Intergenerational transmission of education: The relative importance of transmission channels

Chávez Juárez, Florian Wendelspiess Article Intergenerational transmission of education: The relative importance of transmission channels Latin American Economic Review Provided in Cooperation with: Centro de Investigación y Docencia Económica (CIDE), Mexico City Suggested Citation: Chávez Juárez, Florian Wendelspiess (2015) : Intergenerational transmission of education: The relative importance of transmission channels, Latin American Economic Review, ISSN 2196-436X, Springer, Heidelberg, Vol. 24, Iss. 1, pp. 1-44, https://doi.org/10.1007/s40503-014-0015-1 This Version is available at: https://hdl.handle.net/10419/108961 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. http://creativecommons.org/licenses/by/4.0/ ORIGINAL RESEARCH Intergenerational transmission of education: the relative importance of transmission channels Florian Wendelspiess Cha ´vez Jua ´rez Received: 24 September 2013 / Revised: 4 September 2014 / Accepted: 12 November 2014 ÓThe Author(s) 2015. This article is published with open access at Springerlink.com Abstract This paper aims at quantifying the relative importance of different transmission channels generating the high levels of intergenerational correlations in education, especially in Latin America. A simultaneous equations model is applied to rich survey data from Mexico. The results show that the economic situation of the family has the highest impact, even more than heritability of cognitive abilities. The long-run economic situation seems to matter more than the current consumption level. Parental education affects the schooling outcome directly but also indirectly through the economic situation, which is particularly true for the father. Keywords Intergenerational transmission of education Social mobility  IQ transmission Inequality Mexico JEL Classification: D31 I21 I24 I62 1 Introduction Education is a main ingredient for a successful life in modern societies. However, in many countries the opportunities to get well educated strongly depend on the family background, particularly in Latin America. As a result, we observe very low intergenerational mobility. Understanding the mechanisms generating this intergenerational persistence in education is essential to target policy measures adequately. F. Wendelspiess Cha ´vez Jua ´rez (&) Institute of Economics and Econometrics, University of Geneva, UNI-MAIL, 40 Bd. du Pont d’Arve, 1211 Geneva 4, Switzerland e-mail: [email protected]; florian.wen[email protected] 123 Lat Am Econ Rev (2015) 24:1 DOI 10.1007/s40503-014-0015-1 In this paper, I try to shed some light on this mechanism by applying a simultaneous equations model to data from Mexico. The main goal of the study was to estimate the relative importance of different transmission channels and their interactions. The three main mechanisms put forward in recent theoretical and empirical contributions can be broadly described as being the biological, the economic and the direct education-to-education channel. The biological channel refers to the genetic transmission of ability, often measured by the IQ, which explains a part of the relationship (Anger and Heineck 2010; van Leeuwen et al. 2008; Bjo ¨rklund et al. 2010; Black et al. 2009). Poor families facing credit constraints are an example for the economic channel, because they cannot borrow against the expected future earnings of their offspring, which generates a link between the socioeconomic situation of the parents and the schooling of their children (see for instance Black and Devereux 2010; Attanasio and Kaufmann 2009; Stinebrickner and Stinebrickner 2007; Carneiro and Heckman 2002; Alfonso 2009). Finally, a higher return to education for children with highly educated parents is an argument for the direct education-to-education channel (Black and Devereux 2010). It might also include preferences for education, non-cognitive skills, aspirations and many other factors. The empirical literature focuses on estimating the causal effect of parental education on children’s education. Holmlund et al. (2011) revise this literature and propose a comparison of different methods applied to the same dataset from Sweden. They conclude that the estimates differ substantially across identification strategies and that no method is perfect. They find relatively modest causal effects of parental education and point to the importance of analyzing in more detail other mechanisms explaining the intergenerational transmission of education. They hypothesize about the possibility of an indirect effect of education through better socioeconomic environment that can be offered to children. This conclusion on the need of better understanding the mechanisms is shared by recent literature surveys such as Black and Devereux (2010), Bjo ¨rklund and Ja ¨ntti (2009) and Piketty (2000) who coherently argue that more empirical research must be undertaken to understand the mechanisms behind educational mobility and social mobility in general. Black and Devereux (2010, p. 69) conclude that ‘‘[...] there is still much work to do to pin down which family background factors are most important’’ and Bjo ¨rklund and Ja ¨ntti (2009, p. 516) argue that ‘‘a major challenge for future research is to find out what in the family other than income is important for the future of children’’. This study tries to contribute in the proposed direction by moving from the estimation of one single causal effect to the estimation of a larger system of effects, incorporating simultaneously the three channels previously outlined. This focus on different mechanisms at the same time aims at getting a better understanding of the larger picture—the whole process of intergenerational transmission of education. In this respect, this approach should be seen as a complement to the single causal effect estimation and not as an alternative. 1 Page 2 of 44 Lat Am Econ Rev (2015) 24:1 123 The choice of Mexican data is primarily motivated by the importance of high intergenerational correlations in education in Latin America. Hertz et al. (2007) compare educational mobility of 42 countries including 7 Latin American ones. These seven countries take the first seven places ranked according to their intergenerational education correlation. The country with the highest correlation is Peru (0.66), followed by Ecuador, Panama and Chile. Within Latin American Countries, Mexico displays relatively high intergenerational persistence in education. Dahan and Gaviria (2001) compare 16 Latin American countries using data from the late 1990s and find that Mexico has the second lowest intergenerational mobility level behind El Salvador. de Hoyos et al. (2010) use recent data on social mobility in Mexico. They report correlations between the education in years of parents and children, finding the highest correlation of about 0.6 for the children cohorts born between 1942 and 1951, followed by a reduction of the correlation to about 0.5 for the cohort 1962–1971 and finally a new increase of the correlation to 0.55 for the youngest cohort, composed of children born between 1972 and 1981. According to the same authors, this recent increase is even higher when using different data sources. The same pattern of increasing educational mobility prior to the economic crisis in the 1980s and a subsequent decrease was found by Binder and Woodruff (2002), who use different cohorts to estimate the intergenerational link. Hence, the Mexican case is not only interesting on its own but might be representative for other Latin American Countries. Moreover, another advantage of Mexico is the high-quality data available. The suitability of the survey for this study is underlined by the availability of cognitive ability scores. Nevertheless, the analysis faces a series of empirical challenges in the form of trade-offs. This study tries to find a balance between a more complete model with very high data requirements and a simpler model in which less data are lost due to unavailable information. The main result is that even when controlling for parental education and ability, the economic situation of the family has the largest direct effect on the schooling outcome of children. This important source of inequality of opportunity could be reduced by policy interventions targeting the link between economic requirements and schooling. Moreover, the estimation shows that there are important interactions between the channels, suggesting that the exclusion of some channels might seriously bias estimates. In Sect. 2I will review the literature on the mechanisms of educational mobility motivating my empirical models I present in Sect. 3. In Sect. 4I describe the data used and especially the needed transformations in detail and present some descriptive evidence. In Sect. 5I present the main results, which are complemented by some figures in ‘‘Appendix B’’. Finally, Sect. 6concludes the paper. 2 Theory and empirical evidence on educational mobility Intergenerational mobility in education is a complex phenomenon that does not rely on a single mechanism. The literature identified three main channels of transmission Lat Am Econ Rev (2015) 24:1 Page 3 of 44 1 123 (Chevalier 2004). The first channel is the biological transmission of ability, the second refers to the dependence of schooling outcome on the economic situation of the parents and the third deals with direct education-to-education effects. In this section, I present some theoretical and empirical contributions to the understanding of these channels. 2.1 Ability transmission through genes: the biological channel The direct transmission of abilities, which is not limited to simple IQ transmission, represents a biological explanation of the phenomenon. For instance, Becker and Tomes (1979) use the term endowments acquired from parents to describe this direct transmission. They provide a theory of intergenerational transmission based on rational choices through a human capital theory approach, where the ability level of the offspring is a key determinant of the decision. Their model was consequently extended by Loury (1981) and Solon (2004) and serves as a benchmark in many analyses. Empirically, much work has been done to determine the importance of this channel. In a meta-analysis of 212 IQ studies, Devlin et al. (1997) quantify the genetic transmission and find the broad-sense heritability of IQ to be 48 %. Social scientists put more emphasis on quantifying the overall IQ correlations between parents and children, which might also include environmental effects in addition to the pure heritability measured by Devlin et al. (1997). For instance, Anger and Heineck (2010) use German panel-data with two ultra-short IQ-tests to estimate the parent-offspring relation. They find that a 1-point increase in parents’ score results in a 0.45-point increase in the coding speed (inherent ability) and 0.50point increase in word fluency scores. The estimated coefficients remain stable at the inclusion and exclusion of control variables. Bjo ¨rklund et al. (2010) use Swedish data from military IQ tests and official registers. They estimate intergenerational and sibling IQ correlations. The estimated values are all highly significant and attain values of 0.346 for father-son, 0.510 for siblings and 0.65 for twins. According to the authors, their estimations represent rather a lower bound of the true values. Black et al. (2009) find a similar father-son IQ-correlation (0.38) in a comparable study with Norwegian data. van Leeuwen et al. (2008) go even further in the analysis of IQ-transmission by dividing it further up. No evidence for cultural transmission of the IQ was found and no indication that intelligent parents provide children with intelligence promoting circumstances. Individual differences in intelligence were found to be largely accounted for by genetic differences. Moreover, they find a spousal IQ-correlation of about 0.33 suggesting a relatively high degree of assortative mating. 2.2 Credit constraints and the economic situation: the economic channel According to the logic of the economic channel the intergenerational correlation in education is the fruit of an underinvestment in education by poor families. This idea that poorer families might face credit constraints making the optimal investment in 1 Page 4 of 44 Lat Am Econ Rev (2015) 24:1 123 the human capital of their offspring impossible can be found, for example, in Banerjee and Newman (1994) and Loury (1981). Empirical research was not able to conclude on the exact importance of credit constraints and the economic environment in general. While it seems that the impact of credit constraints is relatively modest in richer countries, some evidence was found that in developing countries the effect is larger. Stinebrickner and Stinebrickner (2007) analyze the situation at a college in the US using panel data of students. They find that a group of students is credit constrained in consumption during their stay at the college, but that many of them are not willing to borrow. Carneiro and Heckman (2002) critically revise the literature on the question of credit constraints. They compute that using modern US data, only about 8 % of students really face short-term credit constraints. They argue that long-term effects, such as the family environment during the whole schooling period of children, play a much bigger role. Winter (2007) elaborates a computable general equilibrium model to evaluate the role of credit constraints in the decision whether to go to college. The model is calibrated for the US economy and predicts observed patterns quite well. The findings contrast the results of few credit constrained students found by other studies and argue that econometric estimates such as in Carneiro and Heckman (2002) are downward-biased. In line with the results of other studies is the observation that the share of people financially constrained has increased (dramatically) over the past decades. Alfonso (2009) presents a study of 4 Latin American countries (Mexico, Chile, Colombia and Peru). She shows that the effect of credit constraints disappears in regression analysis when controlling for long run family variables (parental education, family assets, etc.). However, the relatively small effect of credit constraints increases from the oldest to the newest datasets used in the study. Attanasio and Kaufmann (2009) use Mexican data to analyze the relationship between post-secondary school decisions and subjective expectations. Among other findings on the role of expectations, they show that credit constraints represent an important issue for poor Mexicans, in contrast to some literature coming from higher developed countries, where these effects do not seem to be as present. To sum up, the literature finds evidence for the existence of the economic channel in producing high intergenerational correlations in education. It remains somewhat unclear if short-run credit constraints or the long-run economic situation are more important determinants. It seems, however, that in developing countries, both contribute to the low educational mobility. 2.3 Education to education transmission Finally, the third channel considered is the direct effect of parental education on the schooling attainment of the children. This channel is generally known as the nurture effect, capturing the direct causal effect of parental education (Holmlund et al. 2011; Chevalier 2004). Dickson et al. (2013) show that this direct causal effect starts at very early ages and remains visible years later when comparing students’ performances. Different explanations why parental education should have a direct Lat Am Econ Rev (2015) 24:1 Page 5 of 44 1 123 causal effect can be found in the literature. One possible explanation is that highly educated parents tend to encourage their children more to achieve high levels of education (Merton 1953; Boudon 1973,1974; Sewel and Shah 1968). For instance, Steinberg et al. (1992) show that parental encouragement and parental school involvement have important effects on the school performance of children. Besides this active encouragement and involvement of parents, it can also be argued that the child’s aspirations increase when parents have more education (Sewel and Shah 1968; Ermisch et al. 2006). Ermisch et al. (2006) argue that parental education can alter the productivity of parents’ time investments in children. It could also be argued that expected returns to education depend on parental education. Jensen (2010) shows that students with higher educated parents tend to perceive higher returns to education. Hence, this third channel is motivated by a series of arguments and most likely composed of different sub-channels. The distinction of these different sub-channels is beyond the scope of this paper. In this paper I consider a compound channel linking high parental education to high offspring’s schooling. 3 Model 3.1 Conceptual model of educational mobility Following the literature outlined in the previous section, we can easily illustrate the three transmission channels. Figure 1displays the system of transmission in education suggested by the literature. Generation g Generation g+1 Ability Ability Parental education Economic situation Education =Ability channel =Education channel =Economic channel Fig. 1 Simplified conceptual system. The figure displays the conceptual framework of the analysis presented in this study. Arrows refer to direct causal effects. Only channels that are included in the empirical analysis are included in the scheme 1 Page 6 of 44 Lat Am Econ Rev (2015) 24:1 123 First, there is a direct link between abilities of parents and children, presented with the dotted line. The ability of the parents influences the ability of children, which in turn increases their propensity for education. The economic channel is represented by gray arrows using the compound term economic situation, which includes short-term credit constraints and long-run effects of assets. Finally, the third channel illustrated with solid black arrows represents the direct education-toeducation transmission, which is based on many different hypotheses as explained above. A channel that I do not consider in this study is the health channel. The health status of the child is likely to be influenced by the family background on the one hand (Bradley and Corwyn 2002; Rosa Dias 2009; Delajara and Wendelspiess Cha ´vez Jua ´rez 2013), while it might also have important effects for education on the other hand (Case et al. 2005; Doyle et al. 2009). There are two reasons for not including this channel, both related to the data. First, there is a problem of timing in the health data. While the literature emphasizes on the importance of the prenatal period and early childhood in the health dimension (Heckman 2006; Doyle et al. 2009; Delajara and Wendelspiess Cha ´vez Jua ´rez 2013), in the data I can at most observe the current health status of the child. Unfortunately there is no retrospective information on the child’s health conditions at birth available. Second, as I will highlight in Sect. 4the inclusion of additional variables would seriously reduce the sample and increase the risk of sample selection problems. In the ‘‘Appendix E’’ I present some regressions where I include variables for health and personality traits to illustrate the problems just described. Different strategies are possible to analyze such a framework empirically. One way is to focus on one particular link. For instance, Holmlund et al. (2011) present different methods to estimate the causal relationship between the education of parents and children. In this paper I use two different strategies. First, I focus on a single equation approach where I aim at estimating all the determinants of the child’s education outcome in one regression. In a second step, I move to a simultaneous equations model where I estimate several equations to describe the whole system outlined in Fig. 1. I will now explain the two approaches along with their intuition, advantages and challenges. 3.2 The single regression approach The main goal of the empirical application is to estimate the intergenerational links determining the educational outcome of the child. Therefore, a first empirical approach consists in regressing the educational outcome on the possible intergenerational determinants while controlling for some contemporaneous effects. The intergenerational determinants are parental education and the economic situation of the family. Moreover, I also control for parental age, whether the parents have an indigenous background and some variables capturing the family structure 1 . The most important contemporaneous effect I control for is the cognitive ability of the 1 These variables include the number of children (up to 12 years old) and teenagers (12–18 years old) in the household and a dummy for the first-born child. Lat Am Econ Rev (2015) 24:1 Page 7 of 44 1 123 child. Additionally, I also control for contemporaneous effects such as child labor, government program benefits, state fixed effects and indicators for girls and rural areas. Besides its appealing simplicity, the single regression approach has the advantage that we do not have to impose a lot of structure in the model. Therefore, only the standard assumptions for ordinary least squared must be fulfilled. One concern that could arise is that some variables do not satisfy these conditions and are likely to be correlated with the error term. The most likely reason for this to happen in our context is an omitted variable bias. A first critical variable is the ability level of the child, which might also capture for instance motivation or the ability to perform well in a situation of examination. Both potentially omitted variables are also likely to influence the schooling outcome. To a large extent, these concerns are reduced by the type of cognitive ability measure I am using in this study. The ability measure is based on a short version of the Raven’s progressive matrices test, which is one of the most culture-free and education independent IQ-tests (De ´sert et al. 2009). I discuss this in more detail when describing the data in Sect. 4. A second variable that might suffer an omitted variable bias is parental education, as parental education might also be influenced by preferences and taste for education. If these preferences and tastes are also transmitted to the next generation, we are likely to have an endogeneity problem as well. In order to account for these potential endogeneity issues I also perform instrumental variable regressions for the single regression approach. Father’s and mother’s cognitive ability is used to instrument both the parental education and the child’s ability level. The cognitive ability of the parents should be a strong predictor of both parental education 2 and the cognitive ability of the child. At the same time, the cognitive ability of the parents should not have a direct impact on the schooling outcome of the child. For the case of parental education, I additionally use information on the place of living of the parents when they were 12 years old. A dummy capturing whether they lived in a town or not is used. 3 The idea is that parents living in cities had substantially more access to education than parents living in rural areas. At the same time, the place of living of the parents when they were 12 years old should not directly affect the education outcome of their children today. In the results section, I will present in detail the different tests for the instruments, which clearly indicate that the instruments are valid and strong. Let me first introduce the second estimation approach, where I simultaneously estimate the whole system presented in Fig. 1. 2 The use of parental cognitive ability to instrument parental education could be problematic if the ability measure was influenced by the education. However, as mentioned in the data section, the used RPM test is less education dependent than other measures of cognitive ability. Therefore, I argue that the assumption of no reversed causality might be reasonable. Additionally, I discuss the empirical tests related to the validity of the instruments. 3 The original variable included more categories to describe the situation outside towns. However, they were relatively unclear and did not provide additional explanatory power. For this reason, I regrouped all non-town answers. 1 Page 8 of 44 Lat Am Econ Rev (2015) 24:1 123 adult following the methodology proposed by Rojas (2007), who provides estimates for Mexico based on the subjective well-being approach. 11 The wealth index was obtained by taking the first component of a principal component analysis performed on several household assets and indicators of the housing conditions. A list of the included indicators and their relative importance for the wealth index and its possible relation with parental age are reported in the ‘‘Appendix C’’. The remaining variables included in the study were constructed in a straightforward way according to the standards in the literature and are reported with a short description in Table 1. 4.1.3 Sample size and sample selection Initially 11,273 children and young adults aged between 12 and 25 years were present in the database. From these only 8,155 individuals lived with both parents in the same household. This is a necessary condition for this study, since otherwise no cognitive ability scores of the parents are available. Proxies for other variables such as education of absent family members would be available, but the cognitive scores are not. Missing values in parents’ and children’s characteristics introduced another loss of observations, reducing the sample to 4,266 observations. The large loss of observations is not surprising considering the data requirements of the study and the fact that they are survey data from an emerging country. These data are obviously not as good as administrative data from European countries that were used in some other studies on the topic. It could be argued that the loss of observations introduces sample selection biases. Being fully aware of this fact, I try to show that the sample used in this study produces some very comparable results to findings in the literature and that the analysis is quite robust to changes in the sample. I also estimate the benchmark model with larger samples, where I relax some data requirements. For instance, excluding the channel of the father allows me to take into account the numerous single-mother households and merging the effects of the father and the mother, allows me to include every single-parent household. These larger sample regressions are reported in ‘‘Appendix B’’. 4.2 Descriptive statistics Let us now have a closer look at the data. Table 1presents some univariate descriptive statistics of the sample I use in the econometric models. The different variables are divided into blocks corresponding to their role in the econometric model. The main dependent variable is the education index previously introduced. The index was constructed using the largest sample possible and not only the observations used in the econometric estimation. Therefore, the average value is slightly higher than 1. The same logic applies to the ability measures, which were estimated using all available information. 11 Using the official Mexican equivalence scales based on CONEVAL (2008) gives essentially the same results where only the third digit after the comma changes by at most two units. I prefer to follow Rojas (2007) as his definition is concave in the number of people, while the official equivalence scales are not. Lat Am Econ Rev (2015) 24:1 Page 15 of 44 1 123 Table 1 Variables used in the study Abbreviation Description Mean SD Dependent outcome variable Educ. index Years of education divided by the average years of education of the age group 1.037* 0.310 Endogenous regressors Consumption Average log consumption per equivalent adult 9.829 0.617 Educ. father Father’s years of education 6.348 4.362 Educ. mother Mother’s years of education 5.725 3.806 Ability Child’s ability measure 101.016* 12.910 Exogenous regressors and control variables Age father Age of the father 43.856 7.876 Age mother Age of the mother 40.300 7.139 Ability father Ability measure for the father 100.614* 13.711 Ability mother Ability measure for the mother 97.795* 13.469 Indig. father Dummy variable for indigenous father 0.172 Indig. mother Dummy variable for indigenous mother 0.139 Father city Father grew up in a urban area 0.257 Mother city Mother grew up in a urban area 0.264 Female Dummy for girls (=1) 0.491 Age Age in years 17.321 3.696 Rural Dummy variable for rural areas 0.483 Work02 Dummy for working activities in 2002 0.166 Work05 Dummy for working activities in 2005 0.250 Number children Number of children below 12 years 1.077 1.236 Number teenagers Number of teenagers (12–18 years) 1.676 1.150 Program 1 Dummy for program Alianza para el campo 0.011 Program 2 Dummy for program Coinversio´n social 0.003 Program 3 Dummy for program Cre´dito a la palabra 0.012 Program 4 Dummy for program FONAES 0.004 Program 5 Dummy for program Fondo para la Micro, Pequen˜a y Mediana Empresa 0.006 Program 6 Dummy for any other assistance program 0.029 Program 7 Dummy for program Programa de empleo temporal 0.009 Program 8 Dummy for program PROCAMPO 0.132 Program 9 Dummy for program VIVAH 0.007 Oportunidades Dummy for program Oportunidades 0.255 Descriptive statistics based on the sample of 4,266 observations * Normalization was made with the full sample to use a maximum of information. The mean can deviate slightly from the normalized value due to missing values in other variables 1 Page 16 of 44 Lat Am Econ Rev (2015) 24:1 123 The average and the standard deviation of the fathers’ years of education are slightly higher than for the mothers. The proportion of indigenous parents is around 15 % which corresponds to the national average. The age of parents is measured in years and fathers are slightly older than mothers. About one-quarter of parents grew up in a city. The sample is strongly balanced between girls and boys and also between families living in rural and urban areas. The indicator of rural areas is based on the official definition of rural zones in Mexico and the place of living at the time of the survey. As people might have lived in a different place during their education, I use additional information on migration to correct the variable accordingly. 12 Two variables (Work02 and Work05) capture whether the children were working in 2002 and 2005, respectively. The proportion grows from around 17 to 25 %, reflecting the aging of the cohort. The indicators on the number of children and teenagers allow us to control for the composition of the households. On average, there is one child below 12 years and about 1.6 teenagers present in a household. The set of dichotomous program variables captures the beneficiary status of families for different government programs. The proportions of beneficiaries are generally very low, with the exception of Oportunidades and Procampo where the proportion is above 10 %. More interestingly than the averages of the variables are the relationships among them. I now present some simple linear correlations between important variables. They should provide a good impression of the data and outline some potentially interesting phenomena. On the other hand, they should give us an impression of comparability of the data with data used in other studies. I hope to reduce some concerns regarding the sample selection issues and the definition of some main variables by showing that the descriptive statistics are surprisingly comparable to other studies in the literature. A first issue that one might discuss regarding the data is the use of Raven’s progressive matrices test as a measure of cognitive ability or even IQ. In the sample, the correlation of the ability measure with the one of the father is 0.363. This value is very close to the 0.347 and 0.38 estimated by Bjo ¨rklund et al. (2010) and Black et al. (2009), respectively, both using more detailed IQ measures. The same correlation with respect to the mother was found to be 0.387, which is slightly higher than the father–son correlation. Considering only the two oldest siblings in a family gives a siblings IQ-correlation of 0.506, which is again relatively close to the values reported by Bjo ¨rklund et al. (2010) who find estimates between 0.473 and 0.510. Interestingly, and giving a first evidence for assortative mating, the spousal IQ-correlation is 0.400. The spousal education-correlation based on the years of schooling is 0.646, which is even higher and supports the idea of an important role of non-random spousal selection. 12 Unfortunately, it is not possible to use exclusively the information on the place of living when people where at the age of education, because the variable is measured differently. I correct the variable rural only in cases where people reported that they lived in a city during education and living in rural areas at the time of the survey. The large majority of the individuals (around 90 %) never changed the place of living and, therefore, the information of the place of living at the time of the survey is accurate for the education period as well. Lat Am Econ Rev (2015) 24:1 Page 17 of 44 1 123 Regarding the simple educational attainment correlation between parents and children, a very interesting pattern can be found when splitting the sample into age groups. Table 2presents the correlation between the education index used in this study to proxy the educational attainment of children and their parents’ years of education. The correlations are substantially higher for the older age group as compared to the younger group. 13 Several possible explanations for this can be found. First, the intergenerational transmission is likely to be a cumulative process, thus the older the children become, the larger is the relationship between parental education and the educational outcome of their children. Second, it could also be due to the precision of the education attainment indicator used in this study. The older the children are, the more values the indicator can take and, therefore, the correlations might be estimated with more precision. 14 The correlations for the older age group are slightly below the correlation of 0.55 estimated by de Hoyos et al. (2010) for children born between 1972 and 1981 in Mexico. The likely reason for the difference is that de Hoyos et al. (2010) use older individual with finished education. Looking at the difference from the younger to the older age group, it is very likely to end up with similar values as de Hoyos et al. (2010) if we could include older individuals. Finally, Table 3gives a comparison between the used and the full sample for the main variables of interest. We can see that the differences are not statistically significant for father’s education and both parental ability measures. For consumption the difference is only significant at the 10 % level. For other variables we observe statistically different means, which is not very surprising with that many observations. However, by looking at the column ‘Diff/SD’ we can see that the Table 2 Intergenerational correlation of education Age group Ages Gender NCorrelation with Father Mother All 12–25 Girls 2,095 0.369 0.395 Boys 2,171 0.389 0.377 Secondary and high school 12–17 Girls 1,153 0.312 0.307 Boys 1,183 0.319 0.334 Tertiary 18–25 Girls 942 0.442 0.489 Boys 988 0.465 0.447 The reported correlations refer to the correlation between the years of education of the father and mother, respectively, and the constructed education index. All correlations are computed for the working sample used in this study 13 Note that when computing the same correlation for younger children (say 7–11 years), the values are even lower. 14 This argument is particularly true when considering even younger children at the age of primary school. A previous version of this study included them. The decision to take them out of the study is mainly due to this argument saying that the precision of the education attainment indicator is not sufficient for the youngest individuals. 1 Page 18 of 44 Lat Am Econ Rev (2015) 24:1 123 difference in terms of standard deviation of the variable never exceeds 0.2; thus they are probably not as problematic as the statistical tests might lead us to think. Overall, the data are certainly not perfect and do not attain the standards of highquality administrative data from some European studies. Nevertheless, the working sample does seem to represent the full sample relatively well and permits us to carry out the analysis. 5 Results In Sect. 3I introduced the two approaches to estimate the intergenerational transmission in education. I now present the result following the same structure. First I present the single regression approach where I estimate simple OLS and IV models and then I move to the discussion of the simultaneous equations model. 5.1 Single regression approach Table 4presents the main regression results of the single-equation approach. The first column is a simple OLS estimation, followed by several IV estimates, all using Table 3 Comparison of sample with excluded observations Variable Full sample Used sample Diff. Diff/SD Pvalue Mean SD Mean SD Education index 1.000 (0.331) 1.037 (0.310) –0.037 –0.111 0.000 Log consumption 9.849 (0.641) 9.829 (0.617) 0.020 0.031 0.081 Father’s education 6.416 (4.430) 6.348 (4.362) 0.068 0.015 0.424 Mother’s education 5.941 (4.017) 5.725 (3.806) 0.216 0.054 0.003 Father’s ability 100.620 (13.907) 100.614 (13.711) 0.006 0.000 0.982 Mother’s ability 97.947 (13.832) 97.795 (13.469) 0.151 0.011 0.557 Ability of the child 100.292 (13.621) 101.016 (12.910) –0.724 –0.053 0.003 Mother’s age 40.713 (7.586) 40.300 (7.139) 0.413 0.054 0.003 Father’s age 44.450 (8.645) 43.856 (7.876) 0.594 0.069 0.000 Age 18.104 (3.914) 17.321 (3.696) 0.783 0.200 0.000 Number of children 1.157 (1.278) 1.077 (1.236) 0.080 0.063 0.000 Number of teenagers 1.469 (1.186) 1.676 (1.150) –0.207 –0.175 0.000 Indigenous father 0.160 0.172 –0.011 0.126 Indigenous mother 0.135 0.139 –0.004 0.559 Gender 0.510 0.491 0.019 0.033 Rural area 0.429 0.483 –0.054 0.000 First born 0.371 0.429 –0.059 0.000 The ‘full sample’ includes all individuals in the age range of the study with non-missing values. The column ‘Diff/SD’ refers to the difference between the two samples divided by the standard deviation of the full sample Lat Am Econ Rev (2015) 24:1 Page 19 of 44 1 123 the robust estimator to account for heteroskedasticity. In the model IV-1 I instrument both parental education and the ability level of the child. For the models IV-2 and IV-3 I instrument child’s ability and parental education separately. For presentational reasons, I do not report some control variables such as the age and the indigenous background of the parents and the indicator for rural areas. These variables are not significant. Additionally, I do not report the coefficients of the government program benefits and the state fixed effects to reduce the size of the table. Let us first discuss the main coefficients of the OLS regression, which are all presented with standardized coefficients. The ability of the child has a strong and highly significant effect on the schooling outcome. The direct effect of parental education is also highly significant and positive. The effect of the mother is larger than the one of the father, which is in accordance with the literature. Both indicators for the economic situation of the family display positive and significant effects. Note that this estimation does not directly allow us to conclude about the biological channel, as we do not estimate the link between parental ability and child’s ability. In order to see whether these OLS estimates are reliable, I move now to the discussion of the IV estimates. First, we can see in the models IV-1 and IV-2 that the coefficients of the child’s ability does not change a lot as compared to the OLS estimates. By looking at the endogeneity test based on Baum et al. (2007), we can actually see that the variable is not endogenous and, therefore, instrumenting it is not required. However, this test is only valid under the assumption of valid instruments. To test the validity, I use the Hansen J statistic, which indicates that the instruments are valid. 15 Hence, for the ability measure of the child we do not seem to have an endogeneity problem. 16 As mentioned earlier, this might be due to a large extent to the nature of the cognitive ability test, which is much less related to education and cultural aspects than other ability measures. Let us now turn to parental education. In the models IV-1 and IV-3 I instrument parental education. Contrary to the previous results, we find strong differences in the coefficients between the OLS estimation and the IV estimates. The coefficient for the father increases sharply while the coefficients for the mother becomes much smaller and insignificant. 17 This is surprising and contrary to the findings in the literature where the maternal education seems to matter more. It is, therefore, important to understand where this result comes from. According to the Hansen J-statistic the instruments are valid and the weak instrument test does not point to a problem of weak instruments. In order to better understand the results, let us have a closer look to the first stage regressions presented in Table 5. The Angrist-Pischke F-statistic is very large and suggests that the instruments are strong (Angrist and Pischke 2009). Thus, in terms of the standard test for IV15 The null hypothesis of the test is that the instruments are valid. 16 In the regression IV-2 we could reject the null hypothesis at the 10 % level. I, therefore, performed the endogeneity test on child’s ability only in the model IV-1, where we have clearly valid instruments. The test shows also that child’s ability is not endogenous. 17 However, the two coefficients are not significantly different from each other (pvalue of 0.344 and 0.320 for IV-1 and IV-3, respectively). Hence, they are not contradicting the results found in the OLS regression. 1 Page 20 of 44 Lat Am Econ Rev (2015) 24:1 123 regression, these estimates seem to be valid. However, there is another problem stemming from the underlying nature of the analysis, which goes beyond the standard challenges of IV. Note that both father’s and mother’s education are correlated with the cognitive ability measure and the place of living of either parents. This is a direct result of assortative mating. It is clear that these correlations Table 4 Single equation results (OLS and IV estimates) OLS IV-1 IV-2 IV-3 IV-3b IV-3c Ability of the childþ0.209*** 0.232*** 0.225*** 0.204*** 0.205*** 0.220*** (0.015) (0.084) (0.046) (0.018) (0.018) (0.017) Father’s educationþ0.095*** 0.198* 0.093*** 0.218** 0.245*** (0.018) (0.117) (0.019) (0.098) (0.068) Mother’s educationþ0.143*** 0.030 0.142*** 0.042 0.156** (0.018) (0.094) (0.019) (0.087) (0.061) Wealth indexþ0.134*** 0.128*** 0.132*** 0.126*** 0.128*** 0.151*** (0.020) (0.024) (0.021) (0.024) (0.024) (0.022) Log consumptionþ0.069*** 0.067** 0.068*** 0.062*** 0.065*** 0.090*** (0.018) (0.028) (0.018) (0.024) (0.024) (0.022) Worked in 2002 –0.386*** –0.388*** –0.384*** –0.385*** –0.389*** –0.402*** (0.044) (0.048) (0.044) (0.046) (0.046) (0.046) Worked in 2005 –0.076** –0.080** –0.075** –0.077** –0.081** –0.089** (0.034) (0.037) (0.034) (0.036) (0.035) (0.036) First born 0.076*** 0.081*** 0.076*** 0.079*** 0.082*** 0.083*** (0.029) (0.031) (0.029) (0.030) (0.029) (0.030) Gender 0.072*** 0.071*** 0.073*** 0.071*** 0.070*** 0.070*** (0.026) (0.026) (0.026) (0.026) (0.026) (0.026) Number of children –0.062*** –0.063*** –0.061*** –0.064*** –0.065*** –0.061*** (0.012) (0.012) (0.012) (0.012) (0.012) (0.012) Number of teenagers –0.073*** –0.071*** –0.073*** –0.071*** –0.070*** –0.077*** (0.013) (0.013) (0.013) (0.013) (0.013) (0.013) Constant –0.075 –0.110 –0.078 –0.146 –0.135 0.064 (0.121) (0.196) (0.121) (0.164) (0.167) (0.139) Child’s ability instrumented No Yes Yes No No No Parental education instrumented No Yes No Yes Yes Yes Control variables Yes Yes Yes Yes Yes Yes N4,266 4,266 4,266 4,266 4,266 4,266 Hansen J-statistic 1.658 2.728 1.842 0.864 0.150 Hansen J-statistic (pvalue) 0.198 0.099 0.398 0.353 0.699 Weak instr. test (statistic) 66.828 323.284 113.838 233.928 269.153 Weak instr. test (pvalue) 0.000 0.000 0.000 0.000 0.000 Lat Am Econ Rev (2015) 24:1 Page 21 of 44 1 123 are not causal. The consequence of this is that instrumented variables of the two parents very strongly correlate. I computed the predicted education of the father and the mother using the first stage regression and find a correlation of nearly 0.95, while the actual parental education correlation is close to 0.65. Hence, in the main regression, we have a strong problem of multicollinearity, which can explain why the increase in the coefficient related to the father is compensated by the coefficient related to the mother. This problem can also be highlighted with the additional regressions IV-3b and IV-3c reported in Table 4. In these two regressions I excluded one of the two parents and used only the instruments related to the parent included in the regression. We can see that in both regressions the parameter of the parents is highly significant. Overall, the single equation approach provided very coherent and expected results. The education of the mother seems to matter slightly more than the education of the father. The wealth index seems to matter more than the short-run consumption and the cognitive ability of the child is also an important predictor of the schooling outcome. Finally, the endogeneity tests performed on the IV estimates did not allow us to conclude that we have a serious problem of endogeneity. I now move to the simultaneous equations model which will allow us to learn more about the different channels and their relative importance. 5.2 Simultaneous regression approach Let me now turn to the results of the simultaneous equation model introduced in Sect. 3.3. The possibility of estimating several channels simultaneously permits us not only to avoid some biases due to omitted variables, but also to quantify these biases by running regressions with some excluded variables on the same data. This idea influenced the estimation strategy and made it straightforward to estimate some simplified models alongside the complete model. This first set of estimation results is reported in Table 6. All models are estimated on exactly the same sample to avoid confounding potential differences in the coefficients due to changes in the model on the one hand and due to changes in the sample on the other. Standardized coefficients are reported and should be interpreted as changes in standard deviations Table 4 continued OLS IV-1 IV-2 IV-3 IV-3b IV-3c Endogeneity test (v2 stat.) 2.053 0.175 1.860 1.981 0.186 Endogeneity test (pvalue) 0.562 0.676 0.394 0.159 0.666 All regressions include also additional control variables such as mother’s and father’s age and indigenous background, an indicator for rural areas (none of these is significant). Additionally, state fixed effects and control variables of government aid programs are included but not reported. Robust standard errors are reported and robust endogeneity test following Baum et al. (2007) is used, þdenotes standardized coefficients Significance level * 10 %, ** 5 %, *** 1 % 1 Page 22 of 44 Lat Am Econ Rev (2015) 24:1 123 Table 5 First stage regressions Dependent variable IV-1 IV-1 IV-1 IV-2 IV-3 IV-3 Ability Educ Educ Ability Educ Educ fath. moth. Ability fath. moth. Instruments Father’s ability measureþ 0.198*** 0.182*** 0.063*** 0.179*** 0.169*** 0.055*** (0.015) (0.013) (0.013) (0.015) (0.013) (0.013) Mother’s ability measureþ 0.215*** 0.062*** 0.179*** 0.204*** 0.048*** 0.171*** (0.015) (0.013) (0.013) (0.016) (0.014) (0.013) Father grew up in a town –0.032 0.205*** 0.133*** 0.207*** 0.134*** (0.036) (0.037) (0.035) (0.037) (0.035) Mother grew up in a town –0.035 0.041 0.250*** 0.043 0.252*** (0.036) (0.036) (0.034) (0.036) (0.034) Control variables Wealth indexþ 0.129*** (0.021) 0.179*** (0.016) 0.133*** (0.016) 0.110*** (0.021) 0.171*** (0.016) 0.128*** (0.016) Log consumptionþ 0.052*** (0.018) 0.208*** (0.015) 0.178*** (0.016) 0.028 (0.019) 0.204*** (0.015) 0.176*** (0.016) Worked in 2002 –0.099** (0.043) –0.192*** (0.033) –0.217*** (0.033) –0.078* (0.044) –0.185*** (0.033) –0.213*** (0.033) Worked in 2005 –0.073** (0.035) –0.139*** (0.028) –0.182*** (0.029) –0.058* (0.035) –0.134*** (0.028) –0.179*** (0.029) First born 0.029 (0.029) 0.075*** (0.025) 0.118*** (0.025) 0.020 (0.029) 0.073*** (0.025) 0.117*** (0.025) Gender –0.076*** (0.027) –0.041* (0.023) –0.059** (0.024) –0.072*** (0.027) –0.036 (0.023) –0.056** (0.024) Number of children –0.043*** (0.012) –0.002 (0.010) –0.019* (0.010) –0.043*** (0.012) 0.001 (0.010) –0.018* (0.010) Number of teenagers –0.024* (0.014) –0.034*** (0.011) –0.013 (0.011) –0.021 (0.014) –0.032*** (0.011) –0.012 (0.010) Father’s educationþ 0.078*** (0.019) Mother’s educationþ 0.018 (0.019) Ability of the childþ 0.065*** (0.013) 0.041*** (0.013) Constant 0.641*** (0.129) 1.586*** (0.108) 1.179*** (0.110) 0.444*** (0.130) 1.545*** (0.107) 1.153*** (0.110) Lat Am Econ Rev (2015) 24:1 Page 23 of 44 1 123 of the dependent variable upon a one standard deviation change of the continuous regressors or upon a unit change in dichotomous regressors. Model 1 is the complete model including ability, father’s and mother’s education and the economic situation proxied by two variables. These main regressors were accompanied by control variables such as gender, a rural area dummy, state fixed effects, social program dummies and child labor indicators which are not reported in Table 6. The full estimation results of model 1, including the remaining equations of the model, can be found in Table 11 in ‘‘Appendix B’’. Table 5 continued Dependent variable IV-1 IV-1 IV-1 IV-2 IV-3 IV-3 Ability Educ Educ Ability Educ Educ fath. moth. Ability fath. moth. Control variables Yes Yes Yes Yes Yes Yes AngristPischke F-statistic 69.165 42.813 64.246 206.105 40.996 52.094 AngristPischke pvalue 0.000 0.000 0.000 0.000 0.000 0.000 N4,266 4,266 4,266 4,266 4,266 4,266 Adj. R2 0.254 0.460 0.446 0.258 0.463 0.447 State fixed effects, government program benefits, the rural dummy and parental ethnicity and age are not reported. þdenotes standardized coefficients. Significance level: * 10 %, ** 5 %, *** 1 % Table 6 Estimation results of Eq. (6) Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Consumption 0.073*** 0.156*** 0.086*** (0.018) (0.018) (0.018) Wealth index 0.146*** 0.227*** 0.175*** (0.019) (0.019) (0.019) Cognitive ability 0.218*** 0.287*** (0.015) (0.014) Father’s education 0.086*** 0.272*** 0.114*** (0.018) (0.016) (0.018) Mother’s education 0.136*** 0.282*** 0.151*** (0.018) (0.016) (0.018) Control variables Yes Yes Yes Yes Yes Yes R20.249 0.242 0.230 0.204 0.208 0.231 N4,266 4,266 4,266 4,266 4,266 4,266 Standardized coefficients. Standard deviations in parentheses. Dependent variable: education index of the child. The full system of equations was estimated simultaneously, but only the coefficients of Eq. 6are reported in this Table. Significance level *** 1 %, ** 5 % and * 10 % 1 Page 24 of 44 Lat Am Econ Rev (2015) 24:1 123 education (preparatoria). Table 9provides additional background information of the Mexican education system for the years 2002 and 2005. Finally, Table 10 presents statistics on late entry to the education system based on the Mexican Life Family Survey (MxFLS). Appendix B: Full estimation results and larger sample regressions Table 11 displays in the first column the full estimation results of model 1 already reported in Table 6including all control variables. 18 Let me highlight some interesting results I did not discuss in the main body of the paper. The education production function estimates are very similar for the mother and the father. The cognitive ability and the place of living at the age of 12 years have the large positive and the age and the indigenous background negative effects. For both the longand the short-run economic situation the fact of being indigenous has a negative impact, even when controlling for education. Table 9 Key statistics of the Mexican education system Indicator 2002 2005 Primary Primary completion rate, total (% of relevant age group) 95.98 96.64 School enrollment, primary (% net) 96.51 93.75 Private schools (% of total primary enrollment) 7.95 8.05 Repeaters, primary (% of total enrollment) 5.68 4.64 Lower secondary completion rate (% of relevant age group) 65.26 72.93 Secondary School enrollment, secondary (% net) 58.66 63.84 Progression to secondary school (%) 92.86 93.79 Repeaters (% of total enrollment) 2.10 2.05 Tertiary School enrollment, tertiary (% gross) 21.07 23.31 Source World Development Indicators (http://data.worldbank.org/country/mexico) Table 10 Distribution of entry age to the education system Source Author’s calculations based on the MxFLS using 5,791 individuals between 15 and 25 years old Entry age Proportion (%) Cumulative proportion (%) 5 9.0 9.0 6 72.7 81.7 7 14.5 96.2 8 2.1 98.3 9?1.71 100 18 Except the state fixed effects and dummies for beneficiaries of government programs other than Oportunidades. Lat Am Econ Rev (2015) 24:1 Page 31 of 44 1 123 Table 11 Full estimation results of model 1-different samples Benchmark results Including mothers Highest parental values Coef. Std.Err. Coef. Std.Err. Coef. Std.Err. Equation 1(Ability measure) Father’s ability 0.245*** 0.015 Mother’s ability 0.288*** 0.014 0.385*** 0.011 Parents’ ability (highest) 0.407*** 0.010 Female –0.032** 0.014 –0.015 0.011 –0.012 0.011 Old parents –0.047*** 0.014 –0.052*** 0.011 0.018 0.011 Young parents 0.015 0.015 0.021* 0.012 0.020* 0.012 First born 0.021 0.015 0.020* 0.012 0.022* 0.012 Equation 2(Father’s education) Father’s ability 0.347*** 0.013 Father’s age –0.195*** 0.013 Indigenous father –0.053*** 0.013 Father grew up in city 0.185*** 0.013 Equation 3(Mother’s education) Mother’s ability 0.374*** 0.013 0.357*** 0.010 Mother’s age –0.211*** 0.012 –0.239*** 0.010 Indigenous mother –0.071*** 0.012 –0.076*** 0.010 Mother grew up in city 0.186*** 0.013 0.254*** 0.010 Equation 3’ (For highest parental education) Parents’ ability (highest) 0.365*** 0.010 Parents’ age (highest) –0.246*** 0.010 Indigenous parents (at least 1) –0.078*** 0.010 Parents grew up in city 0.234*** 0.010 Equation 4(Wealth index) Father’s education 0.275*** 0.016 Mother’s education 0.155*** 0.017 0.329*** 0.012 Parents’ education (highest) 0.362*** 0.011 Father’s ability 0.034** 0.014 Mother’s ability 0.118*** 0.015 0.154*** 0.012 Parents’ ability (highest) 0.148*** 0.011 Indigenous father –0.121*** 0.016 Indigenous mother –0.208*** 0.016 –0.276*** 0.010 Indigenous parents (at least 1) –0.256*** 0.010 Father’s age 0.049** 0.021 Mother’s age 0.155*** 0.021 0.133*** 0.011 Parents’ age (highest) 0.117*** 0.011 Equation 5(Consumption) Father’s education 0.300*** 0.016 1 Page 32 of 44 Lat Am Econ Rev (2015) 24:1 123 Table 11 continued Benchmark results Including mothers Highest parental values Coef. Std.Err. Coef. Std.Err. Coef. Std.Err. Mother’s education 0.198*** 0.017 0.407*** 0.011 Parents’ education (highest) 0.444*** 0.011 Father’s ability 0.042*** 0.015 Mother’s ability 0.130*** 0.015 0.154*** 0.012 Parents’ ability (highest) 0.138*** 0.011 Indigenous father –0.053*** 0.017 Indigenous mother –0.116*** 0.017 –0.156*** 0.011 Indigenous parents (at least 1) –0.140*** 0.010 Father’s age 0.087*** 0.022 Mother’s age 0.054** 0.021 0.107*** 0.011 Parents’ age (highest) 0.102*** 0.011 Equation 6(Schooling outcome) Cognitive ability 0.218*** 0.015 0.252*** 0.012 0.246*** 0.012 Wealth index 0.146*** 0.019 0.152*** 0.015 0.155*** 0.015 Consumption 0.073*** 0.018 0.094*** 0.015 0.086*** 0.014 Father’s education 0.086*** 0.018 Mother’s education 0.136*** 0.018 0.158*** 0.013 Parents’ education (highest) 0.172*** 0.013 Female 0.040*** 0.014 0.043*** 0.011 0.046*** 0.011 Rural area –0.007 0.017 –0.007 0.014 0.002 0.014 Oportunidades 0.057*** 0.017 0.041*** 0.013 0.041*** 0.013 Worked in 2002 –0.143*** 0.015 –0.128*** 0.012 –0.122*** 0.012 Worked in 2005 –0.029* 0.015 –0.036*** 0.012 –0.037*** 0.012 First born 0.029** 0.014 0.028** 0.011 0.027** 0.011 Number children –0.090*** 0.014 –0.080*** 0.011 –0.083*** 0.011 Number teenagers –0.100*** 0.015 –0.090*** 0.012 –0.090*** 0.012 Government program dummies Included Included Included State fixed effects Included Included Included Sample size 4,266 6,547 6,690 R20.249 0.256 0.264 The dependent variable for the structural equation is reported in parenthesis in the title of each panel. The coefficients are reported in the first column and the standard errors in the second for each model. All coefficients are standardized, meaning that for continuous regressors the coefficients measure how many standard deviations the dependent variable changes when the regressor changes one standard deviation and for dichotomous variables when the variables turn from zero to one. Significance levels *** 1 %, ** 5 % and * 10 % Lat Am Econ Rev (2015) 24:1 Page 33 of 44 1 123 The second and third regressions are based on enlarged samples. The first enlarged sample includes also the single-mother households and excludes as a consequence the channel of the father. The second enlarged sample considers always the highest values of either the mother or the father. As already mentioned in the main text, the results do not change a lot despite the substantial change in the sample size. The role of mother’s ability increases in the ability equation when not controlling for the ability level of the father. This is due to the correlation among the IQ of both parents. The effect of consumption is slightly higher in the large sample regressions, but remains always considerably smaller than the effect of the wealth index. When merging the education of the two parents, the combined effect is somewhat larger than the effect of the mother in the main regression, but does not attain the sum of the two parental coefficients. The relatively stable results give additional credibility to the results on the main sample used in the study. Appendix C: Discussion of the wealth index In the analysis, I use a wealth index to approximate the long run economic situation of the household. In this appendix, I first present the way it was constructed and then I discuss the concern that such a wealth index could actually capture an age effect of the parents. Construction of the wealth index Let me first discuss how the wealth index is constructed. I use the first component of a principal component analysis performed on various indicators. This allows me to reduce the dimensions and to have a single indicator. In this appendix, I present the descriptive statistics of the indicator variables and the composition of the used wealth indicator. Table 12 displays the mean of each variable and its relative contribution to the wealth index. Table 12 Construction of the wealth index Indicator Mean Contribution (%) Dummy for electricity 0.987 0.94 Dummy for a clean floor 0.847 15.83 Dummy for good quality roof 0.890 8.52 Number of bedrooms 2.321 10.10 Household has a phone 0.346 16.69 Household has a kitchen 0.932 2.46 Clean drainage of feces 0.845 11.57 Clean garbage evacuation 0.657 16.88 Clean cooking energy (gas or electricity) 0.826 17.01 The principal component analysis was performed using the polychoric correlation matrix to account for the non-continuity of the indicator variables 1 Page 34 of 44 Lat Am Econ Rev (2015) 24:1 123 From these figures, we see that the contribution substantially varies across indicators and therefore a simple average of the indicator variable would probably not well describe wealth. Among the most important contributors, we find the clean cooking energy, the clean garbage evacuation, the availability of a phone and the indicator for a clean floor. Rather of minor importance are the indicators for having a kitchen in the household and whether the household has access to electricity. The reason for these low contribution levels is the almost full coverage among the Mexican population and the resulting small variance in these variables. The relationship with the age of the parents The main results of the study show that the long run economic situation proxied by the wealth index is a main channel of transmission from one generation to the next. A potential concern with this variable stems from the fact that household assets could be directly linked to the age of the parents. If older parents have systematically more of these goods and therefore a higher wealth index, then we might actually capture an age effect rather than an effect of the economic channel. In the regressions, I control for the parental age to deal with this concern. Nevertheless, a closer look at the relationship between the wealth index and parental age can help us to reduce the concerns even more. Figure 5displays the non-parametric regression of degree 1 of the standardized wealth index (left axis) as a function of average parental age (left graph) and the child–parents age differential (right graph). The dashed line in each graph is a density estimation of the average parental age and the child–parents age differential, respectively. We can observe that the average of the wealth index is slightly below 0 for the youngest parents. However, the density of such young parents is rather small. For the remaining part of the parental age distribution the average is very close to zero. This is also true in the right graph where the variable on the x-axis is the age differential between parents and the child. The estimator of the mean is very close to zero for all values of the age differential. 0.02 .04 .06 Kernel density of average parental age −2 −1.5 −1 −.5 0 .5 1 1.5 2 Standardized wealth index 20 30 40 50 60 Average parental age Estimated mean 95%−CI Kernel density a 0.02 .04 .06 Kernel density of average parental age −3 −2 −1 0 1 2 3 Standardized wealth index 10 20 30 40 50 Age difference parents−child Estimated mean 95%−CI Kernel density b Fig. 5 Relationship between average parental age and the wealth index. The figure displays nonparametric estimates of the relationship between the wealth index and age of parents and the distribution of parental age. The estimates are based on the working sample used in the main regressions Lat Am Econ Rev (2015) 24:1 Page 35 of 44 1 123 In general, we cannot observe a strong relationship between the wealth index and the age of the parents. Thus, it is unlikely that the wealth index actually captures an age effect of the parents. Appendix D: Identification of the simultaneous equations model In this appendix, I discuss the identification of the model presented in Eqs. (1)–(6) in the main body of the article. To simplify the notation, the endogenous left-hand side variables of the Eqs. (1)–(6) can be combined in the matrix Yand all exogenous variables in matrix X, which includes all exogenous variables in white boxes in Fig. 2. This allows us to rewrite the model in the standard simultaneous equation model (SEM) notation: Y¼BYþAXþnð7Þ where nis a vector containing the error terms of the equations, Bis a zero-diagonal coefficient matrix for the endogenous variables and Ais the coefficient matrix for the exogenous variables. Let me further define Uto be covariance matrix of Xand Wto be the covariance matrix of the disturbance terms n. We impose a condition that the exogenous variables Xare uncorrelated with the error terms in n. The model described before, has the following matrix Band I assume the following covariance matrix 19 W: B¼ 000000 000000 000000 0c1c2000 0c9c10 000 b1b2b3b4b50 2 6 6 6 6 6 6 6 6 4 3 7 7 7 7 7 7 7 7 5 W¼ W11 00000 W22 W23 W24 W25 0 W33 W34 W35 0 W44 W45 0 W55 0 W66 2 6 6 6 6 6 6 6 6 4 3 7 7 7 7 7 7 7 7 5 ð8Þ This model has a lower triangular matrix Bwhich greatly simplifies its identification. However, it is not a recursive model because I do not assume Wto be diagonal. 20 While a recursive model would be automatically identified, the conditions for this model are somewhat more complicated. To discuss the identification of the model I follow Heuchenne (1997) and Paxton et al. (2011). Heuchenne (1997) proposes a sufficient rule for identification based on Band Wexclusively. He 19 The covariance matrix is symmetric. For presentational purpose, I only present the upper triangular version. 20 I only assume uncorrelated error terms for the ability transmission Eq. (1) and the child’s education Eq. (6). This last assumption is confirmed by the IV estimates I will present in Sect. 5.1. Note, however, as I will show below, these restrictions are not required for the identification. 1 Page 36 of 44 Lat Am Econ Rev (2015) 24:1 123 proposes to combine the lower triangle of Bwith the upper triangular of W, which gives us: BnW¼ 00 0 00 02W23 W24 W25 0 00 3W34 W35 0 0c1c22W45 0 0c9c10 030 b1b2b3b4b55 2 6 6 6 6 6 6 6 6 4 3 7 7 7 7 7 7 7 7 5 ð9Þ The number (in bold) on the diagonal indicate how many excluded parameters are above in the same column and to the left of the same row. For instance, the value of 3 in the third row is obtained by counting the two zero values in the third row left to the diagonal and the zero value in the third column above the diagonal. Heuchenne (1997) shows that equation kis identified whenever the corresponding value on the diagonal is bigger or equal to ðk1). We can see that all but Eqs. (4) and (5) satisfy this sufficient condition. Hence, we can conclude that all but the economic situation equations are identified based on the lower triangular form of Band the structure of W. To verify if also Eqs. (4) and (5) are identified, we have to use conditions that are not only based on Bbut also on A, the coefficient matrix of the exogenous variables. All equations in the model pass the order condition saying that an equation is identified if the number of excluded exogenous variables is equal or greater than the number of endogenous variables in that equation minus one (Paxton et al. 2011). The order condition is, however, only a sufficient condition. A stronger necessary condition is the equivalent structures approach, which is an algebraic identification technique (Paxton et al. 2011). For this, let us rewrite Eq. (7) by regrouping all parameters related to the vector Yon the left-hand side. BY¼AXþnð10Þ By doing so, matrix Bhas a unit diagonal and all off-diagonal elements change the sign. This change of notation does not change the system but is more convenient for the computation of the equivalent structures approach. Let us now define a general matrix Mand define the following set of equations: MA ¼AMB¼BMRM0¼Rð11Þ The model is fully identified if the only solution to this system obtained by using the restrictions on A,Band Wis the identity matrix (M¼I). Let us start with the expression of MB ¼B Lat Am Econ Rev (2015) 24:1 Page 37 of 44 1 123 MB ¼ m11 b1m16 b2m16 c9m15 c1m14 þm12 b3m16 c10 m15 c2m14 þm13 m14 b4m16 m15 b5m16 m16 m21 b1m26 b2m26 c9m25 c1m24 þm22 b3m26 c10 m25 c2m24 þm23 m24 b4m26 m25 b5m26 m26 m31 b1m36 b2m36 c9m35 c1m34 þm32 b3m36 c10 m35 c2m34 þm33 m34 b4m36 m35 b5m36 m36 m41 b1m46 b2m46 c9m45 c1m44 þm42 b3m46 c10 m45 c2m44 þm43 m44 b4m46 m45 b5m46 m46 m51 b1m56 b2m56 c9m55 c1m54 þm52 b3m56 c10 m55 c2m54 þm53 m54 b4m56 m55 b5m56 m56 m61 b1m66 b2m66 c9m65 c1m64 þm62 b3m66 c10 m65 c2m64 þm63 m64 b4m66 m65 b5m66 m66 2 6 6 6 6 6 6 6 6 4 3 7 7 7 7 7 7 7 7 5 ¼ 100000 010000 001000 0c1c2100 0c9c10 010 b1b2b3b4b51 2 6 6 6 6 6 6 6 6 4 3 7 7 7 7 7 7 7 7 5 ¼B ð12Þ From the restrictions in the last column of Bwe directly determine m16 to m66, which greatly simplifies MB to: MB ¼ m11 c9m15 c1m14 þm12 c10 m15 c2m14 þm13 m14 m15 0 m21 c9m25 c1m24 þm22 c10 m25 c2m24 þm23 m24 m25 0 m31 c9m35 c1m34 þm32 c10 m35 c2m34 þm33 m34 m35 0 m41 c9m45 c1m44 þm42 c10 m45 c2m44 þm43 m44 m45 0 m51 c9m55 c1m54 þm52 c10 m55 c2m54 þm53 m54 m55 0 m61 b1b2c9m65 c1m64 þm62 b3c10 m65 c2m64 þm63 m64 b4m65 b51 2 6 6 6 6 6 6 6 6 4 3 7 7 7 7 7 7 7 7 5 Using the first 5 rows of columns 1, 4 and 5 we can further simplify to: MB ¼ 1m12 m13 000 0m22 m23 000 0m32 m33 000 0c1þm42 c2þm43 100 0c9þm52 c10 þm53 010 m61 b1b2c9m65 c1m64 þm62 b3c10 m65 c2m64 þm63 m64 b4m65 b51 2 6 6 6 6 6 6 6 6 4 3 7 7 7 7 7 7 7 7 5 Finally, using the first three rows of column 2 and 3 in Ballows us to simplify to: MB ¼ 10 0 000 01 0 000 00 1 000 0c1þm42 c2þm43 100 0c9þm52 c10 þm53 010 m61 b1b2c9m65 c1m64 þm62 b3c10 m65 c2m64 þm63 m64 b4m65 b51 2 6 6 6 6 6 6 6 6 4 3 7 7 7 7 7 7 7 7 5 Hence, using the restrictions of Bwe are able to uniquely identify most of the elements in matrix M: 1 Page 38 of 44 Lat Am Econ Rev (2015) 24:1 123 M¼ 100000 010000 001000 0m42 m43 100 0m52 m53 010 m61 m62 m63 m64 m65 1 2 6 6 6 6 6 6 6 6 4 3 7 7 7 7 7 7 7 7 5 To identify the remaining elements of M, I use the condition MA ¼A. Unfortunately, it is impossible to display the full matrix due to its dimension. I only display the last three rows and transpose them for presentational purpose 21 : c3þm42 d1c11 þm52 d1m65 c11 þm64 c3þm62 d1þm61 u1 c7þm42 d2c15 þm52 d2m65 c15 þm64 c7þm62 d2 c5þm42 d3c13 þm52 d3m65 c13 þm64 c5þm62 d3 m42 d4m52 d4m62 d4 c4þm43 d5c12 þm53 d5m65 c12 þm64 c4þm63 d5þm61u2 c8þm43 d6c16 þm53 d6m65 c16 þm64 c8þm63 d6 c6þm43 d7c114þm53 d7m65 c114þm64 c6þm63 d7 m43 d8m53 d8m63 d8 00 b6þm61 u3 00 m61 u4 00 m61 u5 . . .. . .. . . 2 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 4 3 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5 0 ¼ c3c11 0 c7c15 0 c5c13 0 000 c4c12 0 c8c16 0 c6c14 0 000 00b6 000 000 . . .. . .. . . 2 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 4 3 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5 0 where m42 to m62,m43 to m63 and m61 can be directly identified and are all equal to zero. This simplifies the remaining elements considerably: 21 I excluded the paramters of some control variables to save space. They are not required for the identification. Lat Am Econ Rev (2015) 24:1 Page 39 of 44 1 123 c3c11 m65 c11 þm64 c3 c7c15 m65 c15 þm64 c7 c5c13 m65 c13 þm64 c5 00 0 c4c12 m65 c12 þm64 c4 c8c16 m65 c16 þm64 c8 c6c11 m65 c11 þm64 c6 00 0 00 b6 00 0 00 0 . . .. . .. . . 2 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 4 3 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5 0 ¼ c3c11 0 c7c15 0 c5c13 0 000 c4c12 0 c8c16 0 c6c14 0 000 00b6 000 000 . . .. . .. . . 2 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 4 3 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5 0 Finally, we have six equations with two unknown, which makes it very easy to determine the two remaining elements of M. For instance, using the first equation we can define m65 ¼c3 c11 m64 and plug this into the second row to find that m64 ¼m65 ¼0. Note that using the restrinctions on Aand Ballows us to solve the whole matrix Mand we find M¼I. The full model is therefore identified. Appendix E: Regressions with additional dimensions The results in the main body of the article include only three channels. However, there might be other important channels affecting the intergenerational transmission of education. For instance, health, non-cognitive abilities or personality traits could be transmitted from one generation to the next and affect education. Unfortunately, the data used in this study do not allow to include such channels. There are two main reasons why I cannot include these channels in the analysis. First, including indicators on personality traits would substantially reduce the sample size and, therefore, increase the risk of sample selection biases. Second, for the health dimensions, no retrospective information about the health status of parents is provided. Hence, we could observe the health status of parents at the time of the survey, but not at the relevant time when children were attending school. In this appendix, I present experimental regressions to show what would happen, if despite the problems we would try to include these channels. Table 13 displays the OLS regression reported in Table 4in the main body of the text and an augmented version, where I include some parental health and behavioral variables. The mental health indicator is based on 18 questions about the emotional situation of individuals and combined through a factor analysis. A higher value indicates more emotional problems. Parental height can have an influence as it directly affects birth weight of children (Delajara and Wendelspiess Cha ´vez Jua ´rez 1 Page 40 of 44 Lat Am Econ Rev (2015) 24:1 123