the access of teachers to supervisors of educational programs, or the provision of technological and material resources. Finally, the identification and support of local teacher candidates could be a good longterm strategy to strengthen educational systems and sustain the reduction of inequities (Jaramillo, 2012). 734 V. Lentini et al.
The main limitation of our study is that the registration of acceptance and rejection of contract offers is made on the basis of teachers who are willing to work in certain regions. That is, teachers self-select into the regions according to the score that allows them to compete. Therefore, our results could be underestimating the probability of rejection associated with poverty, and therefore, they should be interpreted as a lower bound. However, this limitation cannot be overcome with the available data, since the Ministry of Public Education does not make contract offers to teachers who, due to their qualities, could be appropriate to hire in schools with more vulnerable students.
Economic constraints in developing countries impose the need for teacher allocation policy designs, including the incentive system, to have clear and measurable objectives. Reducing poverty is a clear and measurable goal. In this sense, our results provide information on possible courses of action to promote educational equity and social mobility. Notes 1. The country has 484 districts, the smallest administrative unit divisions. In a fifth of the districts, poverty measured by households unsatisfied basic needs exceeds 40% (PESH, 2018). 2. 'With 7.9% of GDP, spending on education in Costa Rica is higher than in all OECD countries, but it is inefficient ( … ) in terms of reducing inequality' (OECD, 2018, p. 29). The Gini coefficient in 2019 reached 0.51, increasing in rural areas compared to the previous year. In education, the results of the standardised PISA tests for 15-year-old students show that in Costa Rica they are more influenced by socioeconomic background than in most OECD countries. 3. Examples of particular conditions that teachers have to meet that allows them to request for transfers in some systems are, being a senior teacher (Prost, 2013), having tenure and seniority (Barbieri et al., 2011), or having tenure and evidence of illness, threats to physical integrity, family violence (Art. 101 from the civil service statute, Costa Rica). Teachers not fulfilling certain conditions are bounded to apply for a transfer and have no chance to formally express their preference. In our case, we are using data from acceptance and rejection of contract offers in broad geographical areas, and teachers do not need to meet any criteria to express their availability and register on a candidate list. Therefore, we ensure that under our empirical strategy we have ruled out issues associated to the selection bias present in previous studies on this topic. 4. The classification of rurality in Costa Rica depends mainly of two variables, agriculture as the main economic activity and households that are located in disperse clusters (services and infrastructure access are not part of the definition) https://www.inec.cr/sites/default/files/documetos-biblioteca-virtual/imgmetodologia-indiceurbru.pdf 5. In 2018, only 0.5% of teachers rejected more than one contract in the same year. 6. Transfers are very restrictive but teachers can compete and reject contracts every year. Rejecting it does not entail any retaliation for being permanently competing. This scenario makes it possible that data appropriately reflect teachers' preferences. 7. 30% of teachers working in the central region have rejected an interim offer, and 11% have rejected a permanent offer at least once (Lentini, 2019). 8. In Costa Rica, secondary education offers different alternatives. For this work, we only use data of daytime public schools excluding nighttime public options committed to the adult population. Our procedure is in line with those of other international studies of this nature, which focus on the analysis of schools for generational cohorts of secondary school age. 9. The study only includes public schools. In 2018, these schools concentrated 90% of the population of 12 to 18 years old who attended secondary education (ENAHO, 2018). Information on private schools was not included because it was not available. 10. Information on wages was not available. However, in this paper, we take advantage of a dataset on all high school teachers in Costa Rica. 11. The data of poverty we used was updated by the Costa Rican government to have indicators for the Strategy for Prioritising Human Security, announced in 2018. Data was obtained from the Census 2011 (INEC, 2011) and projected to 2017 per district, but its disaggregated components were not. Therefore, a future research agenda would include separating its components to identify those that teachers find particularly important when making their location choices, when the new Census data from 2022 is released. 12. For an in-depth explanation of the rationale behind the use of HLM see Hox, Moerbeek, and van de Schoot (2017). 13. At the suggestion of an anonymous reviewer, and to add robustness to the findings, we have replicated the analysis for 2019 and 2020. The analysis using 2020 data showed that the results were also consistent with 2018, but the poverty variable reduced the probability of teachers accepting a contract only at its highest levels, i.e. when exceeding 33% of the population in poverty. The estimations are available upon request. We have chosen to present only 2018 data estimations in the article because data from 2019 and 2020 presented some problems. In Costa Rica, the school year begins in February. 2019 was affected by teachers' strikes that started at the end of 2018 that extended for three months, followed by a students' strike. These events ended with the Minister of Education resigning in 2019, and the national standardised tests suspended. In February 2020, the Ministry of Education passed a rule (VM-A-DRH-02-2020) to make teachers' contracts rejection less flexible with the aim of reducing the impact on the student population that was commonly left without teachers at the beginning of each school year (when teachers rejected the positions). 14. The maximum is reached when at the point of the function where the predicted probability is 0.5. The logistic function never reaches the probability of 0 or 1, therefore a fixed minimum effect does not exist. On the other hand, in this type of functions the slope of the parameters forms a ratio of exponential terms, the expected increase is not additive or multiplicative but rather iterative and depends on the value of the predictors, so the coefficient cannot be interpreted as an expected constant change (linear). 15. The main reason for not using the universe of observations is that in deciding to accept less than part-time contracts, teachers may consider circumstances that we cannot observe. Teachers with permanent contracts were also excluded from the sample because less than 5% of them compete every year for new contracts due that they tend to be already working in relatively advantaged districts (MEP, 2018;Lentini & Rom an, 2018). 16. The larger schools have a higher ratio because they have more full-time teachers. Those of smaller size have more teachers per student but are hired for a few lessons (PEN, 2017).