Intergenerational effects of stratified public educational financing in Tiebout School Choice, 1922-2015

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Stratified Public Educational

Financing in Tiebout School

Choice, 1922-2015

Andrew Proctor

Student Number: 11087935

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Master of Science in Econometrics

Faculty of Economics and Business

Amsterdam School of Economics

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Declaration ii

1 Introduction 2

2 Literature Review 4

2.1 Sorting-Based School Choice and Stratified Educational Investment . 4 2.2 Political Economy Effects and Other Consequences of School Choices 6 2.3 Potential Mechanisms for Intergenerational Transmission of

Educa-tional Attainment . . . 8

2.4 Macroeconomic Research on Educational Investment and Intergener-ational Inequality . . . 10

2.5 Empirical Analysis of Intergenerational Persistence in Education . . . 11

3 Data and Estimation Strategy 14 3.1 Identification Strategy . . . 14

3.2 Data and Sources . . . 17

3.2.1 Dependent Variables—Child Outcomes of Interest . . . 19

3.2.2 Calculation of Parental Explanatory Variables . . . 20

3.2.3 Sex and Race/Ethnicity Variables . . . 22

3.2.4 Functional Form of Parental Variables . . . 23

3.3 Econometric Method . . . 24

3.3.1 Educational Outcomes: Attainment Rates . . . 24

3.3.2 Educational Outcomes: Years of Education . . . 27

3.3.3 Earnings Outcomes: Annualized Earnings . . . 28

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4 Results 29

4.1 Educational Attainment Rates . . . 29

4.2 Years of Schooling . . . 32

4.3 Annualized Earnings . . . 33

5 Robustness Checks 34 5.1 Potential Migration-based Violations of the Births-Linked Cohorts Approach . . . 34

5.2 Potential Shortcomings in the Use of Local Share of Educational Fi-nancing as a Measure of Sorting-Driven School Finance . . . 36

6 Conclusions 40 Bibliography 42 Appendix 54 A Tables for Primary Results 54 A.1 Educational Attainment Rates . . . 55

A.2 Years of Education . . . 71

A.3 Annualized Earnings . . . 82

A.4 Tables for Robustness Check . . . 86

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A.1 Descriptive Statistics . . . 54

A.2 Tenth Grade Schooling Attainment Rates - Specification 1 . . . 55

A.3 Tenth Grade Schooling Attainment Rates - Specification 2 . . . 56

A.4 Marginal Effects - Tenth Grade Attainment Rates (S1-S2) . . . 56

A.5 Tenth Grade Attainment Rates - Specification 3 . . . 57

A.6 Tenth Grade Attainment Rates - Specification 4 . . . 57

A.7 Marginal Effects - Tenth Grade Attainment Rates (S3-S4) . . . 58

A.8 High School Diploma Attainment Rates - Specification 1 . . . 59

A.10 Marginal Effects - High School Diploma Attainment Rates (S1-S2) . . 60

A.13 Marginal Effects - High School Diploma Attainment Rates (S3-S4) . . 62

A.14 Two Year College Attainment Rates - Specification 1 . . . 63

A.16 Marginal Effects - Two Year College Attainment Rates (S1-S2) . . . . 64

A.19 Marginal Effects - Two Year College Attainment Rates (S3-S4) . . . . 66

A.20 Four Year College Attainment Rates - Specification 1 . . . 67

A.22 Marginal Effects - Four Year College Attainment Rates (S1-S2) . . . 68

A.24 Four Year College Attainment Rates - Specification 4 . . . 69 v

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A.25 Marginal Effects - Four Year College Attainment Rates (S3-S4) . . . 70

A.26 Years of Education (Poisson) - 10th Percentile . . . 71

A.27 Years of Education - 20th Percentile . . . 72

A.29 Years of Education - Median . . . 74

A.30 Years of Education - Mean . . . 75

A.33 Years of Education - Linear FE Regression - Specification 1 . . . 78

A.37 Annual Earnings - Specification 1 . . . 82

A.38 Annual Earnings- Specification 2 . . . 83

A.41 Migration Robustness Check . . . 86

A.42 Government Spending Robustness Check . . . 87

A.43 Government Spending Robustness Check (Continued) . . . 88

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Introduction

Education has long been an object of study for researchers across a number of different areas of economic research. In particular, educational policy has proved a fertile field for inquiry into not only the dynamics of educational attainment, but also the determinants of income, productivity, and growth.

A key component of this study has been the exploration of how schools are funded and how households are able to choose between schools, be it different public school systems, choice of public or private school, or charter schools. In this ”school choice” literature, the two principal paradigms of school choice, Tiebout choice and public-private choice, are largely premised on the virtue of household sorting into groups with similar interests, with income sorting as the most obvious result.

Yet such educational systems are predicted to promote an income-stratified sys-tem of educational investments, which may in turn influence the determination of household income of children. In studies of inequality and growth, such disparities in educational investment are commonly cited as a major reason for the differing com-parative performance of regions and countries. As a result, it appears possible that sorting-based methods of school finance could generate persistent intergenerational correlations in income and educational attainment, with possible dynamic efficiency implications that could undermine the private allocative arguments supporting these paradigms.

In this study, I examine whether stratified educational financing in public basic education affects the educational attainment and income of the next generation.

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To perform this analysis, I estimate the impact of the average share of public ed-ucational spending derived from local sources during mothers’ basic education on child outcomes at age 25 for the United States. The share of educational financing from local sources suggests itself prominently as a measure of sorting-based school-ing finance for two reasons: first, government financschool-ing (and expenditures) at the local level is the essential component of Tiebout choice, with the premise that more localized government expenditures increases the efficacy of household sorting in the determination of public goods. Moreover, as predicted by Tiebout sorting, at the local level both household composition and public expenditures are highly stratified by income (Herrington 2015 ).

Because available microdata sources are unsuitable to linked intergenerational analyses for the United States, I instead use aggregate outcomes for twenty-five years olds by state and match these cohorts to parental factors using annual, state-specific data on the distribution of mothers’ ages when giving birth. This age of mother at birth data allows for weighted-average estimates of the period of schooling for mothers, and thereby estimates of the share of educational financing for each state’s ”parent” cohort—i.e. those who gave birth to children 25 years before the outcomes observed for each age-25 “child” cohort.

Using these synthetic variables for parental education, I estimate the impact of the local share of education financing on children’s years of education, high school and college graduation rates, and weekly earnings. In each instance, I find significant or marginally significant negative effects of localized school finance on those at the lower end of the outcome distribution, while there are no significant effects observed for educational or income attainment at the upper half of the distribution. These results are supportive of the hypothesis that sorting-based provisioning of public goods inherent in Tiebout choice (and private school choice) may generate negative intergenerational externalities that undercut its purported private efficiency.

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Literature Review

In this chapter, concept and theoretical properties of sorting-based school choice are introduced, with particularly emphasis on the Tiebout school choice model. The stratification predictions of sorting in Tiebout choice, fundamental to the current analysis, is then discussed followed by a review of existing research concerning the effects and especially intergenerational effects of education and school choice regimes.

2.1 Sorting-Based School Choice and Stratified Educational

Investment

Within the study of school choice, it is commonly argued that schools can be made more effective by increasing the ability of families to choose the school best match-ing their own educational preferences. This argument can be traced to the very origins of not only school choice, but also public choice theory more generally, with Charles Tiebout (1956) suggesting that households sorting themselves into neigh-borhoods with similar interests provided a solution to the classic problem of ”a government whose objective it is to ascertain [consumers’] wants for public goods and tax [them] accordingly.” The notion that households sorting themselves into groups with similar preferences will yield the greatest private efficiency underpins much of contemporary school choice literature. Two of the main strands of school choices, both in academic literature and in practice, are the eponymous Tiebout school choice (choosing schooling by choosing one’s neighborhood) and school choice

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between public and private schools, including the use of vouchers. Tiebout school choice, in particular, is the predominant method of school choice, as more than 85% of students continue to be enrolled in traditional public schools. Moreover, Tiebout school choice is notably effective – approximately half of school funding continues to be determined at the local level,1 _{with researchers consistently finding that not}

only do characteristics of school affect choice of residence, but that this strategy has a significant effect on the variety of public schools observed (Urquiola 2005).2

In the economic literature concerning Tiebout school choice literature, a frequent and fundamental proposition is that students can benefit from the ensuring growth in the number and variety of public school schools or school districts from which to choose. Hoxby (2000) provides the basic argument in this respect, stating:

When there are more school districts, it is easier for households to sort themselves into groups that are relatively homogeneous in terms of their preferences with regard to schooling and property. As a result, an equi-librium in which households get schools close to what they privately prefer is more likely to exist.

Hoxby (2000) notes that increased Tiebout choice should both reduce spending on non-preferred schooling methods and increase spending on education aligned with student needs, making schools more efficient. The literature regarding private schools follows a nearly identical argument: private schooling offers parents the ability to pay specifically for the schooling they value by selecting a school that matches their own personal needs and budget (Nechyba 2006).

School choice researchers acknowledge that greater sorting is not without poten-tial costs. Specifically, decentralized decision-making about expenditures for school-ing heavily implies that household income will be the most salient feature in observed sorting—which is to say: income will be the most prominent determinant of school financing. (Hoxby 2000, Bayer and McMillan 2012). This ”stratification” prediction

1_{For individuals observed in the present study–corresponding to cohorts born betwen 1917 and}

1951, the share of educational financing from local sources was 54.97%.

2_{Although Rhode and Strumpf (2003) argue that beyond the mix of public goods nevertheless}

explain the bulk of residential choice.

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of sorting-based choice does not, on its own merits, necessarily represent an adverse outcome, but rather a reflection that spending on additional consumption may be more important for low-income household than additional schooling expenditures. Nevertheless, research concerning school choice admits the possibility that sorting based on income could lower achievement for low-income students and potentially be socially inefficient if there are human capital spillovers between workers (Hoxby 2000) or members of society more broadly (Dee 2004).3 _{Consequently, much of the}

debate in the school choice literature is about whether there is empirical evidence of reduced educational achievement in low-income groups due to sorting and if so, how schooling provision may best balance efficiency with equity concerns.

2.2 Political Economy Effects and Other Consequences of

School Choices

In trying to ascertain the impact of school choice reform on low-income groups, a number studies have extended analysis of sorting-based choice to include con-sideration of potential political economy interactions. Likely the primary area of investigation in this respect has been whether initiatives to change the scope of sorting-based educational funding, most notably court-ordered school finance re-forms, have affected public support for educational spending.

Much of the early emphasis of these studies was on the 1971 Serrano v. Priest California Supreme Court decision, which found inequality among school finance resources among state school districts violated the equal protection clause of the Fourteenth Amendment (Campbell and Fischel 1990). Using political economy prin-cipals, several studies have shown that the response like those resulting from Serrano, which limited local school districts ability to increase their own expenditure, might instead “level down” (Hoxby 2001) educational quality by reducing spending in wealthier school districts while doing little to increase spending among low-income

3_{And indeed, proponents of sorting-based school choice generally support some degree of}

redis-tribution to alleviate these effects. In their view, however, school finance responses should focus on targeted aid rather than dismantling stratification.

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school districts (Fern´andez and Rogerson 1999, Silva and Sonstelie 1995). An ensu-ing consequence of such behavior is that high-income households then appear more likely to leave the public school system in favor of private schools (Downes and Schoeman 1998).

Analyzing a large spectrum of school finance equalization reforms, Hoxby (2001) provides a complimentary empirical analysis that finds similar evidence of “leveling down.” Using estimated counterfactual school financing variables, Hoxby estimates that per-pupil expenditures were consistently reduced by school finance equalizations and that private schooling increased, although she also notes a decrease in dropout rates for low-revenue districts.

In contrast to the relative negative picture of school finance equalization reforms above, other studies have instead found aggregate expenditure effects of equalization reform that are either positive (e.g. Manwaring and Sheffrin 1997, Murray et al. 1998) or variable depending on the specific circumstances (e.g. Downes and Shah 2006, Fern´andez and Rogerson 2003). Crucially, most of these analyses have found that school finance reforms have been successful in increasing spending for low-income students – with further general support for the contention of Card and Payne (2002) that equalization in spending has also been successful in reducing the educational achievement gap among low- and high-income students.

In addition to the role of choice-induced sorting in determining the resources schools have and what methods they employ, a number of other considerations also affect the overall impact of school choice programs. A few such issues include: the potential benefits arising from competition (Hoxby 2000, Dee 1998), poten-tial peer effect consequences, the direction of which is very unclear (Cullen et al. 2006, Epple and Romano 1998, Neidell and Waldfogel 2010), and political economy considerations—how school choice reforms interact with voter support for school funding (Card and Payne 2002, Epple and Romano 2014, Hoxby 2001, Murray et al. 1998).

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2.3 Potential Mechanisms for Intergenerational

Transmis-sion of Educational Attainment

Within the school choice and school finance literature, however, much less attention has been given to whether paradigms based on stratified educational spending could engender negative intergenerational effects resulting in dynamic inefficiency.4 _If

children are affected by the educational attainment and labor market consequences of differential investment during their parents’ education, it seems plausible that this could engender intergenerational persistence in educational attainment, income and productivity.

Educational inequality may be replicated for a number of reasons and their relative importance is hotly contested. However, most economists agree that both genetics and the conditions of a child’s upbringing likely account for some portion of the observed inertia. On the “nurture” side of the issue, parental education is often seen as a causal factor, with the fundamental problem that less-educated parents invest less in their childrens’ education. For less educated households, it appears that both parents and children could both be made better off through higher educational investments (Pronzato 2010). Part of this ”underinvestment” can be attributed to credit constraints—parents are not able to borrow on the future earning potential of their children, so they are limited based on their own wealth and income, which is endogenous to intergenerational educational decisions (Aiyagari et al. 2002, Card and Krueger 1992). A second issue is the limited altruism of parents—they do not optimize between consumption and human capital investment for children as if it were for themselves (Altonji et al. 1997, Das 2007). A third possible reason is that taste for education appears to be endogenous. Recent analyses suggest that parents’ preferences for child education are influenced by their own socioeconomic status and level of educational attainment (Burgess, et al. 2015, Hastings et al.

4_{A classic early conceptualization of this type of problem is found in Lazear (1983), who}

imag-ined a grandchild that would be willing to pay his parent to retroactively migrate to the United States from an area with worse education and income prospects if he could.

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2005, Kirchsteiger and Sebald 2010), as is their propensity to financially invest in their childs’ education (Steelman and Powell 1991). Similarly, analyses suggest that children’s level of motivation and subjective standards of educational attainment are influenced by the educational attainment of their parents (Cohen 1987, Eckstein and Wolpin 2005). Finally, a number of complementary inputs alongside schooling investment decisions also appear endogenous, including parental time investment in their children’s schooling (Guryan et al. 2008), home educational resources, and the health, safety, and behavioral risk environments facing the child (Aizer 2007, Case et al. 2002, Lazear 1983, Murnane et al.).

In addition, there are several reasons to believe that low-income households may be particularly sensitive to the effects of sorting-based determination of school fi-nance. With regards to Tiebout choice in particular, low-income households are at a disadvantage in choosing neighborhoods that reflect their desired level of spending and school quality. The crux of this problem is that ”bundling” of schooling and other amenities in the choice of location makes it harder for low-income households seeking to spend more specifically on schooling—choosing a higher quality schooling generally also entails paying for other amenities as well (Nechyba 2006, Bayer et al. 2007). These additional costs are not just in terms of pecuniary amenities. In-stead, because low-income households generally attach greater relative importance to ethnic composition, job proximity, and proximity to friends and family, which are typically more concentrated in low-income/low-quality school areas, there is a greater burden for such households that would like to invest in better education (Rhode and Strumpf 2003, Hastings et al. 2008). Finally, sorting-based educa-tion provision may tend to exacerbate educaeduca-tional inequalities due to poor access to information for low-income households concerning both their children’s abilities and a school’s quality as measured by its ability to increase achievement for their children (Cullen et al. 2006, Rothstein 2006, Hastings et al. 2007, Hastings and Weinstein 2008). In this case, de facto matching off low-income students with low quality schools and high-income students with high quality students may again cause educational mismatches that are inefficient.

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2.4 Macroeconomic Research on Educational Investment

and Intergenerational Inequality

Arguably, the greatest emphasis on potential long-term effects of educational under-investment and stratification has come from macroeconomic research, particularly work concerning economic growth and inequality. While the magnitude and the significance of estimated growth effects of educational attainment vary among the corpus of studies (e.g. Barro 1991, Durlauf et. al. 2008, Fleisher et. al. 2010, Hanushek et. al. 2000, Maasoumi et. al., 2007), more recent literature has often supported the view that educational underinvestment has a negative effect, with issues such as nonlinearities (Durlauf 2001, Kalaitzidakis et. al. 2001, Temple 2001) and data quality or choice of measure (de la Fuenta and Dom´enech 2006, Delgado et. al. 2014) accounting for much of the supposed noisiness from estimation. In like manner, empirical studies on inequality and growth have also frequently found that inequality negatively affects growth (Aghion et. al. 1999, Panizza 2002, Sylwester 2000), although this finding has similarly been disputed (e.g. Forbes 2000). Taken together, analyses regarding the effect of education and inequality on growth have been cited as a basis for greater public provision of education (Chen 2005, Kirch-steiger and Sebald 2010), an intervention tantamount to reduction in sorting-based educational provisioning.

Given the potential for educational outcomes and inequality to negatively affect growth, macroeconomic approaches increasingly have also begun to explore inter-generational persistence in educational attainment and income (e.g. Blankenau and Youderian 2015, Das 2007, Glomm 1992). The analysis which most directly ad-dresses the intergenerational effects of sorting-based school finance, however, occurs relatively early on—with Kremer’s (1997) construction of a dynastic family model to investigate the effects of household sorting on intergenerational mobility. Like much of the school choice literature, Kremer suggests that the effects of sorting on edu-cational inequality are likely to be very small, with a doubling of household sorting estimated to increase the standard deviation of inequality among family dynasties by 3.5%. In Kremer’s view, the concern over homogeneous socioeconomic sorting in

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the determination of schooling and other community features was therefore a case of ’misleading intuition’ rather than objective reality. The model of Kremer may however be susceptible to criticism over its simplified design — Kremer assumes that sorting and intergenerational transmission of education can be encapsulated simply by parents’ educational attainment and average education of neighbors, calibrated parameters for which are primarily obtained by simple ordinary least squares.

A more recent analysis of stratification and intergenerational mobility is Herring-ton (2015), which features an overlapping generations model characterizing human capital (and equivalently wage) as a production of both educational investment and innate (i.e. biological) ability. In Herrington’s model, parents choose between con-sumption and educational investments, while government determine a level of public expenditures for education and a level of tax progressivity that supports it.5 Despite use of a relatively high level of intergenerational persistence in ability, and a specifi-cation of tastes for eduspecifi-cation in dynasties that is AR(1) rather than endogenous to educational decisions, Herrington’s quantitative model suggests that if the United States were to adopt the public educational investment and progressive taxation of Norway, intergenerational earnings elasticity would be predicted to fall by 10% while the pretax Gini coefficient would be estimated to decline by approximately 5%.

2.5 Empirical Analysis of Intergenerational Persistence in

Education

In conjunction with more theoretically driven analyses of intergenerational persis-tence of education, a number of empirical studies have similarly been concerned with its causes. In analyses of matched parent-child outcomes, often comparing

5_{Taxation in the Herrington model is not specifically for education, but instead supports both}

schooling and non-schooling expenditures. This confounds precise accounting for the role of edu-cational financing stratification with a second issue of the overall effect of tax system progressivity on intergenerational outcomes. However, the general implications of examining both (federal) gov-ernment education spending and its underlying tax progressivity is largely similar to examining the issue of income stratification in educational financing.

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natural-born children to adoptees, researcher have typically found persistence in outcomes even controlling for inherited ability (Black and Devereux 2009, Bj¨ ork-lund et. al. 2006, Bj¨orklund et. al. 2007, Ermisch and Pronzato 2010, Holmlund et. al. 2011, Lefgren et. al. 2012), suggesting that environmental factors associated with a child’s household have a causal impact on their subsequent education and income attainment.

To date, the only empirical study to specifically investigate the role of strati-fication of school financing on intergenerational mobility is Chetty and Friedman (2010). While Chetty and Friedman do not explicitly link stratified educational financing to sorting-driven school choice, they nevertheless share the same basic re-search question as the current study — examining to what extent more localized school financing affects the intergenerational outcomes of children. To address this question, Chetty and Friedman combine estimates of two separate processes utilizing data from Project Star, a large-scale public education experiment occurring in Ten-nessee during the 1980s. First, Chetty and Friedman estimate the predictive value of parental income on schooling quality, with the assumption that more localized school financing is instrumental to variation in school quality which higher income households can then exploit. Chetty and Friedman then combine this estimate with an estimated effect of school quality on child earnings, derived from Chetty, Fried-man, Hilger, Saez, Schanzenbach, and Yagan (2010). Linking these two effects, Chetty and Friedman (2010) infer an overall effect of stratification-based returns to parental income on child earnings. From their estimation strategy, Chetty and Friedman estimate that child earnings at age 27 are increased by $ 110 for each $ 1000 of parental income as a result of income-driven access to better public schools. A major shortcoming of Chetty and Friedman’s analysis, however, is that the effects of stratified educational financing is only insinuated by the authors in the predicted relationship between parental income and schooling quality, thus omit-ting any form of direct investigation for these effects. Even if Chetty and Friedman are correct in assuming local educational financing is the fundamental driver of the correlation between parental income and schooling quality, their subsequent conclu-sion that local financing perpetuates inequality fails to respond to the contention

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of Hoxby and others stating that school finance centralization or equalization will either ”level down” school financing or result in negligible increases for low-income students, while having potentially large negative effects on school quality through efficiency mechanisms.

Nevertheless, both the work of Chetty and Friedman (2010) and much of the preceding literature suggest the possibility that educational investments may have significant intergenerational effects for low-income households. In this case, the stratification resulting from more locally financed schools as favored by the Tiebout choice model may be expected to have dynamic inefficiency considerations which challenge its foundational private efficiency assumptions. Alternately, if the bene-fits of localized school financing to either educational efficiency or support for ed-ucational spending outweigh any negative equity effects, we might instead expect positive intergenerational effects which complement the contemporaneous efficiency arguments. Finally, it is possible that any differential distributional effects of school financing are either negligible or not persistent across generations, in which case contemporaneous considerations may solely be relevant.

In the foregoing analysis, I use estimated parental share of educational spending from local sources to attempt to quantify the magnitude and direction of prospective intergenerational effects of stratified school financing.

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Data and Estimation Strategy

In this chapter, the basic strategy of using birth data on mothers to link aggregate ”child” and ”parent” (i.e. mothers) is introduced, followed by discussion of data used in the analysis, choice of outcomes of analysis and corresponding econometric models, and finally the specification of the models and relevant parental variables.

3.1 Identification Strategy

As mentioned previously, when analyzing the intergenerational effects of income-stratified school financing, the parental share of public school financing from local sources suggests itself as a quintessential measure of stratification. Not only is the degree of local financing for public goods the foundational question of sorting-based Tiebout school choice, but the share of financing from local sources can be thought of a spectrum on which, at one end, lies uniform statewide school revenues and at the other, educational finance purely determined by local neighborhoods’ affluence and appetite for educational investment. The United States moreover offers a good opportunity to investigate these effects, with a scope for sorting-based stratified school financing that is both wide and varied. The average estimated share of financing from local sources in the current sample is just under 55%, with a range from 9.5-94%.

Another appealing characteristic of examining parental share of public school fi-nancing from local sources is that, after controlling for individual and time specifics

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effects as well as household income and overall educational spending, the case for conditional independence seems highly plausible: reverse causality is precluded and omitted variable bias would have to be contemporaneously correlated with the changes in the share of local finance during the approximate period of parents’ ed-ucation while affecting outcomes of young adults at least 25 years removed. Given that public educational financing occurs through a patchwork and intermittent mix of funding decisions at the local, state, and federal levels, the likelihood of such potential violations appear reduced. To test this assumption, in Chapter 5 (Ro-bustness Checks), growth in other areas of government financing over educational tenures are regressed on growth in the local share of educational financing. If the estimated effects are non-negligible, this approach would then indicate a potential conditional independence violation.

Yet, as is common with intergenerational issues, a major challenge for conduct-ing this analysis is the absence of suitable data linked between parent and child that would allow for precise determination of school financing characteristics during parents’ education. This study attempts to overcome that shortcoming by looking at aggregate outcomes for young adults at the state level and then utilizes data on mothers giving birth to create a weighted average estimate of mothers’ expected schooling tenures from which parental education financing variables are derived. Suitable econometric techniques can then be applied to measure the effects of strat-ification of school financing on child cohorts’ education and earnings outcomes.

Such an approach, however has unavoidable shortcomings. First, intergener-ational effects of stratified educintergener-ational financing is here limited to identification through the maternal educational channel. While this constraint is certainly less precise than identification for both mother and father, it is unclear whether edu-cation of the mother or father has more salience in the intergenerational effects of parental education frequently found in the literature. Moreover, some studies have suggested that the primacy of mother or father-based effects may determine on spe-cific conditions of the family, such as the sex of the child or the socioeconomic status of the household.1 In this respect, however, Pronzato (2012) has suggested that

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ternal education is likely more relevant to child outcomes in low-income households, while paternal education is more relevant in high-income households. To the extent that Pronzato’s claim holds, maternal educational identification should be more ap-propriate to the current study’s primary focus on intergenerational effects for low income/educational attainment households (and corresponding, potentially less re-liable for high socioeconomic status households).

A second limitation is that precise calculation in an aggregate cohort setting is restricted by the level of detail in the data, contributing to measurement error. The most notable example of this when using birth data to link generations is the as-sumption that observations at the state level for individuals age 25 are equivalently represented by mothers giving birth in that state 25 years prior, who then further are assumed to be educated in the state in which they gave birth. The intergenera-tional span from mothers’ start of education (assumed at age 6) to child’s outcomes at age 25 is generally between 30-55 years, hence the potential for interstate mi-gration within that span is substantial and a major source of potential bias. Even foregoing the issue of measurement error, however, a weighted average estimate of different parents’ educational shares conceals substantial heterogeneity, particularly when estimates are averaged over many constituent groups, as is the case here (the estimation strategy will be explained in detail in the next section).

Invariably, the issues above make a weighted average approach a highly imperfect measure of the desired parental explanatory variables. The critical question, how-ever, is whether the measures resulting from this approach are relevant predictors of the true parental variables and whether they are conditionally independent of the error in estimation. If these conditions hold, then the natality-linked weighted average of expected educational tenures can serve as an instrument for the true underlying educational tenures of parents.

Given that relevance holds by construction, conditional independence then be-comes the key issue—with immigration figuring prominently as a source of potential violation. If cumulative migration is correlated with trends in educational financing

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(and also affects cohort outcomes), then the conditional independence assumption would not hold. For recent migration, the results of Hern´andez-Murillo, et. al. (2011) suggest that such a selection issue was not a major concern. Specifically, Hern´andez-Murillo and coauthors find that in a national representative panel of individuals over the period 1996-2014, difference in education indicators such as school rankings and attainment rates were negligible between origin and destination states of migration. To determine whether these results extend to the longer du-ration of the current panel, in Chapter 5 I present similar regressions that check if either differences in educational financing or child cohort outcomes are associated with observed interstate migration in the United States over the sample period. Again, should conditional independence hold, then the estimated parental variables are expected to be a valid, albeit noisy, estimate of the true latent variables under consideration.

3.2 Data and Sources

The analysis relies on data from several sources. Outcomes for the 25-year old ”children” cohort comes from the monthly Current Population Survey (CPS) as well as its Annual Social and Economic Supplement, together conducted by the United States Census Bureau. The current analysis utilizes CPS data from the period 1997-2015. The Current Population Survey is a monthly cross-sectional survey of households, hence to produce aggregate estimates for states, means and selected quartiles of outcomes are calculated (using person-specific weights supplied by the Census) for each state and year. The selected outcomes taken from the CPS include education level and weekly earnings. Additionally, means of demographic variables including sex, race, and ethnicity, which are used as covariates in the analysis, are also taken from the Current Population Survey.

Data for the estimation of parental public educational financing comes from both existing datasets and historical reports. In the current analysis, public educational financing data is observed over the period 1922 to 1990, with data from 1922 to 1962

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published biennially in even years.2_{. School financing information for the period}

1922-1958 is taken from the Biennial Survey of Education, a publication of the now-defunct US Office of Education, variously under the Department of Interior or the Department of Health, Education, and Welfare (also defunct). Data for 1960 through 1981 comes primarily from the Digest of Education Statistics, also published by the Office of Education. For the years 1962, 1964, and 1966, data comes from ”Statistics of State School Systems,” published by the Department of Health, Education, and Welfare, while statistics for 1971 are from the ”Estimates of School Statistics,” published by the National Education Association. Finally, information for the period 1982-1990 is take from the Common Core of Data, a district-level dataset published by the U.S. Department of Education. Data for the state of Virginia over the period 1986-1988 is missing from the Common Core of Data, therefore data for 1987 is instead taken from the 1987 Census of Governments, a publication of the Census Bureau. For odd years over the period 1922-1962, and for the missing years of 1986 and 1988 for Virginia, data is interpolated as the simple mean from the years immediately before and after.

Age of mother at birth information is taken from data of the National Vital Statistics System of the National Center for Health Statistics (NCHS). For mothers giving birth after 1967, natality information is available as microdata in a dataset published by the National Bureau of Economic Research (NBER). In these years, age of mother at birth data represents a 50% sample of all birth certifications between 1968 to 1972 and a 100% sample of birth certificates thereafter. Data before 1967 is derived from the NCHS publication, ”Vital Statistics of the United States.” In these reports, mothers’ single year age of birth is reported at the national level for each year, while state-specific age of birth data is presented in four year increments (i.e. 15-19,20-24, etc). Consequently, in order to impute single-year, state-specific distributions of mothers’ ages, I assume that the distribution within the four-year increments have the same relative frequency as within the corresponding age ranges of the national data.

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Additional information used in this analysis includes historical personal income, population, and Consumer Price Index estimates. Annual personal income estimates by state fare made available by the US Bureau of Economic Analysis (BEA). His-torical population estimates are from the US Census Bureau Population Estimates Program, while school age population estimates are generally from the same reports as those for school financing. Over the period 1960-1968, school age population data instead comes from ”Statistics of State School Systems,” while data for 1975-1980 is from ”Statistics of public elementary and secondary day schools,” published by the National Center for Educational Statistics. Finally, historical estimates of the Current Price Index are from the Minneapolis Federal Reserve (2016).

To facilitate the desired intergenerational analysis, this study incorporates both estimates of variables for the synthetic parental cohorts as well as contemporaneous features of the age-25 child cohorts. The analysis also includes multiple outcomes measures for both educational attainment and income of child cohorts.

3.2.1 Dependent Variables—Child Outcomes of Interest

From the education level and weekly earnings microdata of the CPS, three main types of outcomes are delineated: annualized earnings (in dollars), years of ed-ucation, and educational attainment rates (i.e. graduation rates) at the middle school, tenth grade, high school, two-year college, and four year college levels. Be-cause fractional response models are subsequently applied, graduation rates here are (measured as a fractional proportion, with a possible range of 0 to 1.

In testing for intergenerational effects of educational financing, the specific hy-pothesis is that stratified educational financing may have distributional effects—in particular potentially reducing outcomes for lower socioeconomic status households (while effects for wealthier households may be improved or unaffected). Hence, for earnings and years of educational attainment, analysis is conducted at multiple points of the distribution. Given the current study’s focus on potential impacts for lower income/educational attainment households, particular attention is given to attainment percentiles in the lower half of the distribution, including the 10th, 20th, and 40th percentiles, however results are also reported and considered for the

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50th (median), 60th, and 80th attainment percentiles in addition to the mean. Be-cause attainment rates are a cumulative measure, distributional considerations are already inherent to their analysis.

3.2.2 Calculation of Parental Explanatory Variables

Local Share of Educational Financing

The primary parental explanatory variable of interest is parents’ average share of educational financing from local sources (henceforth local share). The estimation procedure for the local share is as follows:

1. First, calculations are performed for the local shares for each state and year in which parents could have been educated.

2. Next, for each 25-year old child cohort, the corresponding mothers are identi-fied in the birth data by subtracting 25 from the child cohort observation year. Hence, for individuals identified as 25 years old in the 2015 Current Population Survey, their mothers are assumed to be reflected in the birth data for 1990. For individuals aged 25 in the year 2014 cohort, mothers are assumed to have given birth in 1999, and so on.

3. For each corresponding year in the birth data, the proportion of mothers with a given age is then calculated (for tractability, ages are restricted to the range 15-39, reflecting approximately 99% or more of births).

4. The average local shares over the expected basic education tenure is then calculated for each age, 15-39, in a given birth year. For mothers who gave birth at age 18 or older, the figures are calculated as the averages for the years in which the mother would be age 6 to 17. For individuals giving birth from age 15 to 17, the educational span is assumed to be from ages 6 to mother’s current age minus 1.

5. The final local share variable for a child cohort is then calculated as the weighted average of the proportions of a specific age multiplied by the age-specific averages of the explanatory variable. Once again, for calculations

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based on a given birth year, the weighted-average estimate represents the parental variable for the cohort twenty-five years after the birth year. For ease of interpretation, local educational share is expressed in percentage terms, so that it’s values may range from 0 to 100.

As an example, the estimated parental local share of educational financing for the age-25 cohort in a given state in the year 2000 would be:

shareST,2000= 1 39 − 14 39 X age=15 prop1975,age× 1 min[17, age − 1] min[17,age−1]_X yr=6 share(1975−age+yr) (3.2.1)

Parental Educational Financing Controls

Additionally, two other features of the parents’ educational tenures are also included as covariates: total educational revenues per school-age child in the population and average personal income in the state (both in thousands of dollars).3 _{These variable}

appear critical to control for, as a state’s overall affluence and level of investment into education are not only primary determinants of educational outcomes, but also may correlate with a state’s degree of localization in school financing. Yet because these very outcomes are the subject of debate concerning the effects of educational financing systems, it would be erroneous to naively include them in the regression in the same manner as the local education share because their evolutions over parental tenure spans could in part be driven by changes in the local share.

Necessarily then, the researcher must assume that educational revenues follow-ing the first observation year of parental local shares for a given child cohort is po-tentially endogenous and thereby disallowed. Likewise, aggregate personal income following the completion of the first possible parent educational tenure of a given cohort may likewise be endogenous. These eventualities limit possible measures for

3_{Because income and educational revenue are reported in nominal dollars, figures are converted}

to 2015 Constant Dollars using the BEA Consumer Price Index. Further, total revenue figures are divided by the school-age (6-17 years old) population for the given state and year. Similarly, income figures are expressed in per capita terms by dividing total personal income by annual estimates of the population for each state.

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educational revenues and state income to proxy values predating the local shares in question (serving effectively as an instrument). Using a lagged proxy, however, is not in itself sufficient to control for intermediate outcome bias of included covari-ates in the general case. Instead, their applicability requires a specific assumption – that conditional on the designated proxy value of local educational shares, parental effects on child outcomes are independent of deeper lags of the local share.

As a result of the lagged proxy approach, endogenous effects of local education shares on the lagged proxy parental covariates are precluded by construction. Fur-ther, while the lagged proxies may potentially be correlated with the lag of the local education share, if the assumption holds that deeper lags hold no additional explanatory power for outcomes variables, then the local education share term is also unbiased.

In the current setting, these assumptions appear. Specifically, deeper lags them-selves fall outside parental educational tenures, thus for lagged local shares to bias lo-cal share estimates, meaningful higher order autocorrelation effects must be present. In an analysis of local share autocorrelation, a 1 percentage point change in any deeper lagged education share is estimated to change the current value by a maxi-mum of 0.005 percentage points, hence higher order autocorrelation appears unlikely. Adopting this methodology to address potential simultaneity or intermediate outcome bias, the lagged proxies are specified in the following manner: for the earliest parent group represented in a given child outcome cohort (those giving birth at age 39), the revenues per school age population proxy is designated as the value observed at age 6, when they are assumed to have began their education. For average personal income, the date corresponds instead to when these mothers would have been 16 - the later point at which point it is assumed that state income would have been unaffected by educational tenures.

3.2.3 Sex and Race/Ethnicity Variables

Finally, a small selections of covariates for 25-year olds in the sample are included. Because the analysis considers possible effects of educational financing on education and income (which may in turn affect many other facets of the state economy),

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care is taken to only include covariates which are not likely to be endogenously determined by school financing. For this reason, only demographic features (ex-pressed as proportions of the population) concerning sex and race or ethnicity of the cohort are included. Ethnicity is categorized by the following categories: white (omitted reference), black, Hispanic/Latino, and other, which combines American Indian/Aleut/Eskimo, Asian / Pacific Islander, mixed ethnic identification and all other designations. While greater specific of ethnic designations would be preferred, the current analysis does not allow for this because of resulting collinearity.

3.2.4 Functional Form of Parental Variables

In addition to selection of relevant explanatory variables, a key issue is the specifi-cation of functional form for the parental explanatory variables. That is to say, it seems likely that effects of explanatory variables in the model could potentially be nonlinear and that the effects of local educational financing could be mediated by the general level of resources available to public school in the state. As preliminary examples, the effect of the local share of educational financing may likely vary ac-cording to how high (or low) the average level of per capita revenues for a given state and year, while per capita educational revenues could themselves have diminishing or non-linear returns. In approaching these problems, more flexible estimation can be pursued, but at the cost of lost power due to the estimation of additional model parameters.

Consequently, results are reported according to four different model specifica-tions. In Specification 1, a more flexible approach is presented, which allows for nonlinear effects of income and revenues using cubic smoothing splines (with four knots, placed at equally spaced percentiles of the original variable’s marginal distri-bution ) and which further interacts local share with revenue splines. Specification 2 omits the Share x Revenue interaction, while maintaining the use of nonlinearities to account for potential nonlinearities. In Specification 3, use of cubic smoothing splines is omitted while the interaction between local education shares and revenues are maintained. Finally, Specification 4 is the most parsimoniously specified model, with only linear effects and no interactions.

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3.3 Econometric Method

3.3.1 Educational Outcomes: Attainment Rates

Theory

To analyze the effect of local shares on educational attainment rates, two economet-ric specifications are pursued, the generalized linear model (GLM) approach and its primary extension to panels, the general estimating equations (GEE) method. The basis of these choices is due to the fractional response nature of attainment rates, which is the population average of a binary outcome (complete / don’t complete). Because the underlying outcome is binary, and likewise the population average is constrained between zero and one, the linear panel regression method both incor-rectly assumes a Gaussian distribution and fails to constrained predictions between 0 and 1, hence fractional response models are instead employed.

Fractional responses in general may be effectively analyzed using a Generalized Linear Model (GLM). A GLM is, as its name suggests, a generalization of regression models based on assumed linear exponential family densities. The GLM model involves specification of a conditional mean function, g(x, ), whose parameterizations corresponds to various nonlinear models and whose distribution corresponds to a linear exponential family density (including Gaussian, Bernoulli, Exponential, and Poisson distributions among others). GLM models then utilize a link function, g−1(·), to transform the expectation of the dependent variable into a predictor which

is a linear (in parameters) function of regressors. For analysis of fractional response, the conditional mean function g(x, β) corresponds to the probit parameterization and is from the Bernoulli family of distributions.

One consideration that is important to not only application of GLM, but all the econometric methods discussed, is that there is likely to be substantial autocor-relation and heteroskedasticity present within the estimation of intergenerational effects of school financing. This is likely to occur for several reasons, chiefly related to the fact that both educational outcomes and wage determination for temporally close cohorts share many common influences. In consideration of both child cohorts

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and parental cohorts, these issues are further compounded. When examining edu-cational effects, even in non-intergenerational contexts, proximal cohorts will have schooling tenures that largely overlap, so that school financing in these years will affect both cohorts, causing regression residuals to be similarly correlated (the same of course can be said of other influences during schooling tenures). This issue is further intensified by the nature of the parental educational variables, as different child cohorts will include subsets of parents that are expected to have precisely the same educational tenures (and wherein moreover there is expected to be error in the attribution of schooling tenures). In relation to childrens outcomes, common influences as children and young adults are similarly expected, with the scope for autocorrelation further accentuated by the fact that, for example, market wages of similarly skilled individuals in one cohort are expected to be determined in part by the wages received by such individuals in the immediate past.

GLM with heteroskedastic-consistent variance estimation is robust to heteroskedas-ticity and autocorrelation, but does not explicitly take the clustering of panel data into account and therefore may be less efficient under these conditions. An extension of GLM models to panel settings, General Estimation Equations (GEE), explicitly accounts for panel clustering and allows for more efficient analysis of fractional response in the presence of serial correlation. First developed by Liang and Zegar (1986), GEE is a method that is asymptotically equivalent to Multivariate Weighted Least Squares, but which allows specification of the conditional variance V (yi | xi)

to be replaced by a “working version” of the variance according to the choice of generalized linear model (Papke and Wooldridge 2008). The GEE estimator, βGEE_,

solves the moment condition:

N X i=1 δg0_i(β) δβ Σ −1 i (yi− gi(β)), (3.3.2)

where the conditional mean function, gi(β) and the working conditional variance

Σ−1_i result primarily from the choice of GLM (Cameron and Trivedi 2009). In the case of fractional response of binary outcomes, the conditional mean function is probit and the working conditional variance is derived from the binomial family.

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GLM in the context of time series, a shortcoming of GEE is that choice of work-ing conditional variance includes specification of a within-group cluster correlation. Correlation may be specified in a number of ways, including the assumption of in-dependence, constant (exchangeable) correlation, AR(1) correlation, or in principle, even correlation with no predefined form (unstructured correlation). However, in more general settings of nonstationary and unstructured data, estimation may com-monly result in a correlation matrix that is not positive definite, in which case GEE estimation will fail to achieve convergence.

Because of the nature of expected autocorrelation and heteroskedasticity in our model, the assumption of independent, constant, or AR(1) correlation matrices seems overly restrictive, yet the current model with unstructured correlation speci-fication is found to suffer from the convergence failure problem. In such instances, use of restrictive correlation specifications without convergence issues, even if they are misspecified, will nevertheless return consistent estimates of coefficients with valid inference (assuming that the conditional mean is correctly specified), albeit with somewhat lower efficiency (Imbens and Wooldridge 2007). In these circum-stances, Wooldridge and Papke (2008) show that although GLM does not exploit the panel structure of data, its efficiency when using fixed effects is similar to GEE, allowing for productive use of both methods. For this reason, in the present study, both GLM and GEE are presented, with GEE documented using both unstructured correlation (albeit non-convergent) and exchangeable correlations. Crucially, both GLM and GEE allow for incorporation of fixed state effects using the time averages of explanatory variable and time specific fixed effects through year indicators, as demonstrated by Papke and Wooldridge (2008).

GLM and GEE Regression Specifications

Using GLM and GEE, the fractional response of graduation rates due to parental education variables and covariates can thus be specified in the following manner:

Φ−1Ehgradratest,yr

i

= x0_st−yrβ + ¯x0_stξ + τyr

gradrate ∼ Binomial,

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where GEE additionally specifies the correlation structure (R) as either: Exchangeable: Ryr(i),yr(j) =    1, yr(i) = yr(j) ρ, otherwise    (3.3.4) Unstructured: Ryr(i),yr(j) =    1, yr(i) = yr(j)

ρyr(i),yr(j), otherwise, ρyr(i),yr(j) = ρyr(j),yr(i)

   where x represents the independent variables of analysis, represents the time average of x for state-specific effects, and τ is a vector of time indicators. For the primary specification (Specification 1) incorporating nonlinear effects, the covariates are as follows: x(st, yr) = [Localshare(st, yr), IncomeSpline1 : 3(st, yr), RevSpline1 :

3(st, yr),

SharexRevSpline1 : 3(st, yr), F emale(st, yr), Black(st, yr), Latino(st, yr), Other(st, yr)].

Specification 3 instead omits splines in favor of first-order specification of covariates, hence we instead have x(st, yr) = [Localshare(st, yr),

Income(st, yr), Rev(st, yr), SharexRev(st, yr), F emale(st, yr), Black(st, yr),

Latino(st, yr), Other(st, yr)]. Specifications 2 and 4 are the same as 1 and 3,

re-spectively, except in that they omit the Share x Revenue interaction. For nonlinear terms in Specifications 1 and 3, the time averages are nevertheless the averages of the linear terms, as per Wooldridge and Papke (2008).

Finally, analyses for attainment rates is once again conducted at four separate ed-ucational attainment levels: tenth grade completion, high school diploma,two-year college, and four-year college.

3.3.2 Educational Outcomes: Years of Education

The second educational outcome of interest is years of educational attainment, ana-lyzed at designated percentiles and the mean. Because years of education is a count, a count panel model with fixed effects may be more suitable to analysis than linear fixed effects panel methods,4 _{with Poisson fixed effects regression generally preferred}

because it is consistent under a weaker set of assumptions than alternatives such as the negative binomial model (Cameron and Trivedi 2009).

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In the present study, the Poisson fixed effects conditional probability function is specified as follows:

Pschoolyearsst,yr | xst,yr, αst

= exp(−αstλst,yr)(αstλst,yr)

schoolyearsst,yr

(schoolyearsst,yr)!

(3.3.5) where λst,yr = exp(−αst + x0st,yrβ) and αst is a time-invariant state specific

er-ror term. The explanatory variables xst,yr are defined in the same manner as with

GLM/GEE, with the exception that year indicators are also taken to be included in xst,yr for notational simplicity. Notably, years of schooling is recentered by

subtract-ing the minimal observed cohort level of schoolsubtract-ing at the 10, correspondsubtract-ing to middle school education. As before, analysis is for two specifications: with and without non-linear terms. Owing again to potential heteroskedasticity and autocorrelation, the Huber-White variance-covariance estimation method is used for producing standard errors.

3.3.3 Earnings Outcomes: Annualized Earnings

Finally, estimated effects of stratified school financing on annualized earnings is analyzed. In contrast to attainment rates and years of schooling, earnings are more likely suited to linear fixed effects regression than nonlinear methods. The regression equations are therefore specified as follows:

earningsst,yr = αst+ τyr+ x0st,yrβ + ust,yr (3.3.5)

The variable selection again is the same as before, with αst representing state

fixed effects and τyr again representing year fixed effects. Fixed effects estimation is

performed with Huber-White robust standard errors to account for autocorrelation and heteroskedasticity.

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Results

In this chapter, results are discussed concerning the estimated parental local share of educational financing on child cohort education attainment, years of education, and annualized earnings are discussed. The share of educational financing from local sources is found to have a negative effect especially at particular educational levels. Consistent with this observation, regression of local share of educational financing on years of education shows an effect that is statistically significant but small in magnitude. Estimated effects on earnings is limited to the 20th percentile in the primary specification incorporating nonlinearities and Share—Revenue interactions, although the strong performance of this model with regards to both significance of variables and goodness of fit tests suggest that this specification may be most appropriate to the intergenerational transmission of income. Results tables are reported in Appendix A.

4.1 Educational Attainment Rates

For analyses of educational attainment rates using GLM and GEE models, evidence of negative intergenerational effects of local financing is strongest in particular for two-year college attainment, while discrepancies between regressor significance in the primary model and in the calculation of marginal effects preliminarily indicates similar relevance (and negative effects) for tenth grade and four-year college com-pletion, however precluding more detailed conclusions about the size of this effect.

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For tenth grade schooling — the lowest level of educational attainment investi-gated, the local share of educational financing is estimated to have a highly signifi-cant effect on child completion both in the primary model, accommodating nonlin-earities and a Share x Revenue interaction, as well as in the parsimoniously specified linear specification that omits any interaction. The Share x Revenue interaction is itself statistical significant in both regression in which it is included. Comparing val-ues for Aikake Information Criterion (AIC) and the Schwarz Bayesian Information Criterion (BIC), Specification 1 which incorporates nonlinearities and interaction effects is found to have the best model fit — even when penalizing inclusion of additional parameters as found in the BIC. Because GLM and GEE are nonlinear models (as too will be Poisson estimation), interpretation of the magnitude of effects within these models requires inspection of the marginal effects 1 Marginal effects in this model, however, are not significant. Greene (2008) notes that such disparities can easily arise because marginal effects are ’testing a hypothesis about a [nonlinear] function of all the coefficients, not just the one of interest,” hence Greene writes that inference should be drawn first from hypothesis tests concerning the model param-eter. As a result, we may tentatively conclude that the local share of educational financing has a negative effect on child cohort educational attainment at the tenth grade level, but because the marginal effects lack statistical significance, any specific conclusions regarding the magnitude of this effect are precluded.

Extending beyond tenth grade schooling, the local share of educational financing is found to have no effect on attainment rates at the level of a high school diploma across all four specifications. On the other hand, for attainment rates at the level of two-year college, the share of educational financing is found to have significant neg-ative effects for all four specification, for both the GLM and GEE models, although estimates for the Share x Revenue interaction are both statistically insignificant and very close to zero. Marginal effects of the local education share in this model suggest

1_{Marginal effects are calculated at deciles of the local education share and at the observed}

values for all other covariates. This distinguishes the average marginal effects in this analyses from ’average marginal effects’ which are instead taken as the marginal effect at the averages of other variables. (Cameron and Trivedi 2009)

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that a 1 percentage point increase in the share of educational financing from local sources for parents implies a 0.12-0.18% decrease in child cohort attainment at the two-year college level.

Finally, results for the four-year college level are broadly similar to those of tenth grade education: the local share of education is either significant or marginally in three of the four specifications examined, but marginal effects are generally not significant. It is worth noting moreover that in the case of four-year college attain-ment, Specification 1, which has the most favorable flexibility properties, provides only very weak evidence against the null, although specifications that render signifi-cant effects are observed to perform comparably to Specification 1 in criterion tests. Hence, at this educational level, while there is tentative support for the view that the local share of educational financing has negative effects on child outcomes, more specific inference appears to be infeasible.

Broadly speaking, it appears that the effects of Tiebout local school financing has tended to have an effect primarily for those on the ”bubble” of high school attainment, either from above or below, with the effects most notably for individuals positioned to move towards attainment at the level of two-year/associates degree and secondarily, for those vulnerable to dropping out.

Concerning not only educational attainment, but all outcomes of analyses, it bears noting that no individual specification appears preferable in all cases. In-stead, each specification present facets of a compromise between model flexibility and model efficiency. In some cases, the greater flexibility of the nonlinear, inter-acted Specification 1 appears to outweigh its loss of precision, while in other cases estimates would seem to suggest that a more parsimonious specification should be exptected to perform equally well. For GEE and GLM, a similarly trade off is present – GEE can more explicitly account for clustering, but it’s efficiency is limited by the necessity to specify a working correlation matrix (although broadly, greater re-liability of results from the GEE model should it make it more often preferable) (as per Papke and Wooldridge 2008).

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4.2 Years of Schooling

In the Poisson panel regression, parental local share of educational financing is found to have significant negative effects at the 10th and 20th percentiles of income attainment in the nonlinear specifications. Notably, however, while these effects are in general highly statistically significant, they are also very small. Marginal effects of a a 1 percentage increase in the local share of educational financing during a parents’ generation is estimated to decrease years of schooling by 0.0045 years at the 10% attainment percentile and approximately 0.001 years at the 20th attainment percentile. Finally, local share of educational financing is marginally significant (p = 0.096) in decreasing mean years of schooling, although the estimated effect is essentially zero. Standard linear fixed effects regression estimates are generally less significant than application of Poisson panel data methods, although both are alike in estimating very small negative effects.

Results form the previous section, examining educational attainment rates at specific levels seemingly offer insight into the phenomenon of highly significant and yet very close to zero estimates impacts of parental school financing on child cohort outcomes. In particular, it appears the effects of included covariates are very nonlin-ear in overall ynonlin-ears of schooling, rather acting in large part more specifically around the high school diploma attainment benchmark. Given that over 90% of individual identified in child cohort outcomes over the duration of the panel were located within a one year band around the grade 12/high school diploma level, it seems likely that fractional response methods like GEE or GLM will be more sensitive to the more unique nature of these processes and can better account for the large heterogeneity in effects of explanatory variables across different years of schooling.