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Leading determinants of education attainment Coelli, Michael B. 2005

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LEADING DETERMINANTS OF EDUCATION ATTAINMENT by MICHAEL B. COELLI B.Comm. (Honours), University of New South Wales, 1990 M.A., University of British Columbia, 2000 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES (Economics) THE UNIVERSITY OF BRITISH COLUMBIA September 2005 ©Michael B. Coelli, 2005 Abstract The objective of this thesis is to examine more closely the effect of parental income on indi-vidual education outcomes. The first paper (Chapter 2) identifies the causal effect of parental income on education. Parental job losses that occur when youth are completing high school have significant negative effects on the university attendance of youth, and increase early school dropout behaviour. This provides evidence of an alarming impact of labour market displacement receiving little prior attention, and of a significant causal parental income effect. Job losses have persistent negative effects on parental income. I estimate a full year-to-year grade transition model to uncover the immediate and lagged effects of parental shocks on the education attendance outcomes of youth, and to test that these shock measures are exogenous. The second paper (Chapter 3) examines the effect of tuition fees on the post-secondary educa-tion attendance of youth from different parental income backgrounds. Universities and community colleges in several Canadian provinces increased tuition markedly over the 1990s, while some provincial governments instituted tuition freezes. I employ this fee variation to identify tuition effects. I also estimate the effect of factors influencing the level of rationing of university and com-munity college places on attendance, namely government funding and cohort size, on attendance. Tuition increases markedly lowered the university attendance of low income youth but affected attendance of youth from middle and high income backgrounds much less. Cohort crowding also affected low income youth more negatively than other youth. I employ information on Canadian youth from the Survey of Labour and Income Dynamics (SLID) in these first two papers. The third paper (Chapter 4) examines the effect of individual high school principals on high school graduation probabilities. My co-authors and I employ a unique administrative data set of all grade 12 students in the province of British Columbia in the 1990s. In this province, there was significant turnover of high school principals within schools, from both rotation of principals from school to school, plus from quits and new hires. This rotation permits the isolation of the effect of the school principal from the effect of schools, student peers and the school neighbourhood. The results suggest that principals, and thus schools, can affect graduation rates. We focus particularly on the effect of school principals on youth from low income backgrounds, as identified by family welfare receipt. ii Table of Contents Abstract ii Table of Contents iii List of Tables vi List of Figures viii Acknowlegements ix Co-Authorship Statement x CHAPTER 1 Introduction and Overview 1 CHAPTER 2 Parental Income Shocks and the Education Attendance of Youth 6 2.1 Introduction 6 2.2 The Literature 9 2.3 Economic Model of Education Attendance Decisions 12 2.3.1 The Youth's Attendance Decision 13 2.3.2 The Parental Transfer Decision 15 2.4 The Canadian Post-Secondary Education System 18 2.5 The Data 22 2.5.1 Features of the Survey 22 2.5.2 Main Measures Employed in the Analysis 24 2.6 Post-Secondary Education Attendance Estimates 30 2.6.1 The Estimated Model 30 2.6.2 PSE Attendance Model Results 33 2.6.3 Persistent and Temporary Income Shocks 40 2.6.4 Breakdown of Effects of Parental Job Loss 41 2.6.5 Discussion of Job Loss Effects 44 iii 2.7 Grade Transition Model of Education Attendance 46 2.7.1 Grade Transition Details 47 2.7.2 Econometric Model 49 2.7.3 Estimation Preliminaries 51 2.7.4 Grade Transition Model Results 53 2.7.5 Test of Exogeneity of Job Loss Shocks 54 2.8 Discussion and Conclusions 58 C H A P T E R 3 Tuition, Rationing and Equality of Access to Post-Secondary Education 61 3.1 Introduction 61 3.2 The Literature 64 3.2.1 Canadian Studies 64 3.2.2 US Studies 66 3.3 Extensions of the Economic Model of Education Attendance 67 3.3.1 The Effect of Tuition on the Decision to Attend 68 3.3.2 Rationing and Acceptance Probabilities 68 3.3.3 Economic Model Extension of Residence and Hours of Work Decisions . . 73 3.4 The Data 75 3.4.1 Provincial Trends in Post-secondary Education in Canada 75 3.4.2 SLID Measures of Post-secondary Attendance Equality 83 3.5 Post-Secondary Education Attendance Estimates 87 3.5.1 The Estimated Model 87 3.5.2 Estimation Results for the Full Sample 90 3.5.3 Estimation Results by Parental Income Group 93 3.6 Estimated Model Extensions 94 3.6.1 Neighbourhood Characteristics 97 3.6.2 Tuition Effects Varied by Individual Characteristics 101 3.6.3 Alternative Supply Side Estimates 102 3.6.4 Effect of Tuition on the Residence and Hours of Work Decisions 105 3.7 Conclusions 108 iv C H A P T E R 4 School Principals and Graduation Rates 112 4.1 Introduction 112 4.2 The Literature 115 4.3 Models of High School Graduation 117 4.3.1 Parametric Model 117 4.3.2 Semi-parametric Model 120 4.4 The Data 124 4.4.1 Data Description 125 4.5 Semi-parametric Estimates of Principal Quality Variance 126 4.6 Parametric Model Estimates 128 4.7 Conclusions 138 C H A P T E R 5 Concluding Remarks 141 Bibliography 145 APPENDICES 151 Appendix A: Final SLID Sample Construction and Panel Attrition 152 Appendix B: Covariates and Data Sources 157 Appendix C: Grade Transition Model Details 162 Appendix D: Financial Aid Eligibility Indicators 166 Appendix E: School Achievement Production Function 168 Appendix F: School Principal Duties and Responsibilities 170 Appendix G: School Principal Turnover Term Construction 172 Appendix H: Grade 11 Achievement Measure 174 v List of Tables 2.1 Post-Secondary Education Attendance Rates 25 2.2 Parental Income Changes - Percentiles of Distribution 26 2.3 Parental Job Loss Prevalence 27 2.4 Regressors in Model - Summary Statistics 32 2.5 University Attendance - Marginal Effects 35 2.6 Other Post-secondary Attendance - Marginal Effects 36 2.7 Parental Shocks and Post-secondary Education Attendance - Marginal Effects 38 2.8 Persistent and Temporary Parental Income Shocks - Marginal Effects 41 2.9 Breakdown of Parental Job Loss Impacts - Marginal Effects 43 2.10 Annual Hours Worked and Income of Youth Aged 19 46 2.11 Job Loss Shocks - Treatment on the Treated Effects 55 2.12 Test of Exogeneity of Job Loss Shocks 57 3.1 Measures of Post-secondary Attendance Equality 84 3.2 Details of Post-Secondary Attendance Inequality 86 3.3 Regressors in Model - Summary Statistics 89 3.4 Post-secondary Education Attendance: Marginal Effects 92 3.5 University Attendance: Marginal Effects 95 3.6 Other Post-secondary Attendance: Marginal Effects 96 3.7 Neighbourhood Characteristics - Summary Statistics 98 3.8 Effects of Neighbourhood Characteristics on University Attendance 100 3.9 Tuition Effects by Individual Characteristics: Marginal Effects 103 3.10 Probit Estimates of Probability of Living with Parents (age 19 or 20) 107 3.11 Tobit Estimates of Hours of Work Decision of Students 109 vi 4.1 Variance in Principal Quality: Semi-parametric Estimates 127 4.2 Summary Statistics for Explanatory Variables 131 4.3 School Graduation Probit Estimates: AH Students 133 4.4 Marginal Effects for Graduation Probabilities 135 A . l Statistical Comparison: Sample for Chapter 2 154 A.2 Statistical Comparison: Sample for Chapter 3 155 A.3 Statistic Comparison: Final Samples Employed and 1996 Census 156 vii List of Figures 2.1 Real Tuition 20 2.2 Provincial Spending on PSE in Canada 20 2.3 Full-time University Undergraduate Enrolment 21 2.4 Full-time Community College Enrolment 21 2.5 Income Effects of Shocks for Main Income Earners 29 2.6 Income Effects of Job Loss by Union Status 29 2.7 Grade Transition Model - Subset of Transitions 48 3.1 University Tuition by Province 77 3.2 Community College Tuition by Province 78 3.3 Provincial Spending on Universities by Province 79 3.4 Provincial Spending on Community Colleges by Province 80 3.5 Age 16 Population Size Indices by Province 81 3.6 University Provided Student Financial Aid by Province 82 3.7 University Student-Faculty Ratio Ill 4.1 School Mean Graduation Rate Distribution 140 4.2 Principal Effect Distribution - A l l Students 140 4.3 Principal Effect Distribution - Welfare Students 140 viii Acknowledgements I sincerely thank David Green, my thesis supervisor, for his most considerable input, support and extraordinary patience over the production of this thesis. I am also heavily indebted to Nicole Fortin, Thomas Lemieux and Craig Riddell, my thesis committee members, for their continual guidance. Their generosity in providing me with their valuable time at a moment's notice was hugely appreciated. I thank the Killam Trusts, Ann & William Messenger and TARGET for financial support while completing my PhD. Their support allowed me to concentrate on completing this thesis rather than worrying where my next meal and rent payment were coming from. I also thank my family and friends back home in Australia who also eased my financial burdens by giving me a place to stay, meals and drinks while visiting back there during my many years of studies. Finally, many thanks to my fellow PhD students who also contributed considerably to the varied aspects of producing this thesis, through coffee runs, lunchtime arguments, office discussion and Friday night beers. In particular, I thank Ron Cheung, Lilia Karnizova, Lester Kwong, Stephanie McWhinnie, Kazu Takechi and Jacob Wong. ix Co-Authorship Statement Chapter 4 was co-written with Professor David Green (Thesis Supervisor, UBC) and William War-burton (Warburton Consulting). My contribution to the production of this piece of research is outlined below. • Identification of research program - a small contribution, as the initial idea was generated by my two co-authors. • Design of research program - an equal contribution in consultation with my co-authors. • Performing the research - a major contribution, including the review of the relevant literature and developing the estimator. • Data analysis - the vast majority of the econometric analysis was conducted by me, in con-sultation with David Green, employing the data set constructed by William Warburton, and transformed by David Green. • Manuscript preparation - 1 prepared the manuscript. x CHAPTER 1 Introduction and Overview Education attainment is a central component of economic success. For individuals, education is strongly related to many measures of well-being. Those with higher education levels earn more on average in the labour market, are more likely to be employed, and have better health outcomes, among other benefits. The returns to a university education in particular are large, and appear to be increasing in the United States over the past few decades. For society, education attainment has been linked to higher rates of technological progress and economic growth. It has also been linked to higher levels of civic participation, lower crime rates, lower rates of teen pregnancy, and less reliance on income transfer programs. There is considerable evidence of the strong relationship between family background and the education attainment of individuals in many countries, particularly in the United States and Canada. Youth with more wealthy parents are much more likely to attend university in particular. This, coupled with the large returns to obtaining higher levels of education, is often argued to be one of the main causes of the intergenerational transmission of inequality. In this dissertation, I analyze more closely the role that family background, and particularly parental income, plays in determining the education attainment of youth. To begin, I identify the causal effect of parental income on education attendance. I then identify the effect of changes in tuition on the equality of attendance at post-secondary institutions. It is important to ensure ourselves that a causal relationship exists if our policy response to any observed inequality in education attendance is to provide subsidies to education. If parental income does not causally affect the education attendance of youth, education subsidies (targeted or otherwise) should be ineffective in lowering inequality. If tuition increases negatively affect the attendance of youth 1 from low income backgrounds more that it affects other youth, it provides further evidence that parental income is a significant determinant of the education attainment of individuals. In chapter 2,1 identify the causal effect of parental income on education attendance of youth using parental income shocks. The large correlation between parental income and the education attainment of youth is well documented. This correlation may arise from observed and unobserved parental characteristics affecting both parental income levels and the education attendance of their children. Characteristics we generally do not observe include academic ability, preferences, dili-gence, culture and mental health. If exogenous shocks to parental income that occur at normal school leaving age affect the post-secondary education attendance of youth, it highlights a sig-nificant causal effect of parental income on education attainment, and the presence of significant financial constraints on post-secondary attendance. I employ parental income shocks following job loss to identify the causal effect of persis-tent parental income shocks. The persistence of income reductions following such job loss (from permanent layoff or redundancy, employer failure and employer dismissal) is considerable, and has been documented by other researchers (Jacobson, LaLonde and Sullivan (1993)). I find that parental job loss leads to significant reductions in the university attendance of youth, and also to increased high school dropout behaviour. This highlights both a large causal effect of parental income on education attendance, and an alarming consequence of labour market displacement that has received little attention to date. I also find that transitory shocks to parental income, unrelated to job loss, have little effect on the education attendance of youth. This suggests that temporary parental credit constraints are not a significant determinant of education attainment. There is a large literature on the relationship between family background and education at-tainment, but studies attempting to identify the causal effect of parental income on attainment are rare. Several of the available studies employ within-family variation in income over time only in identification, and find little evidence of a causal effect. If most of this variation in income is temporary, it may hamper the ability of these studies to identify the underlying causal effect of parental income on attendance, as families may be able to smooth temporary income variations. My analysis separates out more persistent parental income shocks, and finds that only these more persistent shocks affect education attendance of youth. This is a considerable contribution to the literature on parental income effects on education attainment. In Chapter 3,1 estimate the effect of tuition increases and potential rationing of places at post-2 secondary institutions on the education attendance of youth. I focus on the effect of tuition in-creases and rationing on the equality of access to university and community college education. Tuition increases may have competing effects on post-secondary access. Increases may lower de-mand for post-secondary education, particularly among low income youth as they are least able to pay. Tuition increases may also increase supply of post-secondary places, as institutions have more revenue available given government support levels. I find that tuition increases lowered the uni-versity attendance of youth from low income backgrounds considerably, while youth from middle and high income backgrounds were less affected. I also find evidence that increased rationing of university places, related to increases in the size of the high school graduating class (cohort size), also lowered the attendance of low income youth more than it did the attendance of middle and high income youth. I employ the Canadian Survey of Labour and Income Dynamics (SLID) in the empirical analy-ses of both Chapters 2 and 3. This data provides a rich source of longitudinal information on families and the education outcomes of youth, including information on job losses and accurate (tax record) measures of parental income. The data covers the period from 1993 to 2001, a time of considerable variation in tuition levels at the post-secondary level across provinces in Canada. There is a large literature on the effect of tuition on post-secondary education attendance in the United States, but a much smaller one in Canada. My analysis is the first in Canada that employs accurate information on parental income. A number of the US studies, however, employed cross-sectional variation across US states in tuition fees only, and may not have adequately controlled for cross-state differences in unobserved characteristics of education opportunities. In addition, the recent Canadian experience of a sharp contrast in tuition changes across provinces provides the data variation necessary to identify effects. My research should thus provide a more accurate estimate of the true tuition-attendance relationship than the majority of prior studies. In addition, my research on attendance inequality includes an analysis of the effects of potential rationing of post-secondary places on attendance. The effects of cohort size and government funding of education institutions have vastly been ignored in prior analyses of inequality in education outcomes. The final component in my dissertation (Chapter 4) turns to an analysis of high school gradua-tion probabilities for individual youth. A strong relationship between family background and high school education outcomes in the United States and Canada in particular is also well documented. Youth from more wealthy backgrounds have higher measures of school achievement and are more 3 likely to graduate. There is considerable debate on whether schools themselves can actually affect student outcomes such as these. A well-known example of the depth of the debate in the United States is provided by the exchange between Krueger (2003) and Hanushek (2003). The volumi-nous empirical evidence on the effects of the measurable qualities of schools (pupil-teacher ratios, spending) and teachers (education and experience) on student outcomes is somewhat mixed. Analyses focussing on only the measurable qualities of schools and teachers may miss signif-icant effects of schools on student outcomes. A recent example is the work of Rivkin, Hanushek and Kain (2005). In this study, the authors identify a significant impact of individual school teach-ers on achievement gains of elementary school students in Texas. This observed heterogeneity in teacher quality was not necessarily related to the measurable characteristics of these teachers, such as their education and experience beyond the initial year of teaching. In Chapter 4, my co-authors and I continue along this new line of inquiry by identifying the effect of individual school prin-cipals on the high school graduation rates of youth. The analysis is completely separate from the first two analyses in the dissertation (Chapters 2 and 3), and is co-authored with David Green and William Warburton1. It is the first study we are aware of that estimates the effect of individual school principals on high school graduation rates. To identify the effect of school principals on graduation rates, we employ a unique adminis-trative data set of individuals entering grade 12 of public high schools in the province of British Columbia from 1991 to 1996. High school principals were regularly rotated across schools by school districts over this period, and many principals both entered and left the public school sys-tem. We employ this variation (principal turnover) to separate the effect of individual school principals on graduation rates from the effect of schools themselves and the neighbourhoods they draw their students from. We find that school principal quality is quite heterogeneous, with some principals having considerably better success than others in promoting high school graduation in their schools. A one standard deviation increase in the quality of school principal can raise the graduation probability of youth by 4 to 5 percentage points (from an average graduation rate of 81 percentage points). We linked the school administrative data to British Columbia Income Assistance records for individual families using a matching algorithm. From this link we can identify youth from families that have relied on welfare or social assistance payments from the province in the past. Youth from 'My role in this piece of analysis is described in the Co-authorship Statement provided above. 4 such family backgrounds have much lower high school graduation probabilities than youth from non-welfare households. We analyze whether individual school principals have a more marked effect on the graduation probabilities of these "at risk" youth, and find evidence suggesting they may. I provide some concluding remarks in Chapter 5, drawing together the separate analyses of the thesis. I also outline several areas for further research that the work in this thesis directly leads to. 5 CHAPTER 2 Parental Income Shocks and the Education Attendance of Youth 2.1 Introduction Education attainment is a significant determinant of an individual's economic well-being. The wage premium paid to university educated workers is large and has risen in North America over the past several decades. If opportunities for obtaining a university education are related to parental income, rising university wage premia may lead to increasing levels of intergenerational income inequality. There is overwhelming evidence that education attainment is positively correlated with the income levels of parents (see Section 2.2 for details). Youth from families with high income earning parents are much more likely to attend university (four year college) in both the United States and Canada. This correlation may not reflect causality, however, if there are characteristics that affect both parental income and the education attainment of youth. These characteristics may include genetic ability, diligence, mental health, addictions, dependability, culture and individual preferences. Government policies intended to alter parental income levels may not have the desired effect on youth education outcomes if the relationship is not causal. Parental income may directly (causally) affect post-secondary education attendance in at least two ways. Transfers from parents may assist youth to finance post-secondary education attendance. In addition, parental income may be spent on investments in child learning outcomes at the ele-6 mentary, secondary and pre-school levels, increasing the preparedness of youth for post-secondary study. Several recent studies (Shea (2000), Mayer (1997), Levy and Duncan (2000), Blanden and Gregg (2004)) have concluded that the causal effect of parental income on education outcomes is small or even zero. These studies have employed a variety of techniques to identify causal effects. These techniques often use movements in parental income over time within families for identifi-cation. Many such income movements may only be temporary, hampering the ability to identify the underlying causal effect of parental income on attendance. Families can smooth spending over time, in accord with the permanent income hypothesis. They can borrow or run down savings in response to temporary reductions in income to maintain consumption levels. One method to overcome this identification problem is to separate out parental income shocks that are persistent, and to examine the effect of these persistent shocks on education attendance. I take this approach to identification in this chapter. I employ parental job loss to identify persistent negative income shocks. Jacobson, LaLonde and Sullivan (1993) and others have clearly illustrated the persistent negative effect that job loss has on income levels. I define job loss as job ends due to permanent layoff (redundancy), employer business failure or employer dismissal. I employ data on individual youth from the Canadian Survey of Labour and Income Dynamics (SLID) over the 1993-2001 period in my analysis. The particular advantage of this data set is the ability to measure parental income shocks, and then to analyze the effect of these shocks on the subsequent annual education attendance outcomes of youth. I focus on shocks that occur at the time of normal high school completion, when youth are 16 to 18 years old. Education outcomes of youth are then analyzed from age 16 up to age 19 or 20. At age 16, the vast majority of youth are still in high school, and have yet to make their own decisions regarding education attendance. By age 19 or 20, the vast majority of youth have had the opportunity of acquiring the pre-requisites for university entry. The information required for this analysis does not co-exist in the major representative micro data sets employed to analyze the education decisions of youth in the United States. The Panel Study of Income and Dynamics (PSID) does not have detailed year to year education enrolment information for young adults. The National Longitudinal Study of Youth (NLSY) does not collect annual parental income and labour market outcome information for all youth of school-leaving age, as no parental information is collected for youth who leave the parental home. To my knowledge, 7 there exist no studies of the effect of parental income shocks, particularly persistent shocks caused by job loss, on the immediate subsequent education attendance outcomes of youth. To identify the causal effect of parental income on education attainment, it is important to con-trol for those attributes of parents that affect both education attainment of children and parents' own labour market outcomes. I estimate standard discrete choice models of post-secondary edu-cation attendance controlling for a large number of parental, family and individual characteristics. I find that persistent negative parental income shocks attributable to exogenous job loss have sig-nificant negative effects on university attendance. A persistent ten thousand dollar drop in annual parental income lowers the probability of a youth attending university by approximately six per-centage points. A temporary drop of the same magnitude has no effect. This evidence points to an alarming outcome of labour market displacement that has received little attention to date. The finding that these income shocks affect education attendance, even after controlling for parental education and average income levels, provides strong evidence that parental income has causal effects. It also points to the existence of significant financial constraints on attendance, and the importance of transfers from parents in the education attendance decision. These negative effects occurred despite the availability of government-subsidized student loans for youth from low income families. If credit constraints alone precluded youth from attending, parental income shocks that occur at the time of high school completion should not affect attendance when loans are available. Individual investments in higher education are risky, and individual preferences for assuming large debt loads at young ages may be quite heterogeneous across the population. Many youth may be averse to borrowing large amounts to invest in their own human capital even if the expected payoff appears large. There are several risks involved, including course completion risk and wage premium risk. Relaxing borrowing constraints may not be sufficient to ensure all youth can attend post-secondary education. In addition to the standard discrete choice models of post-secondary education attendance dis-cussed above, I estimate a model of the complete set of annual education outcomes for youth from age 16 to age 19 or 20. Each annual education transition is analyzed to determine whether shocks lead to immediate high school dropout behaviour or have lagged effects on university or commu-nity college entry. The full set of education transitions are analyzed in a framework that imposes the natural sequential constraints on education attendance. For example, youth must first complete 8 high school to attend university. In particular, I estimate a full year-to-year age and grade tran-sition model using the technique employed by Cameron and Heckman (2001). The longitudinal data I employ is ideal for estimation using this technique, and including parental income shocks is a considerable extension of the Cameron and Heckman analysis. The results show that persistent parental income shocks measured by job loss lead to both increased high school dropout behaviour and to lower rates of university entry even for those youth who complete high school. One concern with my identification strategy here is that job loss itself may reflect unobserved characteristics of parents that also affect the education decisions of youth. The grade transition model estimates provide a direct test of the exogeneity of parental job loss, providing further evidence that I am uncovering a causal effect of parental income. I include job loss shocks that occur after an education outcome is observed into the estimated model to control for any potential unobserved parental characteristics related to these shocks. These additional shock measures were not statistically significant, and their inclusion did not change the estimated negative effects of the correct job loss shocks on education outcomes. My contribution to the literature here is a clearer identification of the causal effect of parental income on the education attendance of youth. I employ exogenous parental job loss to identify per-sistent negative parental income shocks, and show that these persistent shocks have considerable negative effects on education attendance. Temporary parental income shocks do not affect atten-dance. I identify the pathways by which parental job loss affects education attendance, including early high school drop-out behaviour and reduced university attendance even for youth that com-plete high school. I also show that the parental job loss shocks I employ are truly exogenous. The outline of the chapter is as follows. A review of the relevant literature is provided in Section 2.2. An economic model of the education decisions of youth that focusses on the role of parental income is described in Section 2.3. A description of the Canadian post-secondary education system is provided in Section 2.4. The SLID micro data set is described in Section 2.5. Standard reduced form estimates of the effect of parental income shocks on the post-secondary education attendance of youth are presented in Section 2.6. The full year-to-year grade transition model is discussed in Section 2.7, along with simulations of the effect of parental job loss on education attendance. Section 2.8 concludes. 9 2.2 The Literature The relationship between parental income and the education outcomes of youth has received con-siderable attention in social science and public policy research. Education attainment is strongly related to family background in the vast majority of countries. Shavit and Blossfeld (1993) docu-mented this relationship for 13 countries, including the United States and Canada. There is a vast US literature on the determinants of the education attainment of youth. Many examples are given in the survey of Haveman and Wolfe (1995). Duncan and Brooks-Gunn (1997) compile twelve studies of the consequences of growing up in poverty in the United States on youth outcomes. One of the main conclusions drawn from this research is that parental income is positively associated with the education attainment of their children, but the measured effect varies from study to study and is not always economically large. Recent research has been concerned with identifying the causal effect of parental income on educational attainment. Shea (2000) attempts to identify the causal effect of father's income on the completed years of education of young adults in the United States. He employs job loss, union status and industry of employment of parents as instruments for parental income in a two stage instrumental variables procedure. Variations in long run average parental income caused by what Shea considers as "luck" rather than ability were thus employed to uncover causal effects. Results employing ordinary least squares showed a significant effect of father's income on education levels. The two-stage estimates showed no causal effect, however, except if the father has low education. In this study, I employ job loss as an indicator of a persistent parental income shock rather than an instrument for long run average income levels. I also observe the immediate effect of shocks on education attendance rather than looking at completed years of schooling by individuals in their mid-twenties. Mayer (1997) employs several strategies to identify the causal effect of parental income on a large set of outcomes of US children and youth, including education attainment. One of the strategies she employs rests on including a measure of parental income received after the youth's educational outcome as a control for the unobserved characteristics of parents affecting both in-come and youth outcomes. This strategy resulted in only a small causal effect of parental income on years of schooling by age 24 being identified. Another strategy employed by Mayer was to use variations in income caused by changes in US state welfare rules, and again finds only small 10 parental income effects. Mayer did find a significant negative effect of parental income shocks measured by year to year income drops of 35 % or more on years of schooling. Levy and Duncan (2000) employ a siblings fixed effects strategy to control for unobserved parental characteristics in an attempt to identify causal parental income effects. They find small causal effects of income during childhood and adolescence. Both this study and Mayer's employ variations in income within families over time to identify causal effects. If most income variations within families are temporary, and the effect of these temporary variations on spending are able to be smoothed by families, it is not surprising that small causal effects were found. Acemoglu and Pischke (2001) employ a quite different empirical strategy to estimate the causal effect of parental income on the education attainment of youth. They use changes in the distribu-tion of wages over time to identify the causal effect of parental income on US college enrolment. Their procedure involves conditioning on the income quantile or rank of the parent, which should control for unobservable characteristics of parents affecting both their income and their children's education outcomes. The authors find significant causal effects of parental income using this strat-egy. Mayer (1997) also analyzed the impact of changes in income inequality on the education enrolment rates of youth from different income backgrounds over time. Cameron and Heckman (2001) estimated a sequential age and grade transition model of ed-ucation attainment using data from the NLSY for US youth. A statistically significant effect of parental income on college attendance was found in initial estimates. Once the model was ex-panded to include Armed Forces Qualifying Test (AFQT) scores, however, parental income no longer had a statistically significant effect. The authors interpret this finding as evidence that short term liquidity constraints play no significant role in college attendance decisions and claim tuition subsidies should have no appreciable impact on inequality in college attendance. Early learning outcomes are much more important (raising AFQT scores), so policies aimed at earlier youth out-comes will have a larger effect on inequality in education attainment. I employ the Cameron and Heckman estimation strategy in Section 2.7, but do not include test score information. I instead include measures of parental income shocks, which Cameron and Heckman were not able to do with their data set. Keane and Wolpin (2001) also show that the parental income-education attainment relationship is compatible with a model where borrowing constraints have little impact on college attendance. Borrowing constraints do, however, have a large effect on hours of work and consumption levels 11 while youth are in college. The authors argued against including AFQT scores in estimation. Test scores may actually reflect future expected borrowing constraints, as effort while in high school (which increases AFQT scores) may be related to future education opportunities. Keane and Wolpin (1997) found that college tuition subsidies can change behaviour in high school, increasing high school attendance rates. Using Canadian data, Corak, Lipps and Zhao (2004) analyzed the relationship between family income and attendance of youth at universities and community colleges with information from the Survey of Consumer Finances (SCF) and the General Social Survey (GSS).1 Family income and university attendance are strongly related, but there was no evidence of a strengthening in this relationship in Canada as a whole over the late 1990s. This study updated the results of Bouchard and Zhao (2000) using the GSS for 2001. The relationship between parental socio-economic status and education attainment did strengthen from 1986 to 1994 in the GSS data. No attempt was made to identify the causal effect of parental income on education attendance in these studies for Canadian youth. The SLID micro data has been employed by several researchers to analyze particular aspects of the post-secondary education decisions of Canadian youth. Frenette (2004, 2005a) highlighted the negative effect of distance from the family home to the closest university and college on attendance. Frenette (2005b) analyzed whether post-secondary education access is more equitable in Canada than in the United States. He uses the NLSY97 data for the US estimates and the SLID for Canada. He finds that access is more equitable in Canada in the late 1990s, with the relationship between parental income quartile and university attendance being much stronger in the United States than Canada, even after controlling for parental education and other individual characteristics. Knighton and Mirza (2002) and Drolet (2005) analyzed the simultaneous effects of parental education and parental income on attendance at post-secondary education institutions. None of these studies analyzed the effect of parental income shocks on education attendance. 2.3 Economic Model of Education Attendance Decisions The following economic model of education choice is described in order to motivate my empirical analysis. In line with standard human capital theory, youth are assumed to make an economically 'The analysis using the SCF updated and improved upon earlier work by Christofides, Cirrello and Hoy (2001). 12 rational decision on whether to undertake further study by weighing expected benefits against costs. Expected benefits of higher education include higher salaries, more interesting work, higher occupational prestige, and perhaps utility directly from studying. Costs include direct outlays such as tuition, books, supplies, and potentially the higher costs for traveling and living away from home. A major indirect cost is the income forgone while studying. Parents often assist their children in their education investments by providing financial support for direct education expenses and living costs. A major potential constraint on youth attaining their individually optimal level of education is the incompleteness of loan markets for funding education investments. Private lenders are gener-ally unwilling to lend to youth to finance education, as human capital cannot be repossessed by lenders if default occurs. Returns on educational investments are also uncertain, particularly as they depend on the effort of individuals both during study and during their working lives. Govern-ments and even individual education institutions often provide student loans (or loan guarantees) and some non-repayable grants to students from low income households to minimize this loan market incompleteness. 2.3.1 The Youth's Attendance Decision A partial equilibrium discrete-choice model of the post-secondary education (PSE) attendance decision is considered. This model closely follows Keane (2002). A model with no borrowing constraints will be discussed first, with constraints then added. The features of the model are as follows. (a) Agents live for an infinite number of discrete time periods. (b) Agents have per period preferences over consumption c and leisure I, represented by u(c, I), concave in both arguments. (c) Agents are endowed with L units of time each period, so 0 < I < L. (d) In period 1, agents decide whether or not to attend PSE. Tuition costs are r, while studying requires s units of time. Agents receive direct utility from attendance of (p. (e) In period 1, agents can choose to work any feasible h > 0 units of time at wage rate w\. They also receive a transfer payment y i from parents. 13 (f) In every other period, agents inelastically supply one unit of time to work. The discount factor on future periods is (3 = 1 / ( 1 + p). If the agent attended PSE in period 1, they earn wage W2 + TT each period. If not, they earn iy 2. (g) Agents can choose to borrow any amount b in period 1. From period 2 on, they make fixed annuity payments of rb on the loan (6 can be negative). Lifetime utility of an agent who attends PSE is: oo Vs = m&xu(yi + wih + b — T, L - h - s) + (j) + 'S~]fflu(w2 + 7T — rb, L — 1 ) {hfi} .=1 = maxi t^ i + wih + b — T,L — h — s) + (j> + p~1u(w2 + 7r — rb, L - 1) (2.1) {h,b} Thus our infinitely lived agent model reduces to a two period model, simplifying the analysis considerably. Lifetime utility for an agent who chooses not to attend PSE is: VQ — maxw(j/i + w\h + b, L — h) + p~1u(w2 — rb,L — 1 ) (2.2) {h,b} These two maximization problems can each be solved for optimal work hours h and lending b, subject to 0 < I < L . 2 Assuming an interior solution for work hours (denoted hs and ha for attenders and non-attenders respectively), the point of indifference between attending and not attending (Vs = VQ) is used to construct an approximate decision rule for PSE attendance. The agent chooses to attend PSE if: - + — ^ T + WIS (2.3) r uci0 The term uc\Q is the marginal utility of consumption in period 1, evaluated at the consumption level given non-attendance. Equation 2.3 highlights the trade-off between the benefits of higher education (wage premium ir plus direct utility (f>) and the costs of tuition r plus income foregone (wis). The direct utility from PSE attendance (f> is appropriately weighted by the marginal value of an extra dollar of consumption. The expected wage premium TT and the utility of attendance <fi can be treated as unobserved random variables. Such treatment generates a random utility model. Some agents may have very large dis-utility from attendance, if the effort required to complete studies is considerable. These agents may choose not to attend even when the average monetary payoff is expected to be large. 2Optimal levels for these two decisions will not necessarily be the same for attenders and non-attenders. 14 In this model with no borrowing constraints, the only role for parental transfers in the atten-dance decision is via the direct utility from attendance. Raising y\ lowers ucia given decreasing marginal utility, raising the relative benefits of attendance.3 Note that parental transfers here are not contingent upon the youth choosing to undertake further study. Contingent transfers will be discussed below. Now consider the case where there are borrowing constraints in period 1. Agents cannot borrow in period 1 unless they choose to study. There is also a limit on borrowing given attendance of some fraction 9 of the costs of studying (tuition level r plus wages foregone wis). Consider the case where the constraint binds, and all students borrow the limit.4 Also, assume non-students are constrained to borrow nothing. The borrowing constraint for non-students will be binding if: Uclo > - U c 2 o P (2.4) Here, uc2o refers to the marginal utility of consumption in all periods after period 1. Solving for optimal work hours, and again working from the point of indifference Vs = VQ, the approximate decision rule is now: 7T r ruc2o pucio + — > 0(r + tois) ruc2o puclo + (l-e){r + wlS) (2.5) If the borrowing constraint is binding on PSE attenders, the term in the square brackets is nec-essarily less than one. Taking the simplest case where direct utility from attendance <fi is zero, the presence of borrowing constraints makes it less likely that agents will choose to attend. The left hand side of the inequality in equation 2.5 is reduced more than the right hand side.5 Increas-ing parental transfers y\ will increase the term in square brackets towards unity, mitigating the borrowing constraint and making attendance more likely. If parents choose to make a transfer ys contingent upon their child attending PSE, it directly lowers the cost of attendance, just like a tuition subsidy or a government grant. The decision rule is altered as follows. 7T r ruc2o pUdo ruc2o PUdo + (1 - 6)(T + wlS) (2.6) 3 If the agent has dis-utility from university attendance (<j> < 0), higher parental transfers will result in a lower probability of attendance. Thus extra income assists the agent in avoiding this dis-utility. 4 I f the constraint does not bind, the problem collapses to the case above. 5 If all PSE costs (r + wis) could be borrowed, attendance may be more likely if <j> is positive. 15 2.3.2 The Parental Transfer Decision I now extend the Keane (2002) framework to analyze the parental transfer decision. If parents obtain some discrete increase in their own utility if their children attend PSE, contingent transfers will be rational. Parents may pay their children's tuition, but not give the same amount of money to a child who chooses not to attend. High income parents are able to absorb education costs while still benefitting from children attending. Parents with less income or who suffer negative income shocks may not be able to fund their children's studies without too large a reduction in their own consumption. To illustrate the parental decision on transfers to children, I begin by defining the following indicator function. { 1, if child attends PSE 0 , if not attend PSE attendance is a function of the contingent transfer ysit, where the transfer occurs to child i in time period t, the time period the child attends. Parents will optimally make transfers just large enough to induce a child to attend. Parents make no transfers to children who do not attend (Usit = 0 ) . There are no purely altruistic non-contingent transfers here for simplicity, but including them does not alter the model's predictions. Parents are assumed to live for T periods, and to have I children.6 The maximization problem of the parents can be written as follows, assuming parents can borrow and lend freely at interest rate r. VP = m a r / Y^^u(cpt)+ £/~21isi\y^t] (2.7) ij/ait}t = l,i = l t=\ 1=1 {Cpt,Va Subject to: T / I \ T E y * " E V* / ( l + r) ' > J2 W ( l + rf (2.8) i= l \ t=l / t=l The variable Ypt denotes parental income in period t, and is assumed to be exogenous. It can include labour income, government transfers, gifts, inheritances, in addition to income from assets, including liquidation of such assets. The parameter e denotes the discrete increase in parental utility from a child attending PSE. If the rate of time preference B equals 1 / ( 1 + r) , parents will smooth own consumption to be an equal amount cp each period. n cp = r 1 1 + r t=i \ i=i 6The number of children is assumed exogenous here, as modeling fertility is beyond the scope of this analysis. The number of time periods T can also be infinite as for youth. 16 Parents optimally make positive contingent transfers if the reduction in utility from reduced own consumption is less than e. If there is only one child in the family (I = 1), the problem is straightforward. An approximate decision rule is for parents to make contingent transfers if the following condition holds. e>v!{cp) (7^7) Vsit (2-10) Parents with more income, and thus higher Cp, are more likely to make such contingent trans-fers, given concave utility in own consumption. If there is more than one child, parents may no longer fund all their children through PSE. The probability of attendance, given parental income, may be lower for each child in a larger family, thus family size may affect education attainment.7 If parents suffer some income shock, its effect on the PSE attendance of their children will depend on whether the shock is expected to be temporary or persistent. Families may overcome temporary shocks by borrowing or running down savings. For example, say parents expect income to be a constant amount Yp each period over their working life of T periods. Then a negative shock to income occurs of an amount d in period td, prior to the child attending PSE and potentially receiving transfers from parents. The effect of this shock on the decisions of parents will depend on how long they expect the negative shock to last, that is, how many periods will income be Yp — d rather than Yp. Given no change in transfers to children, the new optimal level of smoothed consumption for the parents cp will be lower after the income shock. Parental consumption will be reduced a small amount if the income shock is expected to only last one period, as parents smooth the effect of the shock over the remaining periods of life. It will be reduced a significant amount if the negative shock is expected to last many periods, as remaining expected lifetime income will be significantly lower. Parents will then re-assess their optimal level of transfers to their children. If the reduction in optimal own consumption is large, the marginal utility of own consumption u'(cp) will rise considerably, given a concave utility function. This makes it less likely that equation 2.10 will hold, and thus less likely that parents will pay for their children's post-secondary education. If parents cannot borrow freely over time periods, and they have not accumulated savings prior to the shock, then even shocks which are expected to be temporary may affect the education attendance 7Which children attend PSE in a family may depend upon the individual preferences or abilities of children for education. Parents may also choose to send the eldest first, and keep sending children until it is no longer optimal to do so. Parents can brag earlier and longer when the elder children attend, so birth order may also determine attendance. 17 of their children. If the negative shock occurs right at the time that the youth would normally enter post-secondary education, parents may be unable to make transfers at that time, which may delay post-secondary entry. The important prediction of this education attendance decision model is that parental income shocks may affect transfers to children, and thus their post-secondary education attendance. Shocks that are expected to be persistent should also have larger effects on attendance than shocks that are only expected to be temporary. In my empirical analysis to follow, I employ job loss as an indicator of a shock that is expected to have persistent negative effects on income. Such shocks may have significant negative effects on youth's education attendance, if parental transfers (and thus parental income) is important in financing youth's post-secondary education attendance. Other observed income shocks, unrelated to job loss and thus potentially only temporary, may have much less significant effects on attendance. 2.4 The Canadian Post-Secondary Education System The vast majority of universities and community colleges in Canada are publicly financed and reg-ulated. Provincial governments provide the majority of funding to these institutions, particularly for the educational component of their operations. If desired, they can also exercise control over tu-ition fees and enrolment levels at publicly-financed institutions. The Canadian Federal government also provides funding to post-secondary education institutions, but mostly to support the research component of their operations. The Federal government also provides funding directly to students, via student loans (or loan guarantees) and scholarships. Funding from other sources, such as en-dowments, private bequests, commercial operations, etcetera, is small for Canadian institutions.8 Universities in Canada are degree granting institutions, with most degrees requiring four years of study (for example, a bachelors degree). Entrance to university requires twelve years of study at elementary and high school in most provinces. In the province of Quebec, however, youth must complete two years of study at a CEGEP after grade eleven of high school.9 The majority of universities in Ontario required a thirteenth year of high school study for university entrance in that province. This requirement was lifted in 2003. Community colleges in Canada do not generally 8Around 13% of university revenue and 8% of community college revenue is from these other sources. 9The Quebec community college system, college d'enseignement general et professionel. 18 grant degrees. They grant certificates and diplomas for studies which take one to three years of full-time study to complete in most cases. I denote community college, CEGEP and trade school study as "other" post-secondary education, and it is a lower level of education attainment than a university bachelors degree. Universities and community colleges in several Canadian provinces increased tuition markedly over the 1990's, particularly in Ontario, Alberta and Nova Scotia. Tuition fees were deregulated in several provinces, while Quebec and British Columbia instituted tuition freezes over this period.10 Movements in average real tuition levels at universities and community colleges in Canada are illustrated in Figure 2.1. University tuition levels in many provinces are approaching the average tuition at public four year colleges in the United States. Provincial government funding of higher education remained stagnant or fell in real terms over the 1990s, as did government funding of most expenditure categories. See Figure 2.2 for movements in average provincial funding of PSE institutions in Canada. Aggregate enrolment at PSE institutions in Canada stagnated over the 1990s but did not decline. See Figures 2.3 and 2.4 for movements in university undergraduate and community college enrol-ment rates over time respectively. Overall education attainment of Canadian youth does not appear to have been negatively affected by the tuition increases and the stagnation in public support for PSE. The main sources of loans and non-repayable grants for post-secondary education students in Canada are the Canadian Student Loan Program (CSLP) and Quebec's Aide financiere aux etudes program. Eligibility for financial aid under both programs is based upon parental income, family size, place of residence and direct education costs (particularly tuition). These loans are subsidized by the government." Only youth from families in the bottom half of the parental income distribution can access any loans from these programs. In the application process, potential student borrowers must provide information on their parent's income, usually from the previous year's tax return. The more parents earn, the amount that youth can borrow from these programs is reduced on an increasing percentage basis. 1 "British Columbia lifted the freeze in 2002, while in Quebec, tuition has still not increased since the mid-1990s. "The subsidy takes the form of no interest being payable on the loans until the student leaves full-time study. There are also provisions in place for loans or loan interest to be written off in the case of severe financial hardship. 19 Figure 2.1: Real Tuition 2000/01 $CAN $3 ,500 $3,000 -$2,500 -$2,000 $1,500 $1,000 $500 $0 - i — i — i — i — i — r - i — i — i — r 1 1 1 1 1 1 1 ] 1 — | — | — I — | — i — | — | — 1 — ! 1970-71 1975-76 1980-81 1985-86 1990-91 1995-96 2000-01 Sources - University tuition provided directly by Statistics Canada's Centre for Education Statistics. Community college tuition taken from statistics reported by the Manitoba Council on Post-Secondary Education. Figure 2.2: Provincial Spending on PSE in Canada 2000/01 $CAN, per person aged 18-24 $3,000 -i 1960 1966 1972 1978 1984 1990 1996 2002 Sources - Provincial spending measures taken from Cansim II tables 478-0007 and 478-0004. Population aged 18-24 taken from Cansim II table 51-0001. 20 Figure 2.4: Full-time Community College Enrolment percent of population aged 18-21 28.0% 24.0% 8.0% •Males - Females 0 " 1 — i — 1970 1975 — i — | — | — | — | — | — | — | — | — | — | — i — | — | — | — i — i — i — i — i — r 1980 1985 1990 1995 2000 Sources - Enrolment taken from Statistics Canada's Cansim cross-tabulation files and from the Education Matters publication. 21 Between 40% and 50% of Canadian community college and university bachelors graduates have student loan debts at the end of their studies. Finnie (2001) provides more details of Canadian student loans.12 Many universities also provide scholarships and bursaries directly to students. This type of support has increased in the 1990s as tuition fees have increased. 2.5 T h e Data 2.5.1 Features of the Survey The Survey of Labour and Income Dynamics (SLID) is a household-level longitudinal survey of Canadians. Approximately 15,000 Canadian households are chosen for inclusion in the Survey every three years. Once a household is chosen for inclusion, all members of the household at that time are interviewed annually for six years, even if they leave the original household at any stage during the period.13 Interviewing survey respondents annually irrespective of where they live is especially important for this study, as youth completing high school may leave the parental home to either work or study. This analysis requires information on the education attendance decisions of youth at the end and following high school. Youth who leave the household are followed to their new residence and surveyed in the same manner as youth who remain in the parental home. The second major advantage of the SLID micro data for this study is the availability of information on the income and labour market outcomes of parents for each year. I employ this information to construct indicators of major parental income shocks over the period when the youth are deciding upon their post-secondary, education attendance. Having both measures of parental shocks and yearly education enrolment information on youth is a particular advantage that the SLID micro data has over the major representative micro data sets employed to analyze the education decisions of youth in the United States. The Panel Study of Income Dynamics (PSID) does not have detailed yearly education enrolment information for l 2Thcre was a shift towards more student financial aid being provided in the form of loans rather than non-repayable grants over the 1990s in several Canadian provinces. The Federal Government has moved in the opposite direction to some degree, with scholarships being provided to students who are both in need and do well in the first year of university study under the Canadian Millennium Scholarship Fund program. This program started disbursing funds to students in 2000, right at the end of my data period. Quebec remains as the one province that provides significant funding to PSE students via non-repayable giants, but these grants are made to the lowest income youth only. '^Individuals who enter a household where a SLID longitudinal respondent resides during this six year period are also interviewed, but are not longitudinal respondents and are not included in this analysis. 22 young adults. The education questions are not very detailed for household members who are not the household head. The National Longitudinal Study of Youth (NLSY) does not collect annual parental income and labour market outcome information for all youth of school-leaving age. In particular, detailed parental income and labour market information is not collected for youth who leave the parental home. The three longitudinal surveys of high school leavers sponsored by the US National Center for Education Statistics (NCES) also do not have parental income and labour market measures beyond a single base year questionnaire. These three surveys are: the National Longitudinal Study of the High School Class of 1972 (NLS-72), the High School and Beyond Sur-vey (HSB-80), which started with high school seniors and sophomores in 1980, and the National Educational Longitudinal Study (NELS-88), which started with a class of 8th graders in 1988. The first longitudinal panel of the SLID runs from 1993 to 1998. The second panel runs from 1996 to 2001. Outcomes for youth from panels one and two are analyzed here.14 In this analysis, youth will first be observed at age 16, when they are still in high school, prior to making their own decisions on education attendance. At this age, the vast majority of youth still live with at least one parent (around 98%). Accurate parental information is thus obtained for almost all youth. I observe the education outcomes of the sample of youth from age 16 until age 19 or 20. By these ages, most Canadian youth have had the opportunity to obtain the education pre-requisites for university and college acceptance. The majority of individuals who attend university and com-munity college begin their attendance by this age. The rate of initial entry into post-secondary education falls considerably after this age. I follow youth from Ontario and Quebec the extra year (age 20) as it takes one more year of study to obtain the pre-requisites for university entry, as de-scribed above. As a result, Quebec and Ontario youth aged 15 or 16 at the start of each panel, and those aged 14, 15 or 16 in the remaining eight Canadian provinces, are included in the analysis. Af-ter exclusion of observations with missing information due to panel attrition and missing measures (item non-response), the final sample I employ covers 1,335 individual youth, from a potential sample size of 2,909. See Appendix A for details of how the final sample was constructed. 1 4 A third panel was begun in 1999. Access to the full SLID data was made possible via the British Columbia Interuniversity Research Data Centre (BC1RDC) at the University of British Columbia. 23 2.5.2 Main Measures Employed in the Analysis Attendance rates for the final sample I employ are presented in the first column of Table 2.1. Overall, 30% attended university, 35% attended other post-secondary education (PSE) only (not university), while the remaining 35% did not attend any PSE within this period. Attendance is defined as any amount of attendance from age 16 to age 19 or 20, as the objective here is to identify access to education opportunities.15 The next three columns of this table present attendance rates for youth from low, middle and high parental income backgrounds. See Appendix B for details of how these parental income quantiles were constructed. Note the strong relationship between parental income and university attendance, but no real relationship between parental income and other post-secondary attendance. These results are consistent with what has been observed by other researchers. Youth from low income backgrounds are much less likely to attend university than other youth. The main objective of this study is to ascertain whether this strong relationship is causal. I employ shocks to parental income to identify causal parental income effects. There is a large amount of volatility in parental income from year to year in my sample, likely capturing both temporary and more persistent income shocks. I calculated changes in parental income for three annual changes and for the change over the entire three year period from when the youth was aged 16 to when the youth was aged 19. Table 2.2 provides percentiles of the distributions of these parental income change measures. Large changes in income can be observed for significant proportions of the sample, both in the annual changes and in the change over the entire three year period. Over ten percent of parents in the sample suffer from a reduction in real (2001 Canadian) income of fourteen thousand dollars or more over the three year period from when the youth is aged 16 to when the youth is aged 19. Year to year reductions of ten thousand dollars or more are also suffered by 10% of the population. I measured parental income by the sum of the total real after tax annual income of the parents the child lives with at age 16. The vast majority of income measures in the SLID survey are taken from tax records, so they should have a high degree of accuracy.16 l5These rates are higher than those depicted in Figure 2.4 as the figures are for current enrolment at institutions divided by the population aged 18 to 21. Not all youth that attend community college attend for this entire 4 year period, thus many youth approaching 21 may already have completed their studies and are thus no longer in the enrolment figures. l6Survey respondents are given the choice of making a self-report of income during a second annual interview in May of each year or allowing Statistics Canada to access their income tax records. Approximately 80% of my sample allow access to tax records at the beginning of each panel, but this rises to 88% by the end of the panel. 24 Table 2.1: Post-Secondary Education Attendance Rates Al l Youth Low Parental Income Middle High University 0.30 0.20 0.28 0.41 Other Post-secondary 0.35 0.32 0.39 0.33 Neither 0.35 0.48 0.33 0.26 Note: 1,335 Observations. Rates measured as any attendance up to second year after normal uni-versity attendance age (age 20 in Quebec and Ontario, age 19 in remaining 8 provinces). Parental income quantiles constructed using average adjusted real parental income over the three years when the youth is aged 16 through 18. In very rough terms, low income youth were those with average 2001 dollar pre-tax annual parental income below approximately $40,000. High income youth were those with parental income above approximately $70,000. Source - Survey of Labour and Income Dynamics. Jacobson, LaLonde and Sullivan (1993) and others have illustrated clearly the persistent effect that job loss can have on income over many years. I employ parental job loss resulting from exogenous factors to indicate persistent negative income shocks in this study. I define parental job loss by a parental main job ending due to: (a) permanent layoff/business slowdown (not caused by seasonal conditions), (b) company going out of business, or (c) dismissal by employer. Only these three reasons for job ends were used to identify job loss. Respondents could identify any of twenty five reasons for job ends, including retirement, finding another job, seasonal job ends, and temporary contract job end. I identified job loss for both the main income earner and the spouse in the youth's family when the youth is aged 16 through 18. Main income earner status was self-reported by parents in the SLID survey.17 Table 2.3 provides summary statistics for these job loss indicators. Significant proportions of parents suffered from job losses. The final column includes measures denoting the average number of youth who suffered from parental job loss at any age from 16 to 18. In the analysis to follow, I find that it is main income earner job loss that is particularly important 1 7For two parent families, 77% of main income earners were male, and 94% of main income earners actually had the higher level of income of the two parents in the family. For lone parent families, 74% of lone parents were female in the sample. Lone parent families composed 15% of the final sample. 25 Table 2.2: Parental Income Changes - Percentiles of Distribution 16 to 17 17 to 18 18 to 19 Change from change change change age 16 to 19 Dollar changes ($000s) 5% -15.7 -17.3 -18.7 -24.1 10% -9.5 -9.6 -10.4 -14.4 25% -2.9 -3.5 -3.5 -4.6 50% 0.2 0.3 0.0 0.8 75% 4.5 4.8 4.4 8.5 90% 11.2 11.8 10.8 19.1 95% 20.5 19.0 18.6 29.9 Percentage changes 5% -40.1 -41.3 -43.5 -55.7 10% -22.4 -22.0 -26.9 -35.6 25% -6.9 -7.5 -8.8 -11.6 50% 0.5 0.7 -0.1 1.9 75% 10.6 10.6 8.6 17.0 90% 25.3 32.1 25.5 46.5 95% 45.9 61.1 52.0 84.9 Note: 1,335 Observations. These numbers represent changes in real (2000/01 Canadian) parental income in thousands of dollars (top panel) and in percentage changes (bottom panel) at the indi-cated points of the distribution of parental income changes. Source - Survey of Labour and Income Dynamics. 26 Table 2.3: Parental Job Loss Prevalence Age 16 Age 17 Age 18 Any age from 16 to 18 Main Income Earner (MIE) 0.091 0.082 0.058 0.110 Spouse of MIE 0.099 0.088 0.070 0.127 Note: 1,335 Observations. These numbers represent the proportion of parents suffering from job loss when the youth is at the indicated age. Job loss is identified as main job ends due to: (a) permanent layoff, (b) employer failure or (c) employer dismissal. I singled out these 3 of 25 possible job end reasons. Source - Survey of Labour and Income Dynamics. in having both persistent negative effects on parental income and large negative effects on the education attendance of youth. Spousal job loss had very little effect on both parental income and the education attendance of youth. Many parents suffer from job losses in more than one year when their child is aged 16, 17 and 18. Of the eleven percent of main income earners who suffered from at least one loss over these years, nearly two thirds suffered from more than one such loss. This may reflect the type of work the parents undertake, or from state dependence in job loss over time. State dependence may occur if a job loser can only find another job that is on average more tenuous. Controlling for parents who suffer multiple job losses is important in the empirical analysis I perform in Section 2.7 below. The persistent negative effects of job loss on income are easily observed in Figure 2.5. The depicted income levels are total annual real after tax income measured in 2001 Canadian dollars for the six years of the SLID panels, for all main income earners in families aged 40 to 59 at the start of each SLID panel. This sample includes more main income earners than in the sample I employ in my main analysis as the data is not confined to parents of youth of school leaving age. The larger data sample was employed here to construct more precise measures of income and the effects of job loss on income. Main income earners suffer significant persistent income declines over the five year period after a job loss. Income remained over $5,000 lower than pre job loss levels five years after the initial job loss, and showed no signs of recovery. Main income earners that do not suffer any job losses over the six years of the SLID panels actually have on average growing real income over the period. These large income declines following job loss are in line 27 with the findings of Jacobson, LaLonde and Sullivan (1993).18 The temporary nature of income changes unrelated to job loss can also be observed in Fig-ure 2.5. I plot the income levels of a particular sub-sample of main income earners that suffered from a decline in income over the first year of each SLID panel of between $5,000 and $15,000 but did not lose a job at this time, or at any time over the length of the panel. For this sub-sample of non-job losers, the large average income decline observed in the second year relative to the first has all but disappeared by the end of the panel. This highlights clearly the temporary nature of most income declines, if those income declines are not related to job loss. The size of income declines resulting from job loss is related to the union status of workers, perhaps reflecting the loss of jobs earning union rents. The income levels over the six years of the SLID panels of main income earner job losers split by union status are plotted in Figure 2.6. Main income earners who were union members to begin with, suffered a job loss and were not employed in a union job by the end of the panels, suffered significant income declines (union status losers). In sharp contrast, union members who found another union job did not suffer any reduction in income over the period (union status keepers). In fact, their real incomes rose over the five years post job loss. Non-union main income earners who suffered a job loss also suffered a significant decline in income over the period, but not quite as large as those losing a union job. In the analysis of the next section, we will see that the effect of parental job loss on the education attendance of youth is much larger for parents with unionized employment prior to the job loss. The effect of job loss on the income levels of spouses, rather than main income earners in families, was much less significant. Annual after tax income was on average only $1,200 lower five years after any initial job loss. This more muted response to job loss can at least in part be attributed to the fact that the average annual level of income of spouses is much lower than main income earner income levels, averaging only $18,000 per year. 1 8Note that parental income fell by on average much larger amounts in the data sample I employ in the analysis to follow than in the larger data set depicted in Figure 2.5. Parental income fell by eighteen thousand dollars (2001 Canadian) on average over the three years following job loss. Main income earner income fell by sixteen thousand dollars itself due to the job loss. Spousal income did not offset the main income earner income decline at all, and even exacerbated it. 28 Figure 2.5: Income Effects of Shocks for Main Income Earners Real 2001 $CAN aftertax income $45,000 $30,000 $25,000 year 1 year 2 year 3 year 4 year 5 year 6 •job losers non-job losers - - - large income decline no job loss $37,000 $28,000 $25,000 Figure 2.6: Income Effects of Job Loss by Union Status Real 2001 $CAN aftertax income of job losers year 1 year 2 year 3 year 4 year 5 year 6 • union status losers union status keepers - - - non-union members Source - Survey of Labour and Income Dynamics. 29 2.6 Post-Secondary Education Attendance Estimates If parental income shocks are correlated with other parental characteristics that affect the educa-tion attendance of youth, controlling for these characteristics is important when identifying causal income effects. As an example of what may be of concern here, job losses were more common in families with less educated parents. As parental education is highly correlated with education attendance, controlling for differences in parental education levels is crucial. The objective in this section is to identify the causal effect of parental income on the educa-tion attendance of youth in a transparent reduced-form framework. I decompose parental income shocks into persistent and temporary components using job loss. The effect of parental job loss on attendance is also broken down by several important characteristics of parents, such as education levels and union status. The effect is also broken down by the gender of youth. In the next section, I estimate a full year-to-year grade transition model. Using those estimates, the effects of persistent income shocks (indicated by job loss) on immediate high school dropout behaviour as well as on eventual post-secondary education attendance outcomes of youth are identified. 2.6.1 The Estimated Model I employ a multinomial logit estimator to investigate the attendance outcomes of youth among the following three options: (a) attend university, (b) attend other post-secondary education (PSE) (non-university) only, and (c) not attend PSE at all. The two-option model of Section 2.3 (attend PSE or not) can easily be expanded to this three-option choice. Youth will choose the option that maximizes their net expected lifetime utility. The choice between university and other post-secondary education will be a function of the higher wage premia paid to university graduates versus community college and trade graduates, and perhaps higher prestige from attending univer-sity. It will also be a function of the higher costs of obtaining a university degree, in terms of higher tuition levels each year, more years of study, and perhaps more effort required to pass courses and obtain the degree. A list of the covariates included in estimation is provided in Table 2.4, along with sample summary statistics. These covariates include measures of parental education, number of children in the family, gender, visible minority status, immigrant status of parents, French mother tongue, city and rural indicators, and indicators of distance to the closest universities and community colleges. 30 I also include a flexible function of real after tax parental income averaged over the three years when the youth is aged 16 to 18. The income function is a three section spline, which includes indicators of parental income quantile (low, medium and high), plus separate linear average income terms within each quantile. The estimated models also include direct measures of tuition fees and university provided financial aid. A description of all the variables employed is provided in Appendix B. As discussed in Section 2.4 above, the main sources of loans and bursaries for undergraduate students in Canada are the Canadian Student Loan Program (CSLP) and Quebec's Aide financiere aux etudes program. Eligibility for financial aid under both programs is based upon parental in-come, family size, place of residence and direct education costs (particularly tuition). Historic eligibility rules were employed to construct financial aid eligibility indicators for each individ-ual in the sample. These measures were not included in the final analysis due to their very close relationship with the individual characteristics already included in the estimated equations. See Appendix D for more information regarding financial aid eligibility indicators. The estimated equations include gender-specific time trends.19 Time trends will account for any changes in average expected wage premia over time.20 Direct utility from education attendance will be a function of the individual ability and preferences of youth. This direct utility is proxied by many of the individual and parental characteristics listed in table 2.4. Note that these characteristics may also affect any individual specific component of wage premia expectations. Usher (2005) finds that individual expectations of the costs and benefits of post-secondary education differ by parental income and education. The opportunity cost of time while studying is proxied by provincial youth unemployment rates, which reflect the probability of obtaining employment if youth do not attend post-secondary education. Empirical evidence suggests that school attendance is counter-cyclical in Canada (see Beaudry, Lemieux and Parent (2000)). Measures of alternative wages such as the minimum wage had no significant effect on attendance probabilities, and were not included in these final estimates. Provincial region indicators are also included in the estimated equations to control for dif-ferences in education systems across Canada. The model was also estimated including the full '^Estimates including gender-specific time dummies in place of linear trends did not change the results to any extent. 20Estimates of contemporaneous average wage premiums were constructed using SLID data, but showed no strong trend over the period under analysis. University premiums were higher for women than men, while other PSE (com-munity college, trades) premiums were higher for men. 31 Table 2.4: Regressors in Model - Summary Statistics Variable Mean Standard Deviation Female 0.488 French mother tongue 0.203 Aboriginal descent 0.028 Visible minority 0.087 Parent immigrant 0.236 Lone parent 0.151 Parents not graduate high school 0.119 Parents other post-secondary only 0.448 Parent completed university 0.190 Real average parental income* 65,930 43,960 Children in family 2.79 1.56 University > 80 km away 0.190 Community College > 40 km away 0.137 Community College tuition* 1,249 679 University tuition* 2,944 770 University financial aid (per student)* 655 272 Observations 1,335 Note: Sources include the Survey of Labour and Income Dynamics and Statistics Canada. Aster-isks (*) denote measures are in real 2000/01 Canadian dollars. 32 set of provincial indicators, but the restriction of including four regional indicators only was eas-ily accepted by the data. By including these regional indicators, the data variation employed for identifying the effects of provincial measures such as tuition fees is within region variation over time, plus across province variation within regions. This model specification relies on there being an integrated labour market in Canada, with a common trend in education wage premia across provinces. Finally, and most importantly, I include parental income shock measures in these estimated education attendance models. These shock measures will capture the effect of unexpected declines in parental income on attendance. If these shocks are expected to be persistent, or if parents cannot access funds to smooth over temporary income shocks, reductions in transfers to children may result, which in turn may lower university and other PSE attendance probabilities. I am already controlling flexibly for average parental income levels in the estimated equations, plus many other background characteristics that affect education attendance. The shock measures should thus pick up the effect of the shocks only, and not merely pick up the effect of characteristics of parents that are more prone to income shocks. 2.6.2 PSE Attendance Model Results Results of multinomial logit estimation of the three option PSE attendance outcomes of youth are presented in Tables 2.5 and 2.6. The marginal effects presented in these tables are the effect of each variable on the probability of attending university and other PSE respectively.21 Standard errors on these marginal effects, reported in parentheses, were corrected for clustering by province and year. Adjusting standard errors for potential clustering is important here as several of the covariates em-ployed, such as tuition, are common to all observations in a province-year cell. Probability weights for longitudinal respondents provided in the SLID data set were employed during estimation. The results for three versions of the attendance model are presented in Tables 2.5 and 2.6. Each version includes one particular measure of parental income shock. In column one, the annual parental income change (in thousands of real dollars) from when the youth is age 18 to age 19 is included. In column two, the change in parental income over the whole period from age 16 to age 2 ' A l l marginal effects were calculated with all indicator variables set to zero and continuous variables set to the values faced by an individual with all indicator variables set to zero (e.g. a male from Ontario turning 16 in 1995). The time trend was set to a value of three, and the children in the family variable was set to three also. 33 19 is included. An indicator of any job loss of the main income earner when the youth is aged 16, 17 or 18 is included in column three. The effect of the individual and parental characteristics on attendance are interesting in their own right. These characteristics are much more significant in predicting university attendance than they are in predicting other PSE attendance. The estimated effects are also little changed by which parental income shock measure is included in the estimates as we look across the columns in Tables 2.5 and 2.6. Looking first at the marginal effects for university attendance (Table 2.5), females are much more likely to attend university than males.22 Youth of aboriginal descent are much less likely to attend university, while visible minorities and youth with an immigrant parent are much more likely.2 3 Having one more child in the family has a small and statistically insignificant negative effect on university attendance. Youth from lone parent families are much less likely to attend university, even controlling for differences in parental income. This negative effect of eleven per-centage points is larger than that found by Ver Ploeg (2002), but is similar to that found by other researchers using information on United States youth.24 Parental education and income levels are strongly positively related to the probability of at-tending university. Parental education has a larger estimated effect than parental income, but both measures are closely related. These results illustrate clearly that university attendance in Canada is a long way from equality, a result also indicated in Table 2.1. Youth from more advantaged backgrounds (higher income, more educated parents) are much more likely to attend university. Changes in community college tuition have a large and statistically significant negative effect on university attendance, while university tuition has a smaller negative effect. These marginal effects represent the impact of a $500 increase in fees in 2000/01 Canadian dollars on attendance.25 This implies a negative cross-price effect from community college tuition on university attendance. It may, however, merely reflect the close correlation in the two tuition measures within provinces. 2 2Note that the marginal effect for the female indicator works through both the estimated coefficient on the indicator itself and the female-specific time trend. The female time trend was set to zero for calculating all marginal effects except for the marginal effect of the female-specific trend itself. In this case the female trend was set at the value of three, the same value set for the overall time trend. 23lndividuals identifying themselves as visible minority are most likely from Asia in Canada, rather than African-American or Hispanics as in the United States. 2 4 Ver Ploeg (2002) found much larger income effects than I have, but her use of predicted income for many indi-viduals may be driving her results. 2 5This is approximately $400 in U.S. currency at 2004 exchange rates and prices. 34 Table 2.5: University Attendance - Marginal Effects Shock Included Income change Income change MIE Job Loss Variable age 18 to 19 age 16 to 19 any age 16 to 18 Female 21.5*** 22.1*** 22.5*** (3.3) (3.5) (3.5) French mother tongue _9 2** _9 4** _9 2** (4.5) (4.4) (4.4) Aboriginal descent -16 9*** -18 1*** (6.0) (5.9) (6.2) Visible minority 15.6 15.6 20.6* (11.4) (11.3) (12.4) Immigrant parent 12.1* 11.8* 10.6 (6.9) (6.7) (6.8) Children in family -0.8 -0.8 -1.1 (1.7) (1.6) (1.8) Lone parent -11.0** -10.9** -11.8** (4.9) (4.8) (5.0) Parents no high school -8.3 -8.2 -9.5 (6.9) (6.8) (7.2) Parents other PSE only 3.5 3.2 3.6 (3.0) (3.1) (3.1) Parent University 35.3*** 34 34 i*** (6.1) (6.1) (6.2) Low parent income -6.9* -6.8* -6.2 (4.0) (4.0) (4.3) High parent income 3.1 3.1 3.5 (3.8) (3.5) (3.9) University > 80 km away -5.0 -5.1 -5.3 (5.7) (5.6) (5.7) Comm. College > 40 km away 3.5 4.1 3.9 (5.9) (6.2) (5.9) Comm. College tuition (+$500) -4.8** _4 9** -5.0** (2.3) (2.3) (2.4) University tuition (+$500) -3.8 -3.6 -3.5 (2.3) (2.3) (2.5) Unemployment rate (+2.5%) -0.9 -0.5 -0.5 (2.2) (2.2) (2.4) University financial aid (+$250) -0.2 -0.6 -0.9 (2.1) (2.1) (2.2) SHOCK MEASURE -1.0 -1.4* -10.0** (0.7) (0.8) (4.7) Note: 1,335 Observations. Marginal effects denote percentage point change in probability from turning indicator variables from zero to one, and increasing continuous variables by amount indi-cated next to covariate name. Standard errors corrected for clustering by province and year are in parentheses. One, two & three asterisks (*) denote significance at 10%, 5% & 1% levels respec-tively. Gender specific time trends, regional indicators, city & rural indicators also included. Table 2.6: Other Post-secondary Attendance - Marginal Effects Shock Included Income change Income change MIE Job Loss Variable age 18 to 19 age 16 to 19 any age 16 to 18 Female 3.7 3.5 3.1 (3.5) (3.5) (3.6) French mother tongue 9.3 9.0 6.3 (7.6) (7.6) (7.3) Aboriginal descent -9.8 -9.6 -9.6 (6.1) (6.3) (6.4) Visible minority 8.9 9.2 6.3 (9.8) (9.9) (9.2) Immigrant parent 1.6 1.7 2.3 (5.6) (5.7) (6.0) Children in family 0.4 0.4 0.4 (0.8) (0.8) (0.7) Lone parent -4.6 -4.3 -3.9 (4.0) (4.0) (4.1) Parents no high school -5.4 -5.4 -5.9 (5.0) (4.9) (5.1) Parents other PSE only 6.1 6.1 5.9 (4.5) (4.6) (4.7) Parent University -1.0 -0.9 -1.5 (4.8) (4.9) (5.0) Low parent income -2.9 -2.9 -2.9 (4.2) (4.1) (4.2) High parent income -0.8 -0.3 -1.0 (3.8) (3.8) (3.8) University > 80 km away -4.2 -4.3 -4.3 (4.2) (4.2) (4.3) Comm. College > 40 km away 1.5 1.5 1.3 (3.4) (3.3) (3.4) Comm. College tuition (+$500) -2.1 -2.1 -1.6 (2.4) (2.5) (2.5) University tuition (+$500) 1.1 1.0 0.5 (3.1) (3.1) (3.0) Unemployment rate (+2.5%) -2.3 -2.1 -2.8 (2.2) (2.3) (2.3) University financial aid (+$250) 6.2*** g [*** g 7*** (2.2) (2.2) (2.3) SHOCK MEASURE 0.6 -0.4 -4.1 (0.7) (0.8) (6.2) Note: 1,335 Observations. Marginal effects denote percentage point change in probability from turning indicator variables from zero to one, and increasing continuous variables by amount indi-cated next to covariate name. Standard errors corrected for clustering by province and year are in parentheses. One, two & three asterisks (*) denote significance at 10%, 5% & 1% levels respec-tively. Gender specific time trends, regional indicators, city & rural indicators also included. 36 Many provinces increased tuition at both universities and community colleges at the same time and by similar dollar amounts. The correlation between the two measures at the provincial level is a considerable 0.7 over the period under analysis. Living further than eighty kilometres from the nearest university had a statistically insignificant negative effect on university attendance.26 There is an insignificant positive effect of living further than 40 kilometres from the nearest community college on university attendance. This may reflect the placement of community colleges in areas of historically low post-secondary attendance in order to encourage increased attendance.27 The regional indicators (not reported) highlighted much higher rates of university attendance in Atlantic Canada and Ontario than in the rest of Canada. The effects of the set of characteristics on attendance at other post-secondary institutions (pri-marily community college) are much less significant than their effects on university attendance. Youth of aboriginal descent are less likely to attend other post-secondary, as they were in attending university, but the effect is statistically insignificant. Parental education and income levels have economically small effects. This illustrates that there is little inequality in other PSE attendance rates overall in Canada, unlike at the university level. The signs of the effects of tuition fees on other post-secondary attendance are economically appropriate, yet statistically insignificant. Higher community college tuition lowers the probability of attending other PSE, providing evidence of a negative own price effect. Increases in university tuition raise the probability of attending other PSE, highlighting a positive cross-price elasticity. There was also a very large effect of residing in Quebec on other PSE attendance (not reported in Table 2.6, reflecting the high rates of attendance at CEGEPs in that province. The estimated impacts of the parental income shock measures on university and other post-secondary attendance are gathered in Table 2.7 for ease of comparison. The marginal effects for three shock measures are taken directly from the bottom rows of Tables 2.5 and 2.6. The final column in the table is the estimated effect of the shocks on not attending any post-secondary education in this period. Marginal effects for changes in income in any one year or over the entire three year period are presented in the top panel of Table 2.7. These marginal effects were calculated for a ten thousand dollar reduction in annual income.28 Even for such a large income decline, very 26Frenette (2005) found significant negative effects in more parsimonious models. 2 7This variable may thus be proxying characteristics of the neighbourhood of residence on attendance probabilities. I analyze the effect of neighbourhood characteristics on attendance in Chapter 3. 2 8Models were estimated including percentage changes in income rather than dollar changes. Results suggested that 37 Table 2.7: Parental Shocks and Post-secondary Education Attendance - Marginal Effects University Other post-secondary No post-secondary Income changes (-$10,000) age 18 to 19 -1.0 0.6 0.4 (0.7) (0.7) (1.0) age 17 to 18 -0.9 -0.2 1.1 (1.4) (0.8) (1.5) age 16 to 17 0.5 -1.1 0.5 (0.7) (1.3) (1.4) age 16 to 19 -1.4* -0.4 1.8 (0.8) (0.8) (1.1) Job loss - any age 16 to 18 Main income earner -10.0** -4.1 14 | ** (4.7) (6.2) (6.2) Spouse of MIE 1.1 2.9 -4.0 (6.4) (4.8) (7.2) Note: 1,335 Observations. Standard errors corrected for clustering by province and year in paren-theses. One, two and three asterisks (*) denote statistical significance of these differences at the 10%, 5% and 1% levels respectively. The full set of covariates listed in table 2.4, gender specific time trends, regional indicators, and city and rural indicators are also included in the estimated models. little impact on attendance is observed. There is a statistically significant decline in university attendance for a $10,000 reduction in income over the entire three year period, but it only lowers the probability of university attendance by 1.4 percentage points. To understand the size of these effects, recall that 30% of youth attend university and 35% attend other PSE in this sample overall. There was also no evidence that positive income changes had smaller effects on attendance than negative changes. The effects of income changes on attendance were symmetric. A job loss for the main income earner in the family, however, lead to a large and statistically significant ten percentage point decline in the probability of university attendance. This is evidence of a particularly alarming outcome of labour market displacement. Spousal job loss shocks, in contrast, have no significant effect on post-secondary attendance.29 Main income earner job loss dollar changes were more significant predictors of attendance. 29Alternative estimates I constructed also showed that new work limitations to the family's main income earner and spousal separation also had ten percentage point negative effects on university attendance. 38 alone affects education attendance here. Given the striking size of my estimated negative effect of parental job loss on the education attendance of youth, I undertook several robustness checks of my estimates. Estimating this large negative effect was robust to the inclusion of twenty-five industry and twenty occupation dummies for the main job of the main income earner parent when the youth was aged 16. I also estimated a specification replacing the regional indicators and time trends with the full set of year times province dummies to control for any regional variation in macro-economic factors or spending measures.30 The estimates of the effect of job loss on PSE attendance were robust to this speci-fication also. I also estimated a probit model of the outcome of university attendance versus the alternative of only other PSE attendance or no PSE attendance at all rather than the three option multinomial logit model. The strong negative effect of parental job loss on university attendance was robust to this estimation also. One concern with the multinomial logit estimator is the underlying Independence of Irrele-vant Alternatives (IIA) assumption. This assumption implies that adding another alternative to the model does not affect the relative odds between two alternatives already included in the model. This appears to be a strong restriction here, as we may think that adding the alternative of other PSE (community college) will change the odds of choosing between university and no post-secondary study. A Hausman and McFadden (1984) test of the IIA assumption, however, could not be re-jected. This test is based on separate binary logit estimation of university and other PSE atten-dance versus non-attendance, and tests if the coefficient estimates from the separate regressions are different to those from the full multinomial logit estimation. No significant difference in the estimated coefficients could be observed. The multinomial logit technique places no ordering on the three education outcomes, unlike the ordered probit technique employed by Hilmer (1998) and others. Ordered models involve estimating much fewer parameters than the multinomial logit technique, but impose restrictions on the effect covariates can have on alternative education outcomes. I estimated ordered logit and probit models and constructed non-nested tests (Vuong (1989)) of these models versus the multino-mial logit model. These tests resoundingly rejected the ordered models, even when employing the Akaike Information Criterion that adjusts the test statistic for the smaller number of parameters 3 0When estimating this specification, all variables that only varied by province and year were removed, such as tuition and unemployment rates. 39 being estimated in the ordered models. 2.6.3 Persistent and Temporary Income Shocks The insignificance of the effect of any observed income changes on university attendance con-trasted with large effects of main income earner job loss deserves further scrutiny. Not all observed changes in parental income may be shocks, and many changes may only be temporary. They may reflect large increases in income in the previous year, perhaps due to the realization of a capital gain. The temporary nature of income shocks unrelated to job loss could be clearly observed in Figure 2.5. Job loss, on the other hand, may reflect a more persistent and unexpected shock to parental income, which have a more marked effect on the education attendance of youth. To uncover the effect of persistent and temporary parental income shocks on post-secondary attendance, I re-estimated the attendance model including the measure of the change in parental income over the three year period from when the youth is aged 16 to when the youth is aged 19 (denoted PlCiyr) split by parental job losers (when the youth was aged 16, denoted MJL16) and non job losers. This three year income change should reflect a persistent decline in income for job losers, but a more temporary decline for parents that did not lose a job. Marginal effects of these persistent and temporary measures of parental income shocks are presented in Table 2.8. The marginal effects for all the remaining covariates are not reported for brevity. A persistent decline in income of ten thousand dollars results in a 6.2 percentage point reduction in the probability of university attendance. In contrast, temporary income declines of the same magnitude have small and statistically insignificant effects on attendance. This suggests that temporary income shocks can be smoothed by families with little impact on the education attendance of their children. On the other hand, parental income shocks that are expected to be persistent have marked effects. Parents do not appear to be subject to credit constraints in terms of making transfers to their children, as temporary income shocks had little effect on post-secondary attendance of youth. This does not necessarily suggest that youth themselves do not face credit constraints related to PSE attendance. Student loans were available to low income students during this period. 40 Table 2.8: Persistent and Temporary Parental Income Shocks - Marginal Effects University Other post-secondary No post-secondary Persistent (-$10,000) -6.2** -1.0 7.2** (PIC'iyr x M JL16) (2.8) (1.7) (3.4) Temporary (-$10,000) -0.3 0.1 0.1 (PICZyr x (1 - M . / L 16)) (0.6) (0.8) (1.1) Note: 1,335 Observations. Marginal effects represent the effect of a $10,000 decline in parental income. One, two & three asterisks (*) denote statistical significance at the 10%, 5% & 1% lev-els respectively. Standard errors adjusted for clustering by province and year are in parentheses. PIC'Mjr refers to the change in parental income over the three year period from when the youth is aged 16 to when the youth is aged 19, while M JL16 is an indicator of main income earner job loss when the youth was aged 16. The full set of covariates listed in table 2.4, gender specific time trends, regional indicators, and city and rural indicators are also included in the estimated models. 2.6.4 Breakdown of Effects of Parental Job Loss The effect of parental job loss on the education attendance of youth may not be the same for all youth. To explore this issue, I break down the effect of main income earner job loss on attendance by various important parental and individual characteristics in Table 2.9. These breakdowns were constructed by including interactions of the shock measure with the parental characteristics in the estimated models, along with the full set of covariates from Table 2.4. Looking first at the top panel, the negative effect of job loss on university attendance is confined to parents with a high school education or less. Remember that I am still controlling for parental education levels in these estimates. More educated workers may find it easier to obtain another well-paying job. Job loss resulted in larger declines in parental income for less educated parents over the three years following the loss also. The income decline for parents with high school or less was fifty percent larger than the income decline for parents with a completed post-secondary education. In addition, more educated workers may have earned more prior to the job loss, and have higher levels of savings which can be used to smooth consumption more easily. Note that Shea (2000) also found a small causal negative effect of average parental income levels, instrumented by job loss, on youth's completed years of schooling for low educated fathers only. There is no asset or wealth information in the SLID for the period I analyze, but there is an 41 indicator of whether the house the family lives in is owned or not by a member of the household.31 Overall, approximately 85% of youth came from households where the house was owned when the youth was aged 17.32 The marginal effects reported in the second panel of Table 2.9 illustrate the effect of job loss interacted with home ownership. Home ownership itself is positively related to attendance, but no statistically significant differences in the effect of job loss on attendance could be observed by home owner status. As was observed in Figure 2.6, large income losses were experienced by parents that lost unionized employment. To investigate the effect of losing a union job on youth post-secondary attendance, I estimated a model including the interaction of an indicator of parental job loss with an indicator of whether the parent that lost the job was a union member, or the job was paid under a collective agreement. The results of this estimation are presented in the third panel of Table 2.9. Job loss for parents with unionized work resulted in negative effects on the university attendance of youth that were twice as large as those on youth whose parents were not unionized prior to the job loss.33 I estimated the differential effect of parental job loss on the education attendance of male and female youth in the fourth panel of Table 2.9. Surprisingly, there is a very large negative effect of parental job loss on the university attendance of female youth, but no significant effect on the post-secondary attendance of male youth. Further analysis revealed that parents of females suffered much larger income declines on average (nearly three times as large) post job loss than parents of males. It is difficult to believe that the gender of youth is having a causal effect on parental income declines. It was also the case that parents of females that lost jobs were more likely to be low educated than the job losing parents of male youth. Even allowing for these differences in family background between males and females whose parents suffered job losses, however, there still appears to be a more significant negative effect of parental job loss on the university attendance of females. Females are on average much more likely to attend university than males in the 1990s. These results suggest that more females are closer to the margin of the attendance decision than males, and/or that parental transfer decisions vary by the gender of 3 lThe house owner could be anyone living in the household, not just the youth's parents. In addition, ownership is indicated irrespective of the amount of borrowing on the house. 3 2The age of 17 was chosen to minimize the occurrence of missing observations in the home ownership indicator. 3 3Due to small samples, I am unable to analyze separately the effect of job loss of union workers split by those who retained union status and those who did not. 42 Table 2.9: Breakdown of Parental Job Loss Impacts - Marginal Effects University Other post-secondary No post-secondary Parent HS or less x job loss -17.3** -15.8*** 33.2*** (7.9) (5.4) (9.0) Parent PSE educ. x job loss -2.2 11.4 -9.2 (5.6) (11.2) (10.0) Parent owns home 9.0 7 5** -16.5** (6.4) (3.6) (7.9) Parent owns home x job loss -10.3 1.7 8.6 (6.3) (5.4) (7.7) Parent rents home x job loss -6.6 -8.0 14.5 (7.8) (8.0) (12.1) Parent union member -4.0 2.5 1.4 (2.4) (2.9) (3.2) Parent union member x job loss -16.2*** -12.2 28.4** (5.9) (8.0) (11.5) Parent not unionized x job loss -8.9 -2.9 11.8* (6.6) (7.4) (6.8) Male youth x job loss 1.4 9.7 -11.1 (7.5) (8.9) (8.5) Female youth x job loss -32 2*** -8.1 41 o*** (8.2) (9.4) (10.4) Note: 1,335 Observations, except the second panel with 1,309 observations, and the third panel with 1,325 observations. Standard errors corrected for clustering by province and year are in parentheses. One, two & three asterisks (*) denote statistical significance at the 10%, 5% & 1% levels respectively. The full set of covariates listed in table 2.4, gender specific time trends, regional indicators, and city and rural indicators are also included in the estimated models. Note that union member in panel three also includes those parents that have a job that is paid under a collective agreement, even if the parent is not a union member. 43 children, particularly in response to negative income shocks. I analyzed several additional breakdowns of the effect of parental income shocks on education attendance. Job loss effects on post-secondary attendance were not more negative in provinces with higher university and community college tuition levels, nor for youth living a long distance from post-secondary institutions. In fact, job loss effects were larger for youth living closer to universities and community colleges rather than far away. The negative effect of job loss was not significantly larger in families with more children either. The effect was no different for older versus younger parents. The effect of job loss was also no larger in periods or provinces suffering from higher unemployment rates overall. The results of these further breakdowns are available upon request. 2.6.5 Discussion of Job Loss Effects Some readers may want to interpret the negative effect of parental job loss on education attendance as something due to the job loss itself rather than due to the negative income shock caused by the job loss. The psychology literature has often discussed the psychological damage that job loss can have on individuals. Parental job loss and subsequent unemployment may lower the self-esteem of the parent and disrupt the family environment, which in turn affects directly the education attendance of youth. There was no evidence in the SLID data, however, that job loss was related to reduced health or increased stress of adults. Starting in 1996, survey respondents were asked to rate their health and their level of stress on five point scales. These self-reports were no worse for job losers than non-losers in the data on average, nor did the reports deteriorate for job losers over the life of the panels. In addition, further analysis showed that the negative effect of parental job loss on education attendance was no larger if the parent suffered from a longer period of unemployment post job loss.34 These results cast some doubt on such psychological explanations of the effect of parental job loss on education attendance. Finally, the results of Table 2.8 highlight the much larger negative effect of parental job loss on university attendance if there were larger income declines accompanying job loss. I thus argue that income drops accompanying job loss are causing declines in university attendance rather than merely job loss itself. There is the possibility that parental job loss may change the youth's expectations of the risk-34Parents who have longer observed periods of unemployment post job loss may have chosen to search longer for a better job match. 44 iness of employment and earnings. Costly investments in education may thus appear more risky to youth whose parents lost jobs. Some affected youth may be more concerned that they cannot repay any student loans if they themselves lose jobs or cannot find appropriate employment. Yet unemployment rates are generally lower for well-educated adults, so youth should rationally sur-mise that higher education levels should lower employment risk. It is not possible to estimate the effect of parental job loss on risk perceptions of youth with the available data. It is a question left for future research. I find a significant negative effect of parental job loss on university attendance but not on the overall level of attendance at other post-secondary institutions, such as community colleges and trade schools. A general downgrading of the level of attendance of youth whose parents suffer job loss may have occurred. Some youth may have responded to parental job loss by attending com-munity college rather than university, while others who would have attended community college if their parents did not suffer a job loss may not attend post-secondary education at all. These two effects on other post-secondary education attendance may have offset each other, resulting in the estimated overall effect of parental job loss on other post-secondary attendance being zero. Youth responded to parental income shocks by attending post-secondary education at lower rates, and possibly in some cases attending community college rather than university. They may also have responded by working more (while studying or not), in order to rely less on parental transfers or even to assist the family by contributing themselves. The average annual work hours and real pre-tax annual income of age 19 youth split by education attendance are presented in Ta-ble 2.10. The difference between youth whose parents suffered job losses and youth whose parents did not are also provided. Note that youth who choose to attend post-secondary education do work a significant amount (part-time and in summers) and contribute themselves to their education and living expenses. Only a small minority of students do not work at all. Other post-secondary stu-dents work and earn more than university students on average, and youth whose parents lost their job both work and earn more if they attend other post-secondary institutions. This suggests that these youth have responded to their parents' job loss by working more. Youth who do not study at age 19 work significantly more and earn more than students. What may be surprising is that youth whose parents suffered job losses and who do not study actually work and earn less than youth whose parents do not suffer from job loss. Two explanations for this result come to mind. First, youth whose parents lost their jobs may live in areas where work op-45 Table 2.10: Annual Hours Worked and Income of Youth Aged 19 No parental job loss Parent lost job Difference Observations Annual work hours University students 581.7 473.9 -107.8 (96.0) 337 Other post-secondary 648.1 898.2 250.1** (118.8) 394 Not students 1,217.7 992.7 -225.0* (132.7) 321 Annual pre-tax income University students 6,423 6,128 -295 (1,511) 342 Other post-secondary 7,305 8,540 1,235 (1,233) 399 Not students 10,972 7,110 -3,862*** (1,122) 328 Note: Standard errors taken from a regression of hours or income on a constant and an indicator of parental job loss are in parentheses. One, two & three asterisks (*) denote statistical significance of the difference between youth with parents suffering job losses and youth with parents that do not at the 10%, 5% & 1 % levels respectively. portunities are more restricted, making it more difficult for the youth to find full-time employment. Second, youth who are in some sense kept from attending education due to their parents' job loss shock may not have had the opportunity to line up an appropriate full-time job (a good match). 2.7 Grade Transition Model of Education Attendance In this section, I estimate a model of the full set of annual education attendance outcomes of youth from age 16 to age 19 or 20. This model is employed to identify the immediate and lagged ef-fects of persistent parental income shocks, indicated by job loss, on those education outcomes. Identifying the particular pathways by which parental job loss affects education outcomes is par-ticularly important when thinking about the timing of possible policy prescriptions. I identify whether parental job loss leads to immediate high school drop-out behaviour, or whether affected 46 youth stay in school but subsequently do not go on to university or community college. The model specification is based directly on the sequential nature of education attendance, where youth must complete certain levels of education prior to progressing to the next level. Using this model, I am also able to construct a specific test of the exogeneity of these job loss indicators to further ensure a causal effect of parental income is being identified. This test should allay any remaining concerns that job loss itself reflects unobserved characteristics of parents that may also affect their children's education attendance. Due to the limited length of each panel in the SLID, the two stage technique decomposing income changes into persistent and temporary components could not be conducted here for job losses at age 17 and 18. Job loss indicators for the family's main income earner alone are included in the model to identify persistent parental income shocks. 2.7.1 Grade Transition Details Education attendance is a sequential process. To complete high school, youth must first complete grade eleven. To attend university, youth must first complete high school or an equivalent. I explicitly model annual education outcomes here while imposing these sequential constraints on each youth's attendance alternatives. A diagram of a subset of the education transitions modeled is provided in Figure 2.7. Youth are first observed at age 16, when they are still in high school, and have completed either nine or ten years of school. A year of high school is generally completed in the middle of a calendar year, with the next grade or level of education (community college or university) beginning in September. The first transition observed is from age 16 to age 17. Youth in grade ten at age 16 can stay in school and complete grade eleven during the calendar year they turn 17, they can attend other post-secondary education (denoted OPSE in Figure 2.7) such as trade school or community college, or they can drop out of education altogether.35 Youth are not legally able to leave school until they turn at least 16 in Canada.36 Youth in grade nine at age 16 can also drop out, attend other PSE or progress to grade ten at age 17. 3 5 Attending other post-secondary education at this age was not common except in Quebec. 3 6Youth who do not attend school at all or attend for less than 4 months during the calendar year are denoted dropouts. 47 Figure 2.7: Grade Transition Model - Subset of Transitions Grade 10 4^  CO Initially Grade 9 Grade 11 OPSE 1st Dropout Grade 10 OPSE 1st Dropout University OPSE 1st HS complete Dropout HS return OPSE 1st Stay out University OPSE 2nd HS return None University OPSE 1st HS return None Age 16 Age 17 Age 18 Age 19 The second transition observed is from age 17 to age 18. Youth who complete grade eleven during the calendar year they turn 17 can complete grade twelve in the middle of the calendar year they turn 18 and then progress to university. They can also go on to other PSE, just complete high school, or drop out. Youth must generally complete twelve years of high school to attend university in Canada. There are two exceptions: Quebec and Ontario. These cases were discussed in Section 2.4, and are modeled explicitly in this grade transition model. Youth in grade ten at age 17 can progress to grade eleven during this second transition, attend other PSE, or drop out. They cannot attend university yet. Youth who dropped out of school during the first transition can stay out, return to high school (denoted HS return in Figure2.7), or in some cases attend other PSE. They cannot attend university yet either. For more details of the construction of the transitions and the transition model, see Appendix C. The third transition from age 18 to age 19 has similar transitions modeled, including transitions for youth who have completed twelve years of high school and for youth attending other PSE. Not all of these transitions are presented in Figure 2.7 due to space limitations. Youth who reported university attendance at age 18 are no longer modeled, as university attendance is defined as the highest attendance level obtainable. A fourth transition from age 19 to age 20 is modeled for youth from Ontario and Quebec only. This was undertaken to give youth from those provinces the extra year they generally require to obtain the pre-requisites for university entrance. 2.7.2 Econometric Model The importance of controlling for unobserved heterogeneity was illustrated clearly by Cameron and Heckman (1998) when estimating these grade transition models. Characteristics such as in-nate academic ability affect the education outcomes of youth, but are generally unobservable to us as researchers. Ignoring these unobservables may lead to biased estimation of the effect of observable characteristics, such as parental income or parental income shocks, on education de-cisions. Selectivity bias that may be caused by the exclusion of such unobserved characteristics is controlled for using the random effects estimation technique proposed by Heckman and Singer (1984). The econometric estimation strategy that I employ follows closely Cameron and Heckman (2001). Let a denote age, where o € {a,a}, with a being the initial age of 16 and a denoting 49 the highest age observed (age 19 or 20). Schooling status at age a is denoted ja, and this status will determine the available schooling choices at age a + 1. Youth with schooling level ja make a choice about their schooling level at age a + 1 from choice set C a j a . Let DajaiC = 1 if choice c G Caja is chosen by a youth of age a with schooling status ja. Let DajaiC> — 0 otherwise, where d ± c. Each education outcome is the result of a rational decision made by the youth. The youth will calculate the expected utility VajatC from each available choice c, then choose the one that maximizes their expected utility. This utility calculation will include the option value of further education attendance in many cases. For example, continuing on in school versus dropping out will keep open the option of attending university. The utility of each choice will be approximated by a linear equation as follows. K , j a , C = Za,ja,cPa,ja,C + ^a,ja,C (2-1 1) The vector Z'aja c is a set of observable characteristics while ea,ja,c is unobservable. The unob-servable is assumed to follow the following simple factor structure. £a,ja,c = Oia<ja<cV + Va,ja,c (2-12) Here 77 is a mean zero random variable with unit variance that is assumed independent of va,ja,c-Both 77 and va,ja,c a r e assumed independent across youth. The random variables va,ja,c W Q assumed to follow extreme value distributions, and are independent of all other va',j^,d"- These assumptions produce an extension of the multinomial logit model. Conditioning on 77 yields the following, where the matrix Zaja denotes the set of ZajatC. Pr(/J a j a, c< = l\Za!Ja,i]) = Pr(argmaxV r a j- 0 ) C = c ' | Z Q J o , 7 7 ) C E c e c a , J O eMK,ja,Ja,ja,c + ua,ja,cv) The main consequence to note from the assumptions of this model is that any dependence be-tween choices DajaiC and -Da'^V" ( 0 7 ^ a') made by any individual youth, conditional on observ-ables, arises from 77, the youth specific effect. To account for this dependence, model estimation involves integrating out the 77 using an approximation of its distribution F(jj). The approximation employed is a discrete distribution with mass points. See Appendix C for details of the estimated likelihood function. 50 This estimation technique is a form of random effects estimation, and is based on the as-sumption that 77 is independent of the set of observable characteristics of youth (the ZajatC for all a,ja e Caja). Although the unobservable r\ is assumed independent of the set of observable characteristics in the full sample, it may, however, be correlated with observable characteristics in any one of the particular estimated transitions (a > a), conditional on past education outcomes. If 77 reflects ability, for example, it may be negatively correlated with parental income for those youth still in school at age 17. This correlation will arise if having low parental income increases dropout behaviour, so only high rj youth from low income backgrounds remain in school at age 17, with low rj and low income youth dropping out prior to age 17. The base case at the initial age of 16 is the determination of whether the youth has completed nine or ten years of high school. This will generally depend on whether or not the youth had to repeat a grade of school prior to age 16, or on wether the youth started school a year later than normal. This may be a function of the youth's ability and motivation, parental inputs into their children's education, and perhaps quarter of birth. It is modeled by a linear in variables logit equation with the full set of individual, parental and environmental characteristics employed in the transition estimates, plus indicators of quarter of birth.37 For each decision among a set of choices Caja, I must normalize one set of parameters (3a,ja,c in order to identify the remaining parameters for that decision. Denote the choice c* as the nor-malization or base case. The parameters Pa,ja,c* and factor loading aa,ja,c* w e r e constrained to zero within each choice set. As a result of this normalization, the remaining estimated coefficients and factor loadings are defined relative to those for the base case. I set the base case to either the dropout or non-progression choice in each decision during estimation.38 2.7.3 Estimation Preliminaries The model I estimate in this section includes parameters governing the initial condition at age 16 and parameters governing three or four annual education transitions (depending on province of residence), with separate parameter sets for each possible beginning education state at each age. •"Quarter of birth may affect years of school completed by a particular age if children turning six years old late in the year are not entered in school until the year they turn seven. This may occur due to parental choice or school district regulation. 3 8The decision of base case between these two states was made on the basis of the number of observations within each choice. 51 The number of possible transitions and the choice sets available both expand considerably as the youth ages. I undertook the following procedures to minimize the number of parameters to be estimated. To begin, in several transitions the number of observations undertaking a particular choice was too small to estimate all the slope coefficients. I therefore estimated choices with fewer than 15 ob-servations with constants only. Choices with between 15 and 30 observations were estimated with a constant and two indicators of parental income quantile only. Factor loadings on the unobserved characteristic rj were set to zero for these choices. In addition, I tested several hypotheses regarding the estimated slope coefficients, and those that were not rejected by the data were imposed in final estimation. Separate constants were retained in each case. The restrictions imposed were: (a) slope coefficients for school dropouts were restricted to be equal across the last three transitions, (b) grade nine and grade ten slope coefficients in the first transition were restricted to be equal, (c) grade eleven slope coefficients in the second and third transitions were restricted to be equal, and (d) high school graduate slope coefficients in the third and fourth transitions were restricted to be equal. I estimated each transition in the model including the set of individual and parental character-istics listed in Table 2.4.39 The provincial level characteristics that change over time were entered at the appropriate level for that year. For example, the university and community college tuition levels that were charged in the province of residence when a particular youth was aged 17 were included in the first transition (age 16 to age 17) for that youth. I included the job loss indicators only in the education transitions that occurred after the job loss itself was suffered. The indicator of a parental job loss when the youth was aged 16 was included in the first transition for that youth. This indicator plus the indicator of a job loss when the youth was aged 17 were included in the second transition. These two plus the indicator of job loss at age 18 were included in the third transition. In addition, controls for multiple job loss were included in the estimated model, as there were many parents suffering more than one job loss over the years when the youth was aged 16 through 18.40 Shocks could thus affect the current transition 3 9 A number of characteristics were dropped from estimation due to statistical insignificance and estimation prob-lems: aboriginal descent, visible minority status, French speaking, city and rural indicators, and university over 40 kilometres away. 4 0This multiple job loss control was simply an indicator of whether the parent suffered more than one job loss shock over the years when the youth was aged 16 through 18. Only one job loss appeared necessary to have negative effects on youth outcomes. Multiple job losses did not lead to appreciably larger negative effects than one job loss 52 and future transitions of youth but not past transitions. In other words, shocks could not affect transitions that are undertaken before they themselves occur. I also tested this restriction on the inclusion of job loss shocks in the model in order to illustrate that these shocks are truly exogenous. The results of these tests are discussed below. I estimated each model both with and without controlling for unobserved heterogeneity. Unlike the results of Cameron and Heckman (2001), controlling for unobserved heterogeneity did not change the model estimates to any significant extent. Only two points of support were required to adequately capture the distribution of the unobservable rj in the data. This low number is common in estimation of models such as this, including the work of Cameron and Heckman (2001). I estimated the unobserved heterogeneity recursively, using the initial condition at age 16 to identify the probabilities on each of the mass points for rj. The model simulations discussed below were constructed using model estimates that included the controls for unobserved heterogeneity. 2.7.4 Grade Transition Model Results I employ the estimates of the full grade transition model to simulate the effect of parental job loss on the annual education outcomes of youth from age 17 to age 19 or 20 (depending on province of residence). These results are presented in Table 2.11. These simulations depict a treatment on the treated effect. It measures the average effect of parental job loss on the education outcomes of those youth who suffered from the shock. Treatment effect construction involved simulating the estimated probability of each annual education outcome for each youth who suffered from parental job loss twice. First, the attendance probabilities are simulated setting the appropriate annual job loss indicator to zero, then they are simulated again setting the indicator to one. The difference between the two simulated probabilities, averaged over all youth who suffered from the particular shock, is the estimated treatment on the treated effect.41 For further details of how the simulations were undertaken, see Appendix C. Looking at the top panel of Table 2.11, parental job loss at age 16 leads to immediate increases alone. Later education transitions include job loss indicators for all ages 16, 17 and 18. Multiple job losers will have these indicators equalling one for more than one age, while single job losers will only have one indicator set to one. The inclusion of the multiple job loss indicator will allow negative effects to be estimated for individual age job loss indicators for all youth, i.e. both multiple and single job losers. 4 1 The probability weights on individual youth in the SLID were employed when forming these averages, as they were during model estimation. 53 in high school dropout behaviour. The probability of dropping out of high school at age 17 is 4.6 percentage points higher for youth who suffer from the shock. This is a large effect as it doubles the average dropout rate at this age in the sample. It is only statistically significant at the 17% level, however. The rate of attendance at other post-secondary education institutions also increases markedly in response to the shock. This increase is primarily observed in Quebec, where there was higher rates of attendance at CEGEPs. Turning now to the second panel, parental job loss at age 17 also increases school dropout behaviour by age 18, and the effect here is statistically significant. In the bottom panel of Table 2.11, the effects of job loss on the education attendance of youth by age 19 or 20 (the final age in this study) are presented. Parental job loss at age 16 and age 18 have significant and large negative effects on university attendance.42 This decrease in university attendance is offset by increases in attendance at other post-secondary institutions, particularly for age 18 shocks. Age 18 shocks also significantly increase school dropout behaviour, with the probability of not graduating high school and not attending PSE twelve percentage points higher. This is again a large effect, doubling the school dropout rate. Age 16 shocks also increase school dropout rates at the end of the period. Youth who dropped out of school straight after the shock at age 16 did not return later to complete high school. I re-estimated this entire grade transition model including annual changes in parental income in place of the job loss indicators. These measures had no significant effects on any of the grade transitions. This is consistent with the multinomial logit attendance model estimates of the previous section. Income changes may be dominated by transitory movements. 2.7.5 Test of Exogeneity of Job Loss Shocks As discussed above, a primary concern when identifying the causal effect of parental income on education attendance is the presence of unobservable characteristics of parents that affect both parental income and child education outcomes. There may be similar concerns with parental job loss shocks. One way to test whether these job loss shocks are exogenous is to include job loss indicators in youth education transitions that occur prior to the job loss as controls for potential unobserved heterogeneity, and to determine whether the inclusion of these controls changes my 4 2The insignificant effect of age 17 shocks on university attendance is attributable to small sample sizes, and the fact that many parents who suffered a job loss when their child was aged 17 also suffered job losses when their child was 16 or 18 in my sample. This led to difficulties in separately identifying the effect of age 17 job losses on education attendance. 54 Table 2.11: Job Loss Shocks - Treatment on the Treated Effects Age 16 shock Age 17 shock Age 18 shock Age 17 Outcome Dropout 4.6 (3.1) Still in high school (3.4) Other PSE (1.4) Age 18 Outcome Dropout 4.2 4 9** (2.6) (2.2) Still in high school _y) 5** -11.2 (53) (7.5) Other PSE 5.5 6.5 (4.5) (4.2) University 2.8 -0.3 (2.8) (6.4) Final Outcome Dropout 5.7** 0.0 12 3*** (2.6) (6.8) (3.7) Still in high school -1.8 -4.2 1.9 (1.2) (4.5) (1.7) high school graduate 3.2 -0.1 -13.0* (3.8) (8.7) (7.5) Other PSE 4.9 5.3 14 3*** (3.9) (6.5) (4.4) University -12.1** -1.0 -15.5** (5.0) (18.4) (6.8) Any PSE -7.2 4.2 -1.1 (4.8) (14.6) (6-3) Note: 1,335 Observations. Standard errors in parentheses. One, two & three asterisks (*) denote statistical significance of these treatment effects at the 10%, 5% & 1 % respectively. Standard errors constructed taking 500 random draws from estimated distribution of model parameters (inverse hessian) and simulating treatment effect using each random draw. Parameters assumed normally distributed when taking random draws. 55 estimates of the effects of the correct job loss indicators on the education outcomes of youth. This procedure is related to one of the estimation procedures employed by Mayer (1997), where measures of income from after an education outcome were included as controls for unobserved characteristics of parents. I constructed this exogeneity test as follows. Age 18 job loss indicators were entered into the first and second transition equations, and age 17 job loss indicators were entered into the first transition equations. An indicator of whether parents suffered a job loss at any age of the youth from 16 through 18 was also placed in the initial condition (grade in school at age 16) equation. A likelihood ratio test of the joint significance of these added job loss measures failed to reject the null hypothesis that these additional shock measures had no effect on any of these earlier education transitions. The test statistic had a probability value of only 0.405.43 Most importantly, including these post-transition job loss indicators in the model did not alter the estimated effects of the relevant shocks on education transitions to any significant extent. If there are unobservable characteristics of parents correlated with job loss, including these post-transition job loss indicators in the estimated model is one method of controlling for any potential unobserved heterogeneity related to such job loss. The treatment on the treated simulations for the model including these post-transition job loss indicators are presented in Table 2.12. The large negative effects of parental job loss on university entry and high school dropout behaviour remain. This finding maintains my confidence that I am identifying the causal effect of persistent parental income shocks on youth education outcomes.44 4 3This exogeneity test may fail for reasons other than unobserved heterogeneity. It may fail if there is state depen-dence in these parental shocks. Some significant shock may have occurred prior to age 16, and due to state dependence, we observe job losses in subsequent years. A significant relationship between these subsequent shocks and the initial condition may be picking up the effect of these earlier shocks. This failure will not occur in any of the subsequent education transitions, however, as there are measures of job loss included in those transitions already. 4 4 I estimated a separate model that included post-transition indicators of job loss for youth that did not suffer from earlier job losses already included in the model. These indicators thus represent new shocks only, avoiding any estimation problems from multiple job loss families. I included age 19 job loss indicators in this model also. A test of the joint significance these new post-transition shock measures could not reject the null of insignificance. I then simulated the effect of these post-transition job loss shocks on the earlier education outcomes, which they should not affect. In all cases these new post-transition job loss shocks had no significant effect on the earlier outcomes. This further maintains my confidence that the job loss shocks I identify are exogenous. 56 Table 2.12: Test of Exogeneity of Job Loss Shocks Age 16 shock Age 17 shock Age 18 shock Age 17 Outcome Dropout 4.9 (3.1) Still in high school _9 5*** (3.3) Other PSE (1.7) Age 18 Outcome Dropout 4.2* 4.3** (2.4) (1.7) Still in high school -11.1** -7.1 (5.3) (7.5) Other PSE 5.2 6.0 (4.9) (4.2) University 1.7 -3.2 (2.9) (7.0) Final Outcome Dropout 6.4** 0.6 12.4*** (2.7) (6.4) (3.3) Still in high school -0.6 -3.7 3.6* (1.3) (4.5) (2.0) high school graduate 2.4 0.0 -15.0* (3.9) (8.9) (7.9) Other PSE 3.5 7.0 15 7*** (4.2) (6.1) (5.0) University -11.6** -3.9 -16.6** (4.9) (16.7) (7.3) Any PSE -8.2* 3.1 -0.9 (4.9) (13.7) (6.3) Note: 1,335 Observations. Standard errors in parentheses. One, two & three asterisks (*) denote statistical significance of these treatment effects at the 10%, 5% & 1% respectively. Standard errors constructed taking 500 random draws from estimated distribution of model parameters (inverse hessian) and simulating treatment effect using each random draw. Parameters assumed normally distributed when taking random draws. 57 2.8 Discussion and Conclusions Persistent shocks to parental income have considerable negative effects on the education attendance of youth. Youth of high school leaving age whose parents lose their jobs are more likely to drop out of high school early and are much less likely to attend university. These outcomes may have significant and long-lasting effects on the economic well-being of these youth. Given the potential severity of these effects, there may be a role for government intervention. Such intervention can be supported on both equity and efficiency grounds. The effect of parental job loss on high school dropout behaviour suggests that intervention may be required prior to post-secondary education entry. The large negative effect of persistent parental income shocks provides evidence of the im-portance of parental income in education attainment. There remains considerable debate about whether the observed correlation between parental income and the education attainment of youth is actually causal. The evidence I find supports the case of a large causal effect. A ten thousand dollar persistent decline in annual parental income lowers the probability of a youth attending uni-versity by a considerable 6.2 percentage points. A temporary decline of the same magnitude has no effect on post-secondary education attendance. My results also identify alarming evidence of one consequence of labour market displacement that has received little prior attention. I find a significant negative effect of parental job loss on university attendance but not on the overall level of attendance at other post-secondary institutions, such as community colleges and trade schools. There appears to be a general downgrading of the level of attendance of youth whose parents suffer job loss. Some youth appear to have responded to parental job loss by attending community college rather than university,45 while others who would have attended community college if their parents did not suffer a job loss now not attending post-secondary education at all. These two effects on other post-secondary education attendance appear to have offset each other, resulting in the estimated overall effect of parental job loss on other post-secondary attendance being zero. Community college attendance is lower cost to students both due to lower tuition payments each year (approximately one half) and half the number of years of study. It may be easier to combine work and study at community college rather than university. Community college 45There was considerable switching from university attendance to other post-secondary attendance identified in my grade transition model results in response to parental job loss when the youth was aged 18, the normal post-secondary entry age. 58 attendance may also be less risky, with the effort and ability required to pass subjects lower. What causes these youth to forgo further education in response to parental job loss? One pos-sibility is that some youth feel they should enter the workforce immediately to assist the family in earning income. Reverse transfers from youth to parents who have lost their job may be oc-curring. Transfers between family members are not observed, however, in the data I employ in the analysis. Another possibility is that youth may no longer be willing to accept transfers from parents who have lost jobs. They may decide that without transfers from parents, even in the form of residing with parents at no cost, education investments are no longer worthwhile, or they may delay further study until after they work for a number of years and save the necessary funds. I only observe youth until age 19 or 20 in my analysis, so cannot observe any significantly delayed entry in response to parental job loss. Even delayed entry is costly for youth, however, as they earn the higher salaries of post-secondary graduates for fewer years. Parental job loss also led some youth to immediately drop out of high school. Such behaviour may suggest youth enter the workforce to assist the family, or that they no longer see the value of completing high school if post-secondary study is not an option for them. Previous research attempting to identify the causal effect of parental income on education at-tainment have generally found much smaller effects than I have. Research employing sibling fixed effects strategies use variation in income across siblings within a family. If the income variation is dominated by temporary changes, it is not surprising that small effects were found. Shea (2000) found small and insignificant causal effects of long run average parental income levels on the com-pleted years of schooling of young adults. He employed job loss, union status and industry status of fathers to instrument long run parental income levels. I find much larger effects from using job loss to indicate persistent negative income shocks. The difference reflects my focus on the effect of job loss on changes in income rather than on long run levels. I also focus on shocks at high school leaving age, whereas Shea analyzed average parental income levels over childhood. 4 6 Student loans were available to youth from low income backgrounds during the period I exam-ine. Despite this, large effects of parental income shocks on university attendance were identified. The evidence points to considerable financial constraints of some form on education attendance, 4 6The difference may also reflect the time period between the shock and the measured education outcome. I observe the immediate education responses of youth to parental job loss, while Shea considered only final years of schooling by age 25. Even if education attendance is only delayed by parental shocks, the costs to youth may be considerable, as they complete education later and earn higher wages over a shorter working life. 59 but suggests that borrowing constraints alone may not be the only form that these financial con-straints may take.47 Transfers of some kind, via parents or directly from governments, may be required to overcome the financial constraints a significant proportion of youth may face. Individual investments in higher education are risky, and individual preferences for assuming large debt loads at young ages may be quite heterogeneous across the population. A proportion of youth may be averse to borrowing to invest in their own human capital even if the average expected financial payoff appears large. Individual youth generally cannot insure against the individual risk of their human capital investments. There are several risks involved, including course completion risk and income return risk (will youth find jobs that utilize their additional education). Provision of student loans overcomes loan market incompleteness, but does not overcome insurance market incompleteness. Parental transfers are one way that parents assume some of the risk of youth's education investments. Several countries have initiated income contingent student loan repayment schemes to provide a particular kind of insurance.48 Such schemes are attracting attention in North America also. 47These results may in part reflect an inflexibility in the Canadian student loan program. Eligibility is based on parental income, with loan amounts reduced as parental income increases. Potential borrowers must provide evidence of their parent's income by submitting their parent's tax returns for the previous calendar year. Income shocks are generally not observed in tax returns till the following year. Students can appeal their eligibility determination given evidence of a considerable change in circumstances, such as parents losing full-time jobs. This process may delay receipt of funds, however. 48The countries include the United Kingdom, Australia and New Zealand. 60 CHAPTER 3 Ttoition, Rationing and Equality of Access to Post-Secondary Education 3.1 Introduction Government subsidization of post-secondary education institutions is common in most countries, keeping tuition fees low or even zero. One main argument for such subsidization is to ensure education is affordable for all youth, irrespective of family background. One common criticism of subsidized university tuition levels is that these government transfers are regressive. Youth from wealthy backgrounds are much more likely to attend university in the vast majority of countries than youth from low income families. In addition, individuals who gain university credentials can earn significantly higher incomes in the labour market over their lifetime. There are several explanations for why university attendance is unequal among youth from different family backgrounds. One explanation is that the costs of attendance, even at subsidized tuition levels, discourages low income youth from attending. Even if student loans are available, the risky nature of individual investments in a university education discourage attendance. The analysis of Chapter 2 highlighted a significant causal effect of parental income on education at-tendance. A second explanation is that youth from low income backgrounds do not wish to attend university as it is not rational for them to do so. Their particular abilities may be more suited to occupations that do not require a university education, or they may have considerable dis-utility from university-level study. A third explanation is that youth from low income backgrounds are 61 not accepted at universities even if they decide they want to attend. University places are often rationed on the basis of measured high school achievement. Youth from low income backgrounds may have lower measured achievement as their parents were less able to invest in their education while young. Tuition fees at universities and community colleges are a major direct cost of attendance in the United States and Canada in particular. Revenue from these fees are also an important source of funding for education institutions. Tuition increases may thus have two competing effects on the opportunities for youth, particularly low income youth, to attend post-secondary education institutions. Higher tuition fees may discourage some youth from attending, as direct costs have risen. Increased tuition revenue may also allow education institutions to provide more places for prospective students given government funding levels, reducing any existing rationing. In addition, education institutions may use any increased tuition revenue to provide scholarships or bursaries directly to less-advantaged youth. The question of whether tuition increases have led to less equal post-secondary education attendance must be answered with empirical evidence. The first objective of this chapter is to answer this question. The second objective of this chapter is to analyze directly whether any possible rationing of places affects equality of access to university and community college. In addition to the standard factors influencing the individual's decision to attend (demand factors), I also analyze the effect of factors that influence the probability of acceptance at a post-secondary education institution on attendance. The standard individual demand factors I employ include parental income, parental education, tuition fees, distance to education institutions, provision of financial aid, etcetera. The specific factors influencing the probability of acceptance I include are provincial government fund-ing of education institutions and cohort size. Cohort size reflects the competition among school leavers for the available places in post-secondary institutions within a province in a given year. Inclusion of these two additional factors is important in understanding education attendance out-comes, and they have vastly been ignored in prior analyses of equality in education outcomes. Universities and community colleges in several Canadian provinces increased tuition markedly over the 1990s, while some provincial governments instituted tuition freezes over the same period. This sharp contrast in tuition changes provides the variation necessary for identifying the effect of tuition changes on post-secondary education attendance. As in Chapter 2,1 employ information on individual youth from the Canadian Survey of Labour and Income Dynamics (SLID) covering this 62 late 1990s period in the analysis. Using this data, I estimate the effect of tuition, provincial spend-ing and cohort size on the university and community college attendance of youth from different family income backgrounds. A number of recent studies have attempted to identify the effect of tuition increases on equality of access to post-secondary education in Canada. The ability of these studies to accurately depict the tuition-attendance relationship by parental income background has been hampered by data limitations. My analysis in this chapter is the first to employ both panels one and two of the SLID to test whether recent large tuition increases have resulted in less equal attendance at universities and community colleges in Canada. Empirical studies of education attainment in the United States generally found a small negative relationship between tuition levels and college attendance, with youth from low income back-grounds most sensitive to changes in tuition levels (see Section 3.2 for details). A number of the these studies, however, employed cross-sectional variation across US states in tuition fees only, and may not have adequately controlled for cross-state differences in unobserved characteristics of educational opportunities. In addition, the recent Canadian experience of such a stark contrast in tuition changes provides strong data variation by which to estimate tuition effects. My research should thus provide a particularly well-identified estimate of the tuition-attendance relationship. My results show evidence that tuition increases have led to less equal university attendance. The probability of university attendance for youth from low income backgrounds fell considerably as tuition fees were increased, while youth from middle and high income backgrounds did not respond significantly to the same tuition increases. Attendance at other post-secondary education institutions (primarily community colleges) was not, however, affected by changes in tuition levels. Cohort size also affected attendance at universities but not at other post-secondary institutions. There thus appears to be significant excess demand for university education in some jurisdictions. The resulting rationing of places affected low income youth much more than youth from wealthy family backgrounds. The outline of this chapter is as follows. The relevant literature on this topic is reviewed in Sec-tion 3.2. I describe an extension of the economic model of Chapter 2 that illustrates the probability of acceptance at an educational institution in Section 3.3. The effect of tuition increases on the post-secondary attendance, residence and hours of work decisions of youth are also discussed. Re-cent trends in standard measures of equality of access to post-secondary education using the SLID 63 data are presented in Section 3.4, along with provincial trends in the variables of interest such as tuition. Multinomial logit model estimates of the post-secondary education attendance outcomes for youth are presented in Section 3.5. The differential effect of tuition increases and cohort size changes on attendance by parental income group is identified here. Several extensions to the basic attendance model are discussed in Section 3.6. Section 3.7 concludes with a short discussion. 3.2 The Literature 3.2.1 Canadian Studies Many studies of the determinants of university and community college attendance in Canada have appeared in recent years. Several have attempted to identify the effects of tuition on attendance, but none have adequately identified the effect of tuition increases on youth from different parental income backgrounds. In many cases, data restrictions have hampered these attempts. As noted in Chapter 2, the SLID micro data has been employed by several researchers to analyze particu-lar aspects of the post-secondary education decisions of Canadian youth. None of these studies, however, tested directly whether tuition increases affected equality of access to post-secondary education. Christofides, Cirello and Hoy (2001) analyzed the relationship between family income and the post-secondary education attendance of youth in Canada from 1975 to 1993 using data from the Survey of Consumer Finances (SCF). They concluded that education attendance became more equal over this period, but a considerable difference in attendance by parental income group re-mains. Tuition had negligible effects on attendance. A significant restriction on the data employed in this study is that parental income could only be measured for youth who live at home, poten-tially biasing any results. The authors included only university tuition levels to explain total post-secondary education (including community college) attendance probabilities. University tuition increases may have led youth to attend lower cost community colleges instead, but their analysis would not pick up such substitution. Finally, the period under analysis does not cover the late 1990s, when the largest movements in tuition occurred in Canada. Bouchard and Zhao (2000) found a widening gap in the university attendance rates of youth from high and low socio-economic status families between 1986 and 1994. These researchers em-64 ployed two waves of the General Social Survey (GSS). No parental income measures are available in these surveys, so socio-economic status (a function of the occupation and education attainment of parents) was employed instead. The widening gap co-incided with increasing tuition at Canadian universities over that period. Due to small sample sizes in the GSS, no analysis could be conducted at the provincial level. Corak, Lipps and Zhao (2004) updated the studies of Christofides, Cirello and Hoy (2001) and Bouchard and Zhao (2000). The authors found no evidence of there being more unequal attendance in the late 1990s in Canada as a whole, when tuition increased markedly. The authors did not separate the analysis by province, however.1 Rivard and Raymond (2004) studied the impact of recent tuition increases on equality of post-secondary education attendance in Canada. They employ information from the Youth in Transition Survey (YITS) on youth aged 18 to 20 in 2000. One drawback of the YITS micro-data is that parental income is not provided. The occupation, gender and province of parents were employed to construct a proxy for parental income. A second drawback is that only three years of information is available. This data period may be too short to find an effect of tuition changes on attendance. The authors only included high school graduates in their sample, which may bias estimates given the arguments of Cameron and Heckman (1998). They also excluded Ontario and Quebec youth, the two largest provinces that had starkly contrasting tuition movements. Results suggested that tuition increases have not affected overall attendance, even when focussing on children from low (imputed) parental income groups only. There is some evidence of an interaction effect between tuition and income. Butlin (1999) found that high school grades had a large effect on university attendance, as did Rivard and Raymond (2004). Only those youth with grades above some particular level are generally accepted at university. School grades, however, may reflect the motivation students have for attending university in the future. If some students do not believe that they will be able to attend university given their family circumstances, the motivation to study hard at school may be reduced. In other words, high school grades may reflect university tuition levels. Including grades in estimation may confound estimates of the effect of parental income and tuition on university attendance. Butlin employed the School Leavers Survey in his analysis. This survey first observed youth aged 18 to 20 in 1991, then followed up the same youth in 1995. 'The authors update the results of Bouchard and Zhao (2000) using the GSS for 2001, and find an improvement in equality of attendance over the 1994 to 2001 period. 65 Finnie, Laporte and Lascelles (2004) analyze the relationships between parental education, family structure and the post-secondary education attendance of youth over the 1990s. The au-thors employed the School Leavers Survey (1991) to analyze the relationship at the beginning of the 1990s. They then employed the YITS (2000) survey to analyze the relationship at the end of the 1990s. They find a strong positive relationship between parental education and the education attendance of youth, and that this relationship has strengthened over the decade. They interpret this as evidence of there being less equal access to university in particular in response to the tu-ition increases. The authors also find a strong negative effect of living with one parent only on post-secondary education attendance, but this negative effect has diminished over the period. No parental income measures are available in either of the two data sources employed in the analysis. Beaudry, Lemieux and Parent (2000) find a significant effect of cohort size on any education attendance rates (high school, university or community college) of youth at the provincial aggregate level. Fortin (2005) also analyzed the effect of cohort size and government spending on aggregate education attainment and attendance in both the United States and Canada. There is essentially no evidence, however, of the effect of cohort size and provincial spending on individual education outcomes nor on the equality of access to post-secondary education in Canada. 3.2.2 US Studies There is a vast US literature on the unequal nature of college attendance, particularly with regards to visible minorities.2 Some examples are given in the survey of Haveman and Wolfe (1995). The overriding conclusion drawn from this literature is that parental income and education matter in the education attainment of youth. Once differences in these family characteristics are controlled for, however, visible minorities are no less likely to attend college than other youth. Heller (1997) updated the influential Leslie and Brinkman (1987) survey of US studies on the effect of tuition fees and financial aid on the demand for higher education. The main conclusions of this survey are: (a) tuition increases and financial aid decreases lead to declines in enrolment, (b) enrolment is more sensitive to changes in grants than to changes in loans or work-study programs, (c) youth from low income backgrounds are most sensitive to tuition and financial aid changes, (d) black students are more sensitive to tuition and financial aid than white students, and (e) students 2This includes attendance at four year colleges, which is the equivalent of university in Canada. Attendance at two year colleges in the United States is comparable to community college attendance in Canada. 66 in community colleges (two-year courses) are more sensitive to tuition and financial aid changes than those at four-year colleges and universities. Hilmer (1998) analyzes the effect of tuition levels on the decision of youth to start education at a university (4 year college), community college (2 year college), or neither. A model employing the assumption that the attendance decision is based on the probability of course completion yields a natural ordering of the three options. Ordered probit estimation was conducted based on this natural ordering. Results suggested that own price effects were negative, while cross-price effects were positive. Mazumder (2003) analyzes the effect of both parental wealth and parental income on post-secondary education attendance in the United States using the Survey of Income and Program Participation (SIPP) data. He finds that wealth levels do have an effect, and that the effect of income, conditional on wealth quartile, is largest for youth from homes in the second income quartile. Card and Lemieux (2000) highlighted the significant effect of cohort size on state aggregate ed-ucation attendance rates of youth in the United States. Bound and Turner (2003) and Fortin (2003) analyzed the effect of both cohort size and government funding of education on college-going be-haviour in the United States, again at the state aggregate level, and found significant relationships. As in Canada, there is essentially no evidence of the effect of cohort size and provincial spending on individual education outcomes nor on equality of access to post-secondary education in the United States. 3.3 Extensions of the Economic Model of Education Attendance I described an economic model of an individual's decision to attend a post-secondary education institution in Section 2.3. The role of parental transfers in this decision was also described. The particular role played by tuition costs in this decision will be elaborated upon below. More impor-tantly, an extension of the model to include a role for potential rationing of post-secondary places is described. The probability of a youth attending PSE will be a function of both the probability of being accepted at an institution and the probability of applying (deciding to attend). This ac-ceptance probability will depend upon the number of available spaces at institutions relative to the number of youth wanting to attend. My empirical analysis in this chapter focuses on the effect of tuition, provincial spending and 67 cohort size on post-secondary attendance. Several extensions to the basic empirical model are considered in Section 3.6 below, including an analysis of the residence (live with parents or not) and the hours of work decisions of students. The effect of tuition increases on the attendance outcome alone may not capture the full impact of those increases. Youth may respond by working more while studying, lengthening degree completion times and reducing academic performance. If youth choose to attend an institution closer to home and remain living with parents, it may put added pressure on parents. The program at the institution closer to home may also not be the best match. Analyzing these outcomes is central to identifying the full effect of tuition increases on youth from different family backgrounds. An extension of the model to analyze the youth's decision to live with their parents or not is also provided below. Details of the hours of work response to tuition increases are also provided. 3.3.1 The Effect of Tuition on the Decision to Attend In the economic model of the decision to attend PSE outlined in Section 2.3, I constructed an approximate decision rule for attendance. Other things remaining equal, increases in tuition will lower the probability of deciding to attend. In the case of no contingent transfers, however, nothing in the decision rule of equation 2.5 predicts that a higher proportion of low income youth will choose not to attend as tuition rises. The proportion of agents at the margin of the decision rule, given non-contingent parental transfers yi, is a function of the distributions of the heterogeneous variables 0 and TT. Tuition increases may not necessarily lead to less equal attendance. If parents choose to make a transfer ys contingent upon their child attending PSE, it directly lowers the cost of attendance, as in equation 2.6. If such transfers are important, responses of youth to tuition increases may differ considerably by parental income. Some parents may find it optimal to raise transfers to overcome any tuition increases to keep their children attending. High income parents should be able to absorb tuition increases while still benefitting from children attending. Parents with less income may not be able to absorb tuition increases without too large a reduction in their own consumption. 68 3.3.2 Rationing and Acceptance Probabilities The model of individual post-secondary attendance decisions is based on the premise that rational agents will choose to attend PSE if the expected net benefits of attendance are positive. If there is excess demand for places at government subsidized tuition levels, however, not all agents who wish to attend will be accepted. Places will be rationed among those applying to attend on some basis. I will analyze the cases of random acceptance rules and acceptance based on high school achievement in turn. Applying to attend a post-secondary institution will be assumed to be costless for simplicity. Thus all agents with positive expected net benefits (enbi > 0) from attending will apply. Using the model of individual choice outlined in Section 2.3, this will be true if equation 2.6 holds. Define the probability of acceptance given application as Pr(acci\applyi). The probability of attendance can then be defined as follows, where 1[..] is the indicator function set to one if the equation in brackets is true, zero otherwise. Pv(attendi) = l[en6; > 0] x Pr(acci\applyi) (3.1) If the rationing rule of PSE institutions is random acceptance (a lottery), then the probability of acceptance (Pr(acCi\applyi)) will be the same for all agents applying in a given jurisdiction (province) in a given year. This probability will equal the number of available places divided by the number of applicants. The number of places will in turn equal total institution revenue divided by cost per student. Costs per student (cps) may be a choice variable for institutions, trading off quality versus quantity of student education according to the institution's objective function, or the objective function of the government. For now cps will be treated as exogenous and constant in real terms over time. Revenue of institutions has three main sources: governments (GR), student tuition payments (tuition fees per student), and other revenue (OR). Other revenue may come from endowment funds, private individuals or companies. revenue GR + OR + (tuition x Places) GR + OR Places = = = (3.2) cps cps cps — tuition The probability of acceptance can then be defined as follows. . . , . Places Places rviaccAapplyi) = — — = — ^ (3.3) v x\wyM A p p h c a t i o n s ^=1l[enbj > 0)] Here N is the total number of agents deciding on whether or not to attend, i.e. the high school graduating class (cohort) in a jurisdiction. It is easy to see that agents in larger cohorts will have 69 a lower probability of acceptance, other things being equal. Putting all this together yields the following equation for attendance. The probability of attendance for an agent i is positively related to institution revenue from government and other sources, and negatively related to the size of the cohort N. „ GR+OR Pr (attendO = l[en6« > 0)] x ( 3 . 4 ) E,-=il[en6j > 0)] As noted in Section 2.3, the individual agent's education decision can be interpreted as a ran-dom utility model. We can construct a measure of the probability that an agent will have a positive expected net benefit from attendance, and thus apply to attend (Pr (applyi)). First, denote a linear approximation to the expected net benefits of attendance as follows. enbi = Xi(3 — (3.5) Here the Xi are observable characteristics of agents, parental attributes and jurisdiction mea-sures (such as tuition levels) influencing the agent's demand for an education. The vector Q denotes model parameters and Ei is an unobservable characteristic affecting the agent's net benefit calcu-lation. The probability of applying to attend PSE is defined as follows, where F(..) denotes a cumulative distribution function for et. Pv(applyi) = Pr(en6l > 0) = F{XiB) (3.6) Now the probability of attendance is: Pr(attendi) = Pv(applyi) x Pr(acci\applyi) GR+OR = FiXiP) x cvs~tuiUon (3.7) E j l i * W ) The effect of many province-wide variables on the probability of attendance given rationing is no longer as clear cut as without rationing. The change in the probability of attendance due to a change in one of these covariates generally has two offsetting components. d p f x i T i ) = p ^ \ a p ^ >< & * (/w) - *w) * f H w l ) (3-8) As an example, suppose the average expected wage premium (X(k)) from attending PSE rises. Increases in the wage premium raise the net benefits of attending (Bk > 0). This will increase the probability of agent i applying to attend. It will also increase the probability of other agents 70 applying, which will increase rationing and lower the probability of acceptance. If the application response of agent i to this wage premium change is close to the average response of other agents in the jurisdiction, the probability of attendance will not change at all. This assumes that the government does not respond to the increased demand for PSE by increasing funding. The effect of tuition changes on the probability of attendance is even more complicated here. Tuition increases raise the cost of attendance, lowering the net benefits of attendance and thus lowering the probability of applying (/3t < 0 ) . Let us denote tuition as covariate X(t). The effect of tuition increases on the probability of attendance can be constructed as follows. a P ray = x ft x - F(W x grfg'J GR+OR + * W ) x ^T'Tf^ (3-9) The final term in equation 3.9 highlights the positive effect of tuition increases on the prob-ability of attendance if there is excess demand and thus rationing. The negative effect of tuition increases on the expected net benefits of attendance are offset by increases in the probability of acceptance in the attendance probability as other agents are also less likely to apply. The increase in places due to tuition increases should raise the probability of attendance for most agents. I now complicate things even more by moving from random allocation of post-secondary places to allocation based on measured high school achievement. Places at universities in many countries are allocated among applicants using measures of the quality of the individual and their preparation for further study. The measures often employed are high school grades. These grades may or may not be based on jurisdiction-wide exams. The economics of education literature posits a production function for individual school achieve-ment (A) as follows. School outcomes, such as grades, are a function (H) of several sets (current and past values) of inputs. A = H(parental inputs, school inputs, peer effects, ability, motivation) (3.10) The last input in this equation (motivation) is included here to highlight the effect of an agent's own post-secondary attendance plans on the effort they make during school. Rational agents be-lieve that being accepted at a PSE institution is a function of their measured school achievement. If they wish to attend after school completion, having already made a net benefit calculation, they may decide to work harder during school, and vice versa. 71 If an agent's achievement at school exceeds some threshold level (Tp), then they will be ac-cepted at an institution conditional on applying. Again assume application is costless so all agents with positive expected net benefits of attendance will apply. The threshold Tp is not known until after application, as institutions set Tp once the set of applicants is known. Institutions then set Tp to ensure all places at their institution are filled. The level of Tp in any given period and jurisdiction will be a complicated function of institutional revenues from government and other sources, tuition levels, cohort size and the attributes of the cohort. Define a linear approximation to the school achievement production function as follows. Ai = Ziy-vi (3.11) Here the Zt are observable agent characteristics, parental attributes, plus peer and school input measures. The vector 7 denotes model parameters and i/j includes both unobservable characteris-tics of individuals and an idiosyncratic error affecting their measured achievement. The probability of PSE attendance for an agent can now be given by the following, where the function F2 denotes a bivariate distribution for the unobserved variables Si and v^. Pv(attendi) = F2{ Xt/3 , Zi7 - Tp ) (3.12) It is reasonable to assume that the unobserved variables £j and will not be independent of one another. The individual unobserved variables affecting the agent's net benefit calculation will also generally affect their achievement during school. It may be innate ability, or any unobserved variable that affects the agent's expected net benefit of attendance. Higher expected net benefits will raise the motivation of the agent to put in effort at school, leading to higher grades and thus a higher acceptance probability. Many of the results of the random allocation case will flow through to this case of institutional rationing by high school grades. Larger cohorts will have lower probabilities of acceptance. Gov-ernment funding will raise attendance, and tuition increases should raise attendance probabilities for many but not all youth. My empirical analysis below estimates a reduced form version of equation 3.12, where no attempt is made to separate the demand and probability of acceptance contributions to attendance outcomes. I estimate the overall effects of the variables of interest (tuition, provincial spending and cohort size) on the post-secondary education attendance probabilities of youth from different 72 parental income backgrounds. Given the model, attendance should be negatively related to cohort size and positively related to provincial spending on PSE institutions. The effect of tuition on attendance could be either positive or negative in the model, depending mostly on the extent of any excess demand. 3.3.3 Economic Model Extension of Residence and Hours of Work Decisions Now consider the agent's decision between remaining in the parental home in period one or living independently. Remaining in the parental home may save the agent rent, food and laundry costs. Denote the dollar savings from living with parents by a. If saving money was the only outcome from remaining in the parental home, all agents would do so, which is not what we observe. Consider the presence of some dis-utility from living with one's parents, denoted by Q, perhaps reflecting lower privacy or freedom. Such dis-utility may be heterogeneous across agents, with a positive mean value for its distribution. For simplicity, the residence decision is assumed to be made after the education attendance decision. The relaxation of this assumption should not alter the decision rules derived from the model, as each decision rule should hold conditionally.3 To begin, consider an agent who has chosen not to attend PSE. Lifetime utility conditional on living in the parental home and assuming no borrowing constraints is: Vho = max 14(7/1 + ct + W\h + b, L — h) — Q + p~lu(w2 — rb,L — 1) (3.13) {Kb} Lifetime utility for an agent living independently is: Va0 = maxji(?/i + w\h + b, L — h) + p~1u(w2 — rb,L — 1) (3.14) {h,b} Maximization yields the following decision rule. Non-students choose to live in the parental home if: ft < a (3.15) If dis-utility, normalized by the marginal utility of consumption given independent living, is less than the savings in expenses, then a rational agent will choose to remain in the parental home. 3Rankings of all four possible outcomes - attend or not and live with parents or not - will depend upon specific parameter values, including whether heterogeneous parameters are correlated with one another. 73 An equivalent residence decision rule can be generated conditional on attending post-secondary and no borrowing constraints. It will be of the same form as equation 3.15, with the marginal utility of consumption term now uc\as, which is evaluated at a different consumption level. Taking the simplest case of no direct utility from attendance (</> = 0), only those agents for which r _ 1 7 r exceeds T+W\S choose to attend. Period 1 consumption will be higher for those optimally choosing to attend than those who do not, given no borrowing constraints. This lowers the marginal utility of consumption for those agents, and thus lowers the probability of those agents remaining in the parental home. Such agents take the extra income from their investment in human capital, smooth it over all periods, and thus avoid any dis-utility from living at home. This implication of the model is reversed when we add borrowing constraints. The decision rules will again be of the form in equation 3.15, but the appropriate consumption levels in the marginal utility terms will be changed. Period 1 consumption is now lower for debt-constrained post-secondary attenders than non-attenders, given parental transfers yx. Debt-constrained agents who choose to attend are more likely to remain in the parental home. Agents who receive very high transfers from parents may not be debt-constrained, so even if they attend, they are less likely to remain in the parental home. The probability of living with parents given attendance will be higher for agents from middle and low income families. The residential choice of agents will also depend on tuition levels if they still choose to attend PSE. Higher tuition will lower period 1 consumption for agents who attend, particularly if there are borrowing constraints. Lower period 1 consumption raises the marginal utility of consumption in period 1, reducing the effect of dis-utility from living with parents on the residence decision. Thus the probability of living with parents should rise as tuition is increased. The effect should be greater for agents with low parental transfers, given a concave utility function. Hours of work will generally increase for agents who still choose to attend PSE after tuition is increased, irrespective of whether there are borrowing constraints or not. The effect, however, will be more pronounced under borrowing constraints, as agents cannot smooth the increased tuition payments over future periods. The first order condition for an interior solution for the optimal hours of work given PSE attendance is as follows. WlUcls = Ulls (3-16) In this equation, u&3 is the marginal utility of consumption in period one, and uns is the 74 marginal utility of leisure in period one. Consumption in period one equals y\ + W\h + b — r and leisure equals L — h — s. If tuition r increases, consumption in period one falls and tt c l s will increase, given a concave utility function. To ensure the first order condition continues to hold, given borrowing b is constrained at the maximum, optimal hours of work h must rise. 3.4 The Data 3.4.1 Provincial Trends in Post-secondary Education in Canada The Canadian post-secondary education system was described in broad details in Section 2.4 above. In this section, I describe provincial movements in PSE aggregate measures such as tuition, provincial spending and cohort size. I employ the within province variation in these measures to identify their effects on the PSE attendance of individuals in the empirical estimates of the next section. As previously noted, the vast majority of universities and community colleges in Canada are financed and regulated by the provinces. If desired, provincial governments can exercise control over tuition fees and enrolment levels at these institutions. Universities and community colleges in several Canadian provinces increased tuition markedly over the 1990s. Tuition fees were dereg-ulated in several provinces. The Quebec and British Columbia provincial governments, however, instituted nominal tuition freezes over this same period. British Columbia lifted the freeze in 2002, while in Quebec, tuition has still not increased since the mid 1990s. Changes in real university tuition levels (provincial average) ranged from minus 14% to plus 46% from 1995-96 to 2001-02, while real community college tuition changes ranged from minus 15% to plus 168% over the same period. Movements in provincial average real tuition levels at universities and community colleges are illustrated in Figures 3.1 and 3.2 respectively.4 The proportion of total university rev-enue obtained from tuition fees rose from around 10% to 20% over the 1990s. The proportion of community college revenue from such fees also doubled from around 7% to 14% over this period. Aggregate enrolment at post-secondary institutions in Canada stagnated over the 1990s, but it did not fall. See Figure 2.3 and Figure 2.4 for movements in university and community college enrolment in Canada respectively. Overall education attainment of Canadian youth does not appear 4University tuition is for studying a Bachelor of Arts undergraduate degree. 75 to have been negatively affected by increases in tuition. Measuring the effect of these tuition increases on the education attendance of youth from different family backgrounds, however, is important when determining the full effect of such policies. The 1990s tuition increases were often rationalized by the need to increase supply of post-secondary places to meet growing demand. Labour market returns to university education in par-ticular remained high in Canada over the period. At the same time, provincial government funding of PSE institutions stagnated or fell in real terms (see Figure 2.2), as did government funding of most expenditure categories. Provincial governments provide the majority of funding to these in-stitutions, particularly for the educational component of their operations. Movements in provincial government spending by province are provided in Figures 3.3 and 3.4 for universities and com-munity colleges respectively.5 These spending measures are quite noisy, with no strong variation across provinces over time readily observable.6 As discussed in the previous section, cohort size should affect the probability that an individual will attend PSE if there are supply constraints at PSE institutions. I constructed a cohort size index to represent the size of the age 16 population in the province relative to the size of this population in 1993. The index is set to 100 in each province in 1993. If, for example, the age 16 population in a province rises by 10% from 1993 to 1998, this index will take the value 110 in 1998. See Figure 3.5 for movements in these indices by province over the period. Note the significant variation across provinces, with cohort size rising significantly in Ontario, Alberta and British Columbia in particular, and falling considerably in Newfoundland and New Brunswick. Increasingly over the 1990s, student financial aid was provided in the form of loans rather than non-repayable grants. Quebec remains as the one province that provides significant funding to low income students via non-repayable grants, but these grants are given to the most disadvantaged youth only. Many universities also provide scholarships and bursaries directly to students. This type of support has increased in the 1990s as tuition fees have increased. See Figure 3.6 for provincial level movements in this source of student support. The steepest increases occurred in Ontario and Alberta. Large increases in university tuition also occurred in these two provinces over the same period. 'Measures of real provincial spending on universities and community colleges are constructed on a per person aged 18 to 24 in the province basis. 6This lack of strong variation will make it difficult to estimate the effect of provincial spending on attendance in my estimates of the next section. 76 Figure 3.1: University Tuition by Province 2000/01 SCAN - arts undergraduates $5,000 $4,500 $4,000 $3,500 $3,000 $2,500 $2,000 $1,500 $1,000 1 1 1 1 1 1 1 1 1 1 1992-93 1994-95 1996-97 1998-99 2000-01 2002-03 •Nfld. Ont. P.E.I. -o—Man. - - N . S . - A — Sask. - - N.B. -+— Alta. •Que. •B.C. Source - Tuition provided directly by Statistics Canada's Centre for Education Statistics. 77 Figure 3.2: Community College Tuition by Province 2000/01 $CAN $3,000 $2,500 A $2,000 H $1,500 $1,000 $500 1 , ! , 1 , ! ! : , 1992-93 1994-95 1996-97 1998-99 2000-01 2002-03 •Nfld. Ont. - P.E.I. - B — M a n . N.S. - A — Sask. - - N.B. •+— Alta. Que. •B.C. Source - Tuition taken from statistics reported by the Manitoba Council on Post-Secondary Education. 78 Figure 3.3: Provincial Spending on Universities by Province 2000/01 SCAN per 18-24 year old $3,600 $3,400 H $3,200 $3,000 $2,800 $2,600 $2,400 H $2,200 4 $2,000 1992-93 1994-95 •Nfld. Ont. P.E.I. - e—Man. 1996-97 - - N . S . -a— Sask. 1998-99 N.B. -Alta. 2000-01 •Que. •B.C. Sources - Provincial spending measures taken from Cansim II tables 478-0007. Population aged 18-24 taken from Cansim II table 51-0001. 79 Figure 3.4: Provincial Spending on Community Colleges by Province 2000/01 SCAN per 18-24 year old $3,000 $2,600 $2,200 $1,800 $1,400 $1,000 $600 A $200 1993 •Nfld. Ont. 1995 P.E.I. - Q — M a n . 1997 - - N . S . - a — Sask. - i r 1999 N.B. - Alta. 2001 Que. B.C. Sources - Provincial spending measures taken from Cansim II tables 478-0004. Population aged 18-24 taken from Cansim II table 51-0001. 80 125 120 115 110 105 100 95 90 85 80 75 Figure 3.5: Age 16 Population Size Indices by Province \ s X i r 1993 - N f l d . — Ont. 1995 - - P.E.I, - e—Man. i 1 1 1 1 r 1997 1999 2001 N.S. - a — Sask. - - N.B. -+— Alta. •Que. •B.C. Source - Population estimates taken from Cansim II table 51-0001. 81 $1,200 Figure 3.6: University Provided Student Financial Aid by Province 2000/01 SCAN per full-time student $1,000 $800 $600 $400 $200 $0 1 1 r 1992-93 1994-95 •Nfld. Ont. P.E.I. Man. 1 r 1996-97 N.S. - A — Sask. 1998-99 2000-01 - N.B. — Q u e . Alta. •B.C. Sources - University Provided Student Financial Aid figures provided directly by Statistics Canada's Centre for Education Statistics. Full-time enrolment figures taken from Statistics Canada's Cansim cross-tabulation files and from the Education Matters publication. 82 3.4.2 SLID Measures of Post-secondary Attendance Equality I employ data from the Survey of Labour and Income Dynamics (SLID) in the empirical analysis of this Chapter, as I did in Chapter 2. The details of this survey are provided in Section 2.5.1. The particular benefit of this data for this analysis is the accurate information on parental income, along with measures of the education attendance outcomes of youth. The sample I employ in this chapter is larger than that employed in Chapter 2 due to lower information requirements here. The final sample I employ here covers 1,874 individual youth, from a potential sample size of 2,909.7 See Appendix A for details of how the final samples were constructed. A simple measure of the level of equality in post-secondary attendance for youth is the ratio of the percentage of youth from high income backgrounds that attend to the percentage of youth from low income backgrounds. This is referred to as the Odds ratio. A similar measure is the difference between these two percentages, referred to as the Gap measure. These two simple measures were constructed for the entire sample, and for the first two panels of the SLID separately, with the results presented in Table 3.1. For the entire sample, high income youth are 2.25 times more likely to attend university than low income youth. This difference is non-existent for attendance at other PSE institutions only (mostly community colleges). In fact, low and middle income youth are more likely than high income youth to attend other PSE. Overall, high income youth are most likely to attend any type of PSE institution due to their much higher probability of attending university. Over this entire sample period, Canada is a considerable distance from equality in education attendance. Parental income was calculated as the average annual real8 parental income after tax over the three years when the youth was aged 16, 17 and 18. The parentage of youth was determined by the family structure of the household when the youth was aged 16, that is, whether the youth lived with both parents or only one at that age. I also adjusted parental income for cost of living differences between different family sizes and between city and rural residents using Statistics Canada's annual measures of Low Income Cut-offs (LICOs).9 Youth were divided into three equal groups (high, middle and low) using these adjusted parental income measures.10 In very rough terms, low income youth were those with average 2001 dollar pre-tax annual parental income below approximately 7In Chapter 2, the usable sample was 1,335 observations. 8Nominal income measures were deflated by the Canada-wide Consumer Price Index. 9Living cost measures are constructed tor four sizes of urban areas and for rural areas. 1 0Youth were divided into these three quantiles for each panel separately using the appropriate weights in the SLID. 83 Table 3.1: Measures of Post-secondary Attendance Equality Parental Income Attending A l l Low Middle High Odds Gap Both Panels University 31.7 19.5 30.6 43.9 2.25 24.4 (1.1) (1.8) (1.8) (1.8) Other PSE 35.8 36.1 38.8 32.8 0.91 -3.3 (1.1) (1.9) (1.9) (1.9) Any PSE 67.5 55.6 69.4 76.7 1.38 21.1 (1.1) (1-9) (1.9) (1.9) Panel One University 32.5 18.8 31.8 45.8 2.43 26.9 (1.5) (2.6) (2.6) (2.5) Other PSE 32.3 32.4 37.1 27.5 0.85 -4.9 (1.6) (2.8) (2.7) (2.6) Any PSE 64.8 51.3 68.9 73.2 1.43 22.0 (1.5) (2.7) (2.6) (2.5) Panel Two University 30.8 20.2 29.3 42.0 2.08 21.8 (1.5) (2.6) (2.7) (2.5) Other PSE 39.3 39.6 40.6 38.0 0.96 -1.6 (1.6) (2.7) (2.8) (2.6) Any PSE 70.2 59.8 69.9 80.1 1.34 20.2 (1.5) (2.6) (2.7) (2.5) Notes: 1,874 observations. Source - Survey of Labour and Income Dynamics. Rates of post-secondary education attendance by parental income quantile and SLID panel (Panel one aged 18 in 1995-97, Panel two aged 18 in 1998-2000). Standard deviations are in parentheses. PSE refers to post-secondary education. 84 $40,000. High income youth were those with parental income above approximately $70,000. See Appendix B for more details on the reasons underlying my adjustment of parental income. There is no evidence that attendance became more unequal over the second half of the 1990s for Canada as a whole. In fact, the measures show attendance has become slightly more equal from panel one to panel two of the SLID. Panel one youth would normally enter university from 1995 to 1997, panel two youth from 1998 to 2000. The Odds measure for the university attendance of high income versus low income youth improved from 2.43 to 2.08 over the period. This overall im-provement co-incides with the findings of Corak, Lipps and Zhao (2004) employing an alternative Canadian data set. A much different story emerges when I calculate movements in these measures of attendance equality separately for provinces that froze tuition levels over the late 1990s (Quebec and British Columbia) and the remainder that increased tuition. The results of splitting the measures into tuition freezer and tuition increaser provinces are presented in Table 3.2. Equality of attendance at the university level improved considerably from panel one to panel two in the two provinces that froze tuition. The Gap in university attendance rates between high and low income youth narrowed from 29 percentage points to 11 percentage points in those two provinces. This same measure deteriorated in provinces that raised tuition levels. The Gap widened from 23 percentage points to 28 percentage points. The relative change between the two regions is a very large 23 percentage points. Difference in difference tests of the statistical significance of these relative changes showed that the relative widening of the gap in response to tuition increases was statistically significant at the 5% level." This points to tuition fee increases leading to a significant reduction in the equality of access to a university education in Canada over the period. Average nominal university tuition increases over the second half of the 1990s ranged from 20% in Manitoba to 60% in Ontario. For community colleges, tuition increases were even larger. They ranged from 33% in P.E.I, to 200% in New Brunswick. No negative effect of tuition increases on equality in attendance at other post-secondary institutions was found, however. Note the higher university attendance rates in tuition raiser provinces overall, even for low income youth. This may reflect the larger capacity of universities in tuition raising provinces to "The difference in differences estimator employing the Odds ratio of PSE attendance equality was constructed as ^° = [ O ^ f ) ~ (^J?)] ~~ K ^ T " ) ~~ C^n" ) ] ' H e r C ' h a n d ' r e * e r t 0 l l i g h a n d ' 0 W i n c o m e y ° u t n respectively, r and / refer to raiser and freezer provinces respectively, while 1 and 2 refer to the appropriate SLID panel. The Gap measure ( A 9 ) is of the same form, with the ratios of probabilities replaced by differences. 85 Table 3.2: Details of Post-Secondary Attendance Inequality Parental Income Attending A l l Low Middle High Odds Gap University Freezers in PI 22.7 7.2 26.5 36.2 5.03 29.0 (2.4) (4.0) (4.1) (4.2) Freezers in P2 24.1 20.3 21.5 31.0 1.53 10.7 (2.4) (3.8) (4.3) (4.2) Raisers in PI 38.8 27.6 35.2 50.8 1.84 23.2 (1.9) (3.4) (3.3) (3.1) Raisers in P2 35.2 20.1 33.9 47.8 2.38 27.7 (1.9) (3.5) (3.3) (3.0) D in D TESTS 4.04 22.8** Other PSE Freezers in PI 49.2 45.6 57.9 44.0 0.96 -1.6 (2.4) (4.1) (4.2) (4.4) Freezers in P2 50.4 46.4 58.6 47.5 1.02 1.1 (2.4) (3.9) (4.5) (4.3) Raisers in PI 21.5 22.5 23.5 18.8 0.83 -3.7 (1.9) (3.5) (3.4) (3.2) Raisers in P2 32.3 33.9 29.8 33.1 0.98 -0.8 (1.9) (3.6) (3.4) (3.1) D in D TESTS 0.08 0.02 Any PSE Freezers in PI 71.9 52.8 84.4 80.2 1.52 27.4 (2.4) (4.0) (4.1) (4.3) Freezers in P2 74.4 66.7 80.2 78.6 1.18 11.8 (2.4) (3.8) (4.4) (4.3) Raisers in PI 60.2 50.1 58.8 69.6 1.39 19.5 (1.9) (3.5) (3.3) (3.1) Raisers in P2 67.5 54.0 63.8 80.9 1.50 26.8 (1.9) (3.5) (3.4) (3.1) D in D TESTS 0.45* 22.9** Notes: 1,874 observations. Source - Survey of Labour and Income Dynamics. Rates of PSE attendance by parental income quantile, SLID panel, and provincial region (provinces with tuition increases versus tuition freezers). One, two & three asterisks (*) denote significance of difference in differences tests (D in D TESTS) at 10%, 5% & 1% respectively. Standard deviations are in parentheses. PSE refers to post-secondary education. 86 accept potential students. It may also reflect greater demand for university education in those par-ticular provinces, particularly if the alternative community college system is not as well developed in those provinces as it is in Quebec and British Columbia (the two tuition freezer provinces). The university attendance rate for youth from low income backgrounds and tuition freezer provinces in panel one appears unusually low at 7.2 percentage points. Some readers may be con-cerned that this one number may be driving the large observed reduction in equality of university attendance just discussed. This low observed rate of university attendance, however, reflects the observed individual characteristics of youth in these provinces in the first SLID panel and this in-come level. Those youth came from families with parents who had quite low levels of education. I estimated the probability of university attendance for youth using individual and parental charac-teristics alone (not tuition levels, etc). The predicted probability of university attendance for youth in this cell was an average of 11 percentage points, not too far above the observed 7.2 percentage points. Once I control for parental education levels and other observable individual characteristics in the analysis of the next section, these individual observations will not drive the estimated effects of tuition increases on attendance. 3.5 Post-Secondary Education Attendance Estimates 3.5.1 The Estimated Model As in Section 2.6 of the previous chapter, I employ the multinomial logit technique to estimate the post-secondary attendance outcomes of Canadian youth among the following three options: (a) attend university, (b) attend other PSE only (primarily community college), and (c) not attend PSE at all . 1 2 A list of the covariates included in estimation is provided in Table 3.3, along with sample summary statistics for the larger sample employed in this chapter. These covariates again include measures of parental education, average real parental income, number of children in the family, gender, visible minority status, immigrant status of parents, and indicators of distance to the closest universities and community colleges. A description of all the variables is provided in l 2Note that Hausman and McFadden (1984) tests of the Independence of Irrelevant Alternatives (IIA) assumption of the multinomial logit technique could also not be rejected using this larger data set. In addition, non-nested tests (Vuong (1989)) of ordered logit and probit models versus the multinomial logit model again resoundingly rejected the ordered models, even when employing the Akaike Information Criterion that adjusts the test statistic for the smaller number of parameters being estimated in the ordered models. 87 Appendix B. Most importantly for this analysis, the estimated models include measures of tuition fees and provincial government funding of universities and community colleges, plus cohort size. The measures I employ refer to values for the province in which the individual resided at age 16 and while still attending high school. Youth may move to a different province to attend university in particular, yet moving involves considerably higher costs. Universities in the near vicinity are the least cost alternative, thus tuition levels at universities and community colleges within the province are the appropriate measure when considering the cost of access to post-secondary education.13 Information about education opportunities are also more readily available to high school students for institutions within their province.14 As discussed in Section 3.3, cohort size and provincial funding of universities and community colleges may affect an individual's probability of post-secondary attendance. These variables will determine the probability of acceptance at an institution if there is excess demand for places at subsidized tuition levels. Measures of cohort size and provincial funding of post-secondary educa-tion have rarely been included in previous research on individual education attendance outcomes, particularly in studies of equality of access. Inclusion of these cohort size and provincial funding measures in the estimated model affects the interpretation of the estimates. I am no longer estimat-ing an approximate attendance decision rule like most prior analyses of individual PSE attendance, and like the analysis of Chapter 2. I am now estimating the reduced-form effects of both demand and supply factors on the probability of attendance. To separate out the effects of various factors on the decision to attend and the probability of acceptance is beyond the scope of this research. It is left for future work.15 According to the economic model outlined in Section2.3, parental transfers (contingent or not) are determined by parental income and the number of children in the family. The model revealed 1 3 Quebec universities charge the lowest tuition fees for students from homes within the province. Out of province students are charged a tuition fee over twice as high at Quebec universities. Universities in other provinces do not charge higher fees to out of province students. 14It is not possible to establish whether youth attended post-secondary institutions outside the province they attended high school in the SLID data with any accuracy. l5Without separate measures of both the decision to attend and final attendance given acceptance, it is difficult to identify both effects separately. Only final attendance measures are available in the SLID micro data. It may be possible to empirically identify both effects with attendance measures alone, if individual continuous (rather than discrete) variables are available that affect the decision to attend but not the probability of acceptance, and vice versa. The search for such variables continues. 88 Table 3.3: Regressors in Model - Summary Statistics Variable Mean Standard Deviation Female 0.484 Aboriginal descent 0.024 Parent immigrant 0.239 Visible minority 0.091 Lone parent 0.166 Parents not graduate high school 0.114 Parents other post-secondary only 0.445 Parent completed university 0.203 Real average parental income* 66,158 42,406 Children in family 2.78 1.44 University > 80 km away 0.338 Community College > 40 km away 0.128 University tuition* 2,893 784 Community College tuition* 1,189 705 University financial aid (per student)* 640 271 Province cohort size index (1993=100) 103.5 5.7 University provincial spending (per 18-24)* 2,527 375 Comm. College provincial spending (per 18-24)* 1,259 732 Observations 1,874 Note: Sources include the Survey of Labour and Income Dynamics and Statistics Canada. Aster-isks (*) denotes measures are in real 2000/01 Canadian dollars. 89 that parental transfers and the costs of education such as tuition enter the marginal utility terms of the attendance decision rule in a non-linear manner. Youth from wealthy backgrounds may respond less to tuition movements than youth from low income households. This suggests either entering interacted parental income and tuition terms in the estimated equation or separate estimation of attendance outcomes by parental income group. I employ the second approach in this analysis.16 3.5.2 Estimation Results for the Full Sample Results of multinomial logit estimation of the three option post-secondary education attendance outcomes of youth are presented in Table 3.4. The marginal effects presented in the table are the effect of each covariate on the probability of attending university (first column) and other post-secondary (second column).17 Indicators for parental income quantile are included in these estimates, but are not interacted with any other variables in the estimated equations. As in the estimates of the previous chapter, standard errors were corrected for clustering by province and year, and probability weights provided in the SLID were employed during estimation. The marginal effects of the set of individual characteristics on attendance mirror those reported in the analysis of Chapter 2 employing a smaller data set, as we would expect. Some characteristics are now statistically significant where they were not in the analysis of Chapter 2 (see Tables 2.5 and 2.6). This merely reflects the larger sample size available for this analysis. The overall size and sign of the marginal effects remain the same. Individual characteristics are much more significant in predicting university attendance than they are in predicting other post-secondary attendance. Females are much more likely to attend university than males.18 Youth of aboriginal descent are much less likely to attend university, while visible minorities and youth with an immigrant parent are much more likely. The number of children in the family appears unrelated to education choice. Parental education and income i6Preliminary estimates highlighted the insignificance of linear measures of parental income in attendance proba-bilities. 17These marginal effects were calculated with all indicator variables set to zero and continuous variables set to the values faced by an individual with all indicator variables set to zero (e.g. a male from Ontario turning 16 in 1995). The time trend was set to a value of three, and the children in the family variable was set to three also. l 8Note that the marginal effect for the female indicator worked through both the estimated coefficient on the indica-tor itself and the female-specific time trend. The female time trend was set to zero for calculating all marginal effects except for the marginal effect of the female-specific trend itself. In this case the female trend was set at the value of three, the same value set for the overall time trend. 90 levels, however, are strongly positively related to the probability of attending university. This again highlights that university attendance in Canada is a long way from equality. Increases in community college tuition have a sizable and statistically significant negative ef-fect on university attendance, highlighting a negative cross-price effect at the university level. A $500 increase in community college tuition lowers university attendance by nearly four percentage points. This result may be identifying a negative effect on university attendance, if community college is chosen as an alternative pathway to subsequent university attendance. The estimated negative effect may also reflect the close correlation in the two tuition measures within provinces. Many provinces increased tuition at both universities and community colleges at the same time and by similar dollar amounts. The correlation between the two measures at the provincial level is a considerable 0.7 over the period under analysis.19 Geographic variables are statistically insignificant predictors of university attendance. There is a sizable yet insignificant positive impact of living further than 40 kilometres from the nearest community college on university attendance. This may reflect the placement of community col-leges in areas of historically low post-secondary attendance in order to encourage more attendance. This variable may thus be proxying characteristics of the neighbourhood of residence. The impact of neighbourhood characteristics on attendance will be analyzed further in the next section. The regional indicators (not reported) highlighted the much higher rates of university attendance in At-lantic Canada and Ontario (the omitted region) than in the rest of Canada. There was no overall time trend in attendance, but there was a positive trend in female university attendance over the period (the gender specific time trends are not reported for brevity). Cohort size has a strongly significant negative effect on university attendance. A five per-centage point increase (roughly one standard deviation) in the size of a youth's cohort lowers the probability of attending university by approximately 3.5 percentage points. Provincial spending, on the other hand, had no statistically significant effect on university attendance. This may reflect the noise in these measures of spending. Note that inclusion of these additional covariates did not change the estimates of the remaining coefficients to any significant extent.20 ''Estimates that included just the university tuition level or the community college tuition level also yielded a large negative marginal effect of approximately five percentage points on university attendance from a $500 increase in tuition. 20Including these measures did raise the effect of university provided financial aid while it made more negative the effect of the unemployment rate. Importantly, the effect of community college and university tuition on both other PSE and university attendance probabilities did not change. 91 Table 3.4: Post-secondary Education Attendance: Marginal Effects Attending University Other post-secondary Female 14.6*** 4.8** (3.6) (2.3) Aboriginal descent .9 i * * -3.9 (3.7) (7.1) Visible minority 12.9* 0.9 (7.5) (6.4) Immigrant parent 9 4*** 7.1 (3.4) (6.8) Lone parent -4.4 4.5 (3.1) (4.2) Parents no high school -5.0 _9 2** (4.0) (4.4) Parents other PSE only 3.6* 5.2 (2.0) (3.6) Parent university 31.5*** 1.5 (5.8) (3.6) Middle parent income 9 4** 4.6 (3.7) (3.5) High parent income 14 i * * * 4.3 (4.9) (4.6) Children in family -0.5 -0.5 (1.0) (0.8) University > 80 km away -3.0 -3.4 (2.8) (3.5) Comm. College > 40 km away 4.4 -1.4 (4.8) (3.2) University financial aid (+$250) . 2.4 3.6 (1.7) (2.2) University tuition (+$500) -2.6 2.6 (1.7) (3.9) Comm. College tuition (+$500) -3.9** -3.7* (1.6) (1.9) Cohort size (+5%) -3.5** 0.2 (1.4) (1.4) University Prov. spend (+$700) -0.3 2.3 (1.3) (1.7) Comm. College Prov. spend (+$350) -4.3 -0.5 (3.3) (4.6) Note: 1,874 observations. Marginal effects denote percentage point change in probability from turning indicator variables from zero to one, and increasing continuous variables by amount indi-cated next to covariate name. One, two & three asterisks (*) denote significance at 10%, 5% & 1% respectively. Standard errors corrected for clustering by province and year are in parentheses. Gender specific time trends, French mother tongue, the provincial unemployment rate, regional indicators, and city and rural indicators also included. The marginal effects on attendance at other post-secondary institutions for all youth are pre-sented in the second column of numbers in Table 3.4. These estimates suggest that females are only marginally more likely to attend other PSE than males. Aboriginal descent, visible minority, immigrant parent and lone parent status have little effect on this outcome also. The probability of other PSE attendance is lower if both parents have less than a high school education. Higher parental education levels have economically small effects. Parental income levels also have eco-nomically small effects despite estimated multinomial logit coefficients on these covariates being statistically significant. This suggests that other PSE attendance is quite equal in Canada, which is consistent with the raw attendance probabilities by parental income quantile reported in Table 3.1. Tuition fees have the economically appropriate effects on other post-secondary attendance. Higher community college tuition lowers the probability of attending other PSE, providing evi-dence of a negative own price effect. A $500 increase in college tuition is predicted to lower the probability of a youth attending other PSE by 3.7 percentage points. Remember that approximately 36% of youth in this sample attended other PSE only by age 19 or 20. A $500 increase in univer-sity tuition increased the probability of attending other PSE by 2.6 percentage points, highlighting a positive cross-price elasticity. This effect is not statistically different from zero, however. Geographic variables are economically and statistically insignificant predictors of other post-secondary attendance. The exception here is the indicator for Quebec, which is very large and statistically significant. This reflects the high rate of attendance at CEGEPs in that province. Neither cohort size nor provincial spending has statistically significant effects on other PSE attendance. Supply constraints appear more considerable at the university level than at the com-munity college and trade school level. 3.5.3 Estimation Results by Parental Income Group To identify whether tuition increases have led to less equal post-secondary education attendance, I estimated the post-secondary attendance models separately for youth from the three parental income groups. The marginal effects of each covariate on university attendance are reported in Table 3.5. These estimates highlight the much larger effects of tuition on the university attendance of low income youth (first column). Both community college and university tuition levels have large negative effects on university attendance for low income youth, but not for youth from middle 93 and high income backgrounds. Low income youth appear to be much more sensitive to tuition.21 Marginal effects of each covariate on other post-secondary attendance are reported in Table 3.6. Community college tuition has statistically insignificant effects on attendance at other PSE for all three income groups. There are positive effects of university tuition on other PSE attendance for all income groups, but again the effects are not statistically significant. The tuition increases of the late 1990s in many Canadian provinces appear to have led to more unequal attendance at university, but not at other PSE institutions. Estimation by parental income group identified a negative effect of cohort size on the probabil-ity of university attendance for all income groups, with the largest negative effect on youth from low income backgrounds. This suggests that increased competition for university places generally squeezes out youth from low income backgrounds. These youth may have a lower probability of university acceptance if their measured high school achievement is on average lower. Youth from middle and high income backgrounds may receive more support from parents (tutors, attending better schools, better role models, etcetera) during school years to boost their measured school achievement levels. The marginal effects reported by parental income group also highlight several other interesting differences in the effect of family background characteristics on post-secondary attendance. The positive effect of being female on other PSE attendance is confined to middle and high income youth. There is a large positive effect of immigrant parent status and a negative effect of family size on other PSE attendance for high income youth only. The positive effect of parental education on university attendance is smaller for low income youth. Living beyond 80 kilometres of a university is a large detriment to university attendance for low income youth only. 3.6 Estimated Model Extensions I analyzed several extensions of the attendance outcome model. These extensions are discussed in turn here. 2 1ModeI estimates that included just university tuition or just community college tuition rather than both also showed the same pattern. 'Low income youth were very sensitive to tuition changes, middle income youth not sensitive at all, and high income youth moderately sensitive, with regards to university attendance. 94 Table 3.5: University Attendance: Marginal Effects Parental income Low Middle High Female 36.4*** 11.5*** 18.9*** (8.3) (4.3) (4.7) Aboriginal descent -11.9 -10.1** -18.1* (16.9) (4.1) (9.9) Visible minority 33.9*** -4.6 34.4** (10.5) (3.4) (17.2) Immigrant parent 22.5* 15.5** 6.3 (12.1) (7.1) (11.8) Lone parent -10.2 -4.1 15.6 (8.0) (3.8) (15.0) Parents no high school -11.2 -2.7 -16.4 (8.2) (5.4) (10.3) Parents other PSE only 2.9 10.7** 0.0 (8.9) (4.8) (7.1) Parent university 22.8* 38.4*** (11.9) (9.5) (5.3) Children in family -1.4 0.0 -3.1 (2.2) (0.9) (2.5) University > 80 km away -19.5** -0.3 0.2 (8.0) (4.2) (9.7) Comm. College > 40 km away 11.6 8.9 -0.3 (13.7) (6.9) (9.6) University financial aid (+$250) -2.7 2.1 7.3* (5.9) (2.6) (4.2) University tuition (+$500) -13.3* -0.5 0.7 (7.4) (3.0) (6.3) Comm. College tuition (+$500) -12.7** -2.2 -7.9* (6.2) (1.8) (4.7) Cohort size (+5%) -13.0*** -2.0 -7.5* (4.8) (1.5) (4.0) University Prov. spend (+$700) 2.0 2.3 -5.5 (5.4) (2.3) (4.9) Comm. College Prov. spend (+$350) -14.8 0.6 -14.8 (10.6) (6.0) (11.1) Observations 554 677 643 Note: Marginal effects denote percentage point change in probability from turning indicator vari-ables from zero to one, and increasing continuous variables by amount indicated next to covariate name. One, two & three asterisks (*) denote significance at 10%, 5% & 1% respectively. Stan-dard errors corrected for clustering by province and year are in parentheses. Gender specific time trends, French mother tongue, the provincial unemployment rate, regional indicators, and city and rural indicators also included. 95 Table 3.6: Other Post-secondary Attendance: Marginal Effects Parental income Low Middle High Female -8.9 7.2 3.2 (5.8) (6.0) (5.5) Aboriginal descent 1.4 -12.8** 33.5 (16.5) (5.4) (26.6) Visible minority -5.7 1.7 -7.8 (9.4) (15.9) (10.1) Immigrant parent -7.7 0.4 18.8 (8.1) (8.0) (12.2) Lone parent 4.1 7.7 16.2 (5.3) (9.2) (13.4) Parents no high school -7.8 -8.1 -4.7 (8.1) (7.9) (7.7) Parents other PSE only 3.7 7.8 -0.1 (7.8) (5.3) (5.7) Parent university 8.1 5.6 -12.0* (11-9) (7.7) (6.5) Children in family 0.6 -0.7 -5.1* (1.1) (1.8) (2.8) University > 80 km away -2.4 -0.3 -6.2 (8.7) (5.8) (7.0) Comm. College > 40 km away -11.5** 6.7 _9 3** (5.6) (6.6) (4.3) University financial aid (+$250) 1.0 4.0 8.6* (4.3) (3.9) (5.0) University tuition (+$500) -3.2 7.6 6.1 (5.8) (7.7) (8.9) Comm. College tuition (+$500) -0.6 -4.2 -3.0 (4.6) (3.8) (5.2) Cohort size (+5%) 5.0 -0.6 3.0 (4.5) (2.4) (3.3) University Prov. spend (+$700) 4.4 3.3 -0.6 (3.6) (4.4) (3.3) Comm. College Prov. spend (+$350) 20.7 -8.5 0.5 (13.4) (7.6) (10.4) Observations 554 677 643 Note: Marginal effects denote percentage point change in probability from turning indicator vari-ables from zero to one, and increasing continuous variables by amount indicated next to covariate name. One, two & three asterisks (*) denote significance at 10%, 5% & 1% respectively. Stan-dard errors corrected for clustering by province and year are in parentheses. Gender specific time trends, French mother tongue, the provincial unemployment rate, regional indicators, and city and rural indicators also included. 96 3.6.1 Neighbourhood Characteristics There is a large literature on the effect of neighbourhood characteristics on various outcomes of youth, including health outcomes, criminal behaviour, school achievement and education attain-ment. An example for Canada is the study by Cartwright and Allen (2002), who identify the effects of neighbourhood characteristics on school achievement. One important pathway by which neighbourhood characteristics may affect the education outcomes of youth is via the presence of role models. If there are a number of adults in the neighbourhood who have achieved success via post-secondary education, this may encourage local youth to pursue such a path. If the majority of adults with whom the youth comes into contact have not attained a post-secondary education, the benefits of doing so may not be at all obvious. The positive relationship between attendance and living beyond 40 kilometres of a community college identified above appears counter-intuitive on face value. However, if community colleges are located by provincial governments in areas that have historically low post-secondary attendance rates in order to encourage increased attendance, this reverse causation may be what is being uncovered. Low education attendance neighbourhoods may be characterized by populations with characteristics that do not encourage participation in further education. For example, there may be very low levels of education among adults in the neighbourhood. Fifteen measures of neighbourhood characteristics were included in an additional set of post-secondary attendance model estimates. Measures of neighbourhood characteristics were drawn from the 1996 Census.22 These characteristics were linked to individuals using census tracts where available (city dwellers) and using census subdivisions where not.23 Summary statistics for the neighbourhood characteristics are reported in Table 3.7. The full set of fifteen neighbourhood characteristics are jointly statistically significant in the estimated model at the 1% level. The set of marginal effects for these neighbourhood characteristics on university attendance in multinomial logit estimates for all youth are presented in Table 3.8.24 These marginal effects 2 2Four additional characteristics were included in preliminary estimation but were dropped here as none were even close to being statistically or economically significant. The dropped characteristics were neighbourhood density, percent of lone parent families, the 25 and over employment rate, and average rental rates. 2 3 I f the population of the tract or subdivision was below 2,000 people aged 15 and over, averages for the pop-ulation of the census division were used. This adjustment was undertaken to ensure the estimated neighbourhood characteristics were not too noisy. 24Standard errors of the estimated parameters were adjusted for potential heteroscedasticity and for clustering by the neighbourhood and year level. 97 Table 3.7: Neighbourhood Characteristics - Summary Statistics Variable Mean Standard Devn. Minimum Maximum Young - % popn. 16 and under 24.2 4.3 4.8 42.6 Aged - % popn. 65 and over 11.3 5.1 1.5 36.5 Immigrant - % popn. 14.9 15.0 0.0 65.2 Visible minority - % popn. 9.6 15.3 0.0 73.1 Aboriginal descent - % popn. 2.3 4.4 0.0 81.0 French mother tongue - % popn. 23.5 37.5 0.0 99.8 Non-official mother tongue - % popn. 13.9 15.5 0.0 72.4 Attending school - % aged 15 to 24 65.0 9.8 28.1 92.9 Not graduate H.S. - % 15 and over 35.5 10.1 10.3 70.1 Some PSE - % 15 and over 27.4 4.5 11.7 42.3 University educated - % 15 and over 12.1 8.3 1.1 50.8 Unemployment rate - 25 and over 9.0 5.5 1.0 45.4 Median income 19,701 4,998 8,710 41,508 Low income - % popn. 18.6 9.7 1.8 70.9 Value of dwellings 144,943 100,923 37,658 769,888 Observations 1,874 Source: 1996 Canadian Census 20% sample. 98 denote the change in the probability of attending university attributable to a one standard deviation increase in each neighbourhood characteristic from the sample mean level of each characteristic. Marginal effects for all other covariates in the estimated model are not reported for brevity, but are available upon request. The characteristics that affected university attendance probabilities the most were percent immigrant (positive but not statistically significant), percent visible minority (negative), the unemployment rate (negative), and median income (positive). Note that the neighbourhood unemployment rate here is measured at one point in time (1996). I am already controlling for the provincial level unemployment rate when the youth would normally enter post-secondary education in these estimates to proxy the opportunity cost of studying (age 18 except Quebec, where it was age 17). These provincial level unemployment rates, which vary over the cycle in my estimates, were not at all statistically significant. Other analyses, such as Beaudry, Lemieux and Parent (2000), have found that education attendance is generally anti-cyclical, with higher attendance when unemployment is high. The neighbourhood unemployment rate is picking up general unemployment rates in that locality only. In neighbourhoods where unemployment is particularly high on average, I find that youth are significantly less likely to attend university.25 The only neighbourhood characteristic that significantly affected other PSE attendance (es-timates not reported) was the percent of the adult population with a university degree. Higher percentages with a university degree were related to lower other PSE attendance. The inclusion of these neighbourhood characteristics did not alter the estimates of the remain-ing parameters in the multinomial logit model to any real extent. In particular, the effect of commu-nity college and university tuition on attendance probabilities remained the same. The coefficients on the distance to PSE institutions measures were actually slightly larger and more statistically significant rather than less after inclusion of these measures. Distance appears to be a robust factor affecting attendance decisions. Inclusion of neighbourhood characteristics more than doubled the size of the positive effect of the Atlantic Canada indicator on university attendance also. Neighbourhood characteristics may affect the attendance outcomes of youth in cities differently to youth in small urban and rural areas. It is possible to imagine that the benefits of education may be more obvious to city dwellers even if their own neighbours are not well educated. To explore 2 5It is possible that high unemployment rates in some neighbourhoods reflect firm failure or downsizing leading to large numbers of layoffs. Thus many individual parents in these neighbourhoods may have suffered from job loss, leading directly to lower university attendance for their children, as estimated in Chapter 2. This cannot explain all the negative effect of local unemployment rates on attendance, however. 99 Table 3.8: Effects of Neighbourhood Characteristics on University Attendance Variable Multinomial logit coefficient s.e. Marginal effect s.e. Young - % popn. 16 & under -6.69 4.51 -2.3 1.7 Aged - % popn. 65 & over -4.37 3.30 -1.9 1.5 Immigrant - % popn. 6.38 4.15 14.3 10.2 Visible minority - % popn. -4.93** 2.20 -5.5** 2.4 Aboriginal descent - % popn. 2.98 2.05 1.2 1.0 French mother tongue - % popn. 1.18 1.17 2.8 4.9 Non-official mother tongue - % popn. -0.30 2.56 -1.7 3.1 Attending school - % aged 15-24 1.66 1.51 2.0 1.7 Not graduate high school - % 15 & over 4.93 3.87 6.2 5.4 Some PSE - % 15 & over 1.38 5.00 0.4 2.1 University educated - % 15 & over -0.65 4.63 -2.0 34.6 Unemployment rate - aged 25 & over -0.06** 0.03 -2.8** 1.4 Median income 0.12** 0.06 6.8 4.6 Low income - % popn. 0.03 0.02 3.5 3.1 Value of dwellings 0.00 0.00 -2.2 2.1 Note: 1,874 observations. Marginal effects denote the percentage point change in probability from increasing each neighbourhood characteristic by one standard deviation from mean levels. One, two & three asterisks (*) denote statistical significance at the 10%, 5% & 1% respectively. Stan-dard errors corrected for clustering by neighbourhood and year are in parentheses. A l l individual controls are also included in the estimated model, but results for those controls are not reported. 100 this hypothesis, I included interactions of the fifteen neighbourhood characteristics with the city (over 100,000 residents) indicator in separate model estimates. These fifteen interacted variables were just jointly statistically significant at the 1% level. Neighbourhood characteristics that had notably different effects on city dwellers were average education and income levels. Living in an educated and more wealthy neighbourhood had a much stronger positive effect on university attendance probabilities in large cities than in rural and small urban areas. The negative effect of neighbourhood unemployment rates on attendance was confined to rural and small urban areas. 3.6.2 Tuition Effects Varied by Individual Characteristics I examine the effect of tuition increases on post-secondary attendance probabilities separately by parental income group in the main analysis of Section 3.5.3 above. The objective was to determine whether tuition increases have coincided with less equal PSE attendance on the parental income margin. The evidence suggests that for university attendance the hypothesis holds. Tuition in-creases may also have different effects on youth based on other background measures apart from parental income. Varied effects by family size or by distance to PSE institutions readily come to mind as possibilities. To explore this issue further, I constructed additional estimates of the ef-fect of tuition on attendance for different sub-samples of the data. These results are presented in Table 3.9. The marginal effects reported in Table 3.9 represent a $500 increase in both university and community college tuition. As noted above, tuition increases at the university level were matched by community colleges in most jurisdictions, so these marginal effects reflect a common policy change. Each row of marginal effects in the table are constructed from separate multinomial logit estimations, controlling for the full set of covariates. The marginal effects in the top panel of Table 3.9 imply that females are more sensitive to tuition changes than males. This result is consistent with the results of Chapter 2, where the uni-versity attendance of females was much more negatively affected by parental income shocks than males. These results again suggest that more females are closer to the margin of the university attendance decision than males, or that parental transfer decisions may vary by the gender of chil-dren. Recall that females are on average much more likely to attend university than males in the 1990s. It is also the case that the university attendance of females is less strongly correlated with 101 parental education and parental income levels overall than for males in my sample. Closer analy-sis of parental transfer decisions by the gender of children, particularly in response to income or education cost changes, may be warranted, and is left for future work. The tuition effects reported in the second panel of Table 3.9 suggest that children from larger families are more sensitive to tuition changes than children from smaller families, particularly at the other post-secondary level. This makes intuitive sense, as parents with many children may find it especially difficult to fund all their children's post-secondary education when tuition rises. The results in the third panel of Table 3.9 suggest that youth living closer to universities are marginally more tuition sensitive than youth living further away. Tuition costs may be a smaller portion of the total costs of university attendance for youth who have to leave the family home to attend university. The tuition effects reported in the bottom panel of Table 3.9 suggest that youth with less ed-ucated parents are no more tuition sensitive than youth with more educated parents. This is a somewhat surprising result if we think that parental education and parental income are correlated. The estimates of Section 3.5.3 implied that tuition effects were very large for low income youth, essentially zero for middle income youth, and moderate for high income youth. The analysis in Chapter 2 also highlighted the large effect that parental income shocks had on the university atten-dance of youth with less educated parents. Reconciling these results is an area for future research. 3.6.3 Alternative Supply Side Estimates I included measures of cohort size and provincial spending on universities and community colleges in the estimates of Section 3.5 to capture the effect of any potential rationing of places at post-secondary institutions on the attendance of individuals. In this subsection, I explore further the potential role of rationing on attendance. Universities and community colleges obtain their revenue from several sources other than provincial governments and tuition fees. These institutions also obtain revenue directly from the Canadian Federal Government, particularly for research. Funding is also obtained from "other" sources, such as endowments, private bequests, commercial operations, etcetera. This type of funding is small for Canadian institutions. Around 13% of university funding and 8% of commu-nity college funding is from these "other" sources. I included separate measures of federal and 102 Table 3.9: Tuition Effects by Individual Characteristics: Marginal Effects Attending University Other post-secondary Observations Female _11 g*** -4.3 862 (4.3) (4.6) Male -6.9 1.0 1,012 (6.4) (3.6) 1-2 children -6.7 10.9 864 (4.8) (8.2) > 2 children -10.2** -10.1** 1,010 (4.8) (4.6) University > 40 km away -7.1 4.4 937 (5.5) (6.8) University < 40 km away -10.6** 2.0 937 (5.0) (7.4) Parent post-secondary -8.9** 3.3 1,212 (4.3) (6.1) Parents high school or less -7.3 -6.1 662 (6.1) (3.9) Note: Marginal effects denote percentage point change in probability from increasing both univer-sity and community college tuition by $500. One, two & three asterisks (*) denote significance at 10%, 5% & 1% respectively. Standard errors corrected for clustering by province and year are in parentheses. Each row reflects a separate estimation. The full set of covariates are included in each estimation, except those indicators of the particular sample split. 103 "other" revenue for universities and community colleges in extended models of PSE attendance. As with provincial government spending on post-secondary institutions, these revenue variables were not statistically significant predictors of attendance. The number of places universities can provide for potential students is not only affected by institutional revenue. Changes in the cost of providing an education can also affect supply. One major way universities can change the cost of providing places is by increasing class sizes. Such increases may reflect changes in technology or changes in the quality of education provided. A straightforward measure of changes in class size is student-faculty ratios at universities. There has been a strong increase in student-faculty ratios over the 1990s, as depicted in Figure 3.7. Due to data limitations, no equivalent measure can be constructed for community colleges in Canada. I included provincial-level measures of student-faculty ratios at universities in extended model estimates. No statistically significant effect of these ratios on university attendance was discernible in these estimates, however, and there was little change in the effect of tuition, cohort size and provincial spending on attendance once these measures were included. Including cohort size and provincial funding of post-secondary institutions directly in the esti-mated models implies that rationing is always occurring in all provinces of Canada. This may not be the case, as some jurisdictions may have enough supply to meet demand for places, particularly in the Maritime provinces and Ontario where attendance rates are much higher than the rest of the country. One simple way to check for potential rationing differences across jurisdictions is to see whether increases and decreases in cohort size have similar effects on attendance. One could imagine that rationing will be less of an issue in provinces of declining populations of youth. I estimated an expanded model of post-secondary attendance including cohort size measures split by provinces that experience increases, decreases and little change in cohort size over the period. There was no evidence of any different effect of cohort size on attendance across the three groups. To further analyze this issue, I also estimated a model of post-secondary attendance including the provincial spending measures split by provinces that raised spending, lowered spending, or did not change spending to any significant extent over the period. Most of the effects of these separated provincial spending measures were not statistically significant, as was the case for the provincial spending measures in aggregate. However, increases and stable levels in provincial spending on community colleges did have a negative effect on university attendance. This suggests that expan-sions of community college programs in certain provinces may have induced some students away 104 from university attendance. 3.6.4 Effect of Tuition on the Residence and Hours of Work Decisions Increases in tuition may have effects on youth outcomes beyond attendance at a post-secondary institution. Such increases may also affect whether youth decide to attend an institution close to home in order to live with parents and save on living expenses. Youth who still choose to study despite rising tuition costs may also need to work more while studying. If these effects are stronger for youth from low income families, it may suggest inequitable effects of tuition increases are not confined to university attendance outcomes alone. In this subsection, I analyze the residence and hours of work decisions of youth and their response to tuition increases. These two decisions of youth were modeled in Section 3.3 above. The percentage of post-secondary students in my sample recorded as living with at least one parent was very high (80% to 90%) for all parental income backgrounds. The living arrangement reports were taken at the end of the second year after normal completion of university entrance requirements, i.e. age 19 or 20 depending on province. Non-students were much less likely (around 70%) to live with their parents at the same age, with their higher disposable incomes from work and no education expenses. Average hours of work were also reasonably high for students from all backgrounds. University students worked on average around 500 to 600 hours over the calendar year corresponding to the second year after normal completion of university entrance requirements. Other post-secondary students worked even more hours. Many students work during the summer. Only 16% of students in my sample worked no hours at all. For non-students, around 10% worked no hours at all at the same age, and average hours of work were around 1400. Note that my living arrangements measure may not accurately indicate all youth who may reside separately from the parental home while studying. When Statistics Canada contacts SLID households for the annual questionnaire, the person contacted in the household may answer for all family members. The contact person is asked to include all family members who normally reside in the household. If a family member is currently residing elsewhere to attend "school" (perhaps in university residences) but returns to the family home to live during school breaks, they are to be included as members of the respondent household. We may still consider these youth who return to the family home during school breaks as saving on some living costs by doing so. Youth who 105 do not return to the family home during school breaks appear more independent. We may expect that youth with more wealthy parents, who would generally receive higher parental transfers, will also be more able to live independently year-round. I estimated probit models of the bivariate decision of whether to live with parents or not sepa-rately by student type: university students, other post-secondary students and both types of students combined. Marginal effects for these models are presented in Table 3.10. The results indicate that female students are less likely to live at home, while visible minority and immigrant students are more likely. Students from middle and high parental income backgrounds are actually more likely to live at home. More siblings lowered the probability of living at home for other post-secondary students but not for university students. Students who resided in cities at age 16 are more likely to live at home. Students from rural areas and students who resided at some distance from a university at age 16 were less likely to live at home, as expected. Tuition has a difficult to interpret negative effect on the probability of living at home for stu-dents, but the estimates are not statistically significant. Rational choice would imply that tuition increases should lead some students to remain living in the parental home to save on living ex-penses. One possible explanation for this result is that some students moved away from home in order to prove that they were living without the support of their parents, and thus eligible for student loans, even if their parents' income was considerable. Small sample sizes precluded estimation of residence decision rules for university students and other post-secondary students separately by the three parental income groups. I did construct estimates for the sample of students attending any PSE (university and other PSE combined) sep-arately by parental income group. These estimates are not reported here for brevity. The main result from these estimates is that there was no evidence of tuition increases having a more positive effect on the probability of low parental income students living with parents than on students from middle or high income backgrounds. As in the entire sample (the third column of Table 3.10), the estimated effect of tuition on the probability of living at home was negative for all income groups, but the estimates were statistically insignificant in all cases. I also constructed Tobit estimates of the hours of work decision of students separately by stu-dent type: university students, other PSE students and both types of students combined. The results are reported in Table 3.11. The dependent variable is the number of hours spent working in the calendar year corresponding to the age of the second year after normal completion of university 106 Table 3.10: Probit Estimates of Probability of Living with Parents (age 19 or 20) Variable at university at other PSE at any PSE Female -7.6 -4.3 -5.9 (7.1) (4.4) (5.6) Aboriginal descent 9.0 11.6 (9.5) (8.0) Visible minority 4.0 19.5** 12.3 (7.3) (12.3) (7.9) Immigrant parent -0.5 12.6* 5.8 (7.3) (8.4) (7.6) Lone parent 5.0 2.8 4.7 (5.8) (7.5) (7.1) Parents no high school 10.6** 7.1 11.0 (6.8) (7.8) (6.5) Parents other PSE only 0.5 -1.3 1.7 (4.5) (4.9) (4.3) Parent university -6.4 -14.9 -5.6 (6.2) (12.3) (6.2) Middle parent income 7 4** 12.9** 14 3*** (4.9) (7.6) (5.3) High parent income 8.3** 13.2*** 15.1*** (5.8) (8.3) (6.3) Children in family 2.4 -6.5*** -1.3 (1.9) (3.2) (1.5) City resident ( > 100,000) 6.6 12 9*** 12.6*** (6.2) (9.0) (6.0) Rural resident -8.2 -2.9 -7.7 (6.9) (5.8) (5.6) University > 80 km away -6.0 -2.7 -7.3 (5.8) (7.0) (5.7) Comm. College > 40 km away -5.3 5.1 -0.3 (6.9) (5.4) (4.5) University financial aid (+$250) 4.2* - -0.5 (2.4) (2.7) University tuition (+$500) -6.5 - 4.2 (7.2) (5.3) Comm. College tuition (+$500) - -8.6 _\\ 4** (6.8) (5.5) Observations 541 542 1,078 Note: Marginal effects denote percentage point change in probability from turning indicator vari-ables from zero to one, and increasing continuous variables by amount indicated next to covariate name. One, two & three asterisks (*) denote significance at 10%, 5% & 1% respectively. Stan-dard errors corrected for clustering by province and year are in parentheses. Gender specific time trends, French mother tongue, unemployment rate, and regional indicators also included. entrance requirements (age 19 or 20 depending on province). The estimates show that visible minority university students work significantly fewer hours than other students. Students whose parents did not complete high school worked much fewer hours also. Tuition increases had no discernible effect on hours of work. Note also that youth from high income families did not work fewer hours than those from low income families. This result may reflect the impact of financial aid eligibility, where only low income youth can obtain student loans. The correlation between income groups and eligibility make it difficult to discern separate effects. Finally, I estimated separate Tobit models by parental income group for all post-secondary students combined. These results are also not reported for brevity. Tuition levels had no effect on hours worked for youth from middle and high income backgrounds. Surprisingly, there was a statistically significant negative effect of tuition on the hours of work of youth from low income backgrounds. 3.7 Conclusions In this study, I find that tuition increases in the late 1990s have led to more unequal university at-tendance in Canada. Tuition increases had a significant negative effect on the university attendance rates of youth from low income backgrounds, but much smaller effects on youth from middle and high income backgrounds. The effect of tuition increases on attendance at non-university post-secondary education institutions (community college in particular) was essentially zero, however, with no discernible differences in the effect across parental income groups. Given the much higher labour market returns to a university education, it suggests that these tuition increases may lead to a more pronounced intergenerational transmission of income inequality. Tuition increases did not appear to lower attendance at other post-secondary institutions, de-spite the increases at community colleges being almost as large in dollar values as university tuition increases. This result may be interpreted as a general downgrading of post-secondary education attendance in response to tuition increases. Some youth may have switched from university to community college attendance, while others switched from community college attendance to no post-secondary attendance at all. These two effects may leave other post-secondary attendance rel-atively unchanged in response to tuition increases. Attendance at Community college is still less expensive for students both due to lower tuition payments each year (approximately one half) and 108 Table 3.11: Tobit Estimates of Hours of Work Decision of Students Variable at university at other PSE at any PSE Female 72.0 31.8 20.8 (283.8) (320.9) (290.4) Aboriginal descent -389.7** -61.7 -69.1 (184.0) (167.3) (154.1) Visible minority -217.5** -2.4 -147.5 (86.3) (342.1) (137.1) Immigrant parent -74.2 -19.0 -52.6 (86.6) (168.3) (102.0) Lone parent -48.7 18.1 -8.9 (168.1) (150.7) (163.1) Parents no high school -274.5** -305.9 -306.9** (116.6) (186.6) (142.3) Parents other PSE only 112.6 -149.3 -39.2 (92.6) (138.6) (120.2) Parent university 56.3 -129.7 -103.3 (106.0) (161.1) (147.9) Middle parent income -160.8 102.5 -38.8 (103.0) (217.8) (150.8) High parent income -61.8 154.2 25.7 (97.1) (178.3) (135.1) Children in family 2.7 43.2 19.8 (25.7) (33.6) (28.3) City resident (> 100,000) -49.4 216.0 85.0 (45.1) (139.5) (88.3) Rural resident -81.6 -111.4 -103.0* (65.2) (85.9) (62.6) University > 80 km away 103.4 193.5 171.2 (78.6) (161.7) (109.3) Comm. College > 40 km away -80.9 -182.6 -139.3 (88.2) (123.9) (99.9) University financial aid -19.3 - -36.4 (22.1) (28.7) University tuition -1.2 - 2.6 (14.0) (18.0) Comm. College tuition -13.0 5.2 (19.2) (11.1) Observations 538 536 1,066 Note: These are Tobit parameter estimates. One, two & three asterisks (*) denote significance at 10%, 5% & 1% respectively. Standard errors corrected for clustering by province and year are in parentheses. Gender specific time trends, French mother tongue, unemployment rate, and regional indicators also included. 109 half the number of years of study. It may also be easier to combine work and study at a community college rather than at a university. This result is generally in line with the results of Chapter 2, where youth appeared to respond to parental income shocks by downgrading their post-secondary education attendance in a similar manner. Cohort size also affected the probability of attendance at the university level for Canadian youth, implying that there may be significant rationing of places at the university level. Youth from larger cohorts were less likely to attend university even after controlling for many individual characteristics, tuition and provincial spending on post-secondary institutions. This suggests that the higher level of competition for university places resulting from larger cohorts is binding on youth. There was a larger negative effect of cohort size on university attendance for youth from low income backgrounds. Rationing may be causing some of the observed inequality in university attendance in Canada. Low income youth may have lower measured achievement during high school, reducing their probability of acceptance at university. My analysis identified some evidence that neighbourhood characteristics affect the post-secondary education attendance decisions of youth. The average income levels of neighbours was positively related to university attendance probabilities. University attendance was lower for youth from neighbourhoods with larger proportions of visible minorities and with higher unemployment rates. The effect of tuition increases on the residence (live with parents or not) and hours of work decisions of youth were small and statistically insignificant. There was also no evidence of an unequally larger effect on youth from low income backgrounds in these decisions. The main effect of tuition increases on the outcomes of youth was observed in attendance outcomes, not on these other margins of adjustment youth could have undertaken in response to rising tuition. The larger negative effect of tuition increases on the university attendance of low income youth may suggest that Canada's student loan program has not kept pace with increases in tuition. Student loan limits were essentially constant over the 1995 to 2001 period, the period I analyzed. Student loan limits have been increased more recently. It will be interesting to see whether these increases can help to reverse the rise in inequality of university attendance that I have identified. 110 22.0 21.0 20.0 19.0 18.0 17.0 16.0 15.0 14.0 Figure 3.7: University Student-Faculty Ratio Full-time equivalent student per full-time faculty T 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 j 1 1 1 1 1 1 1 1 1 1 1970 1974 1978 1982 1986 1990 1994 1998 Sources - University faculty numbers provided directly by Statistics Canada's Centre for Education Statistics. Student enrolment figures taken from Statistics Canada's cross-tabulation files and from the Education Matters publication. Ill CHAPTER 4 School Principals and Graduation Rates 4.1 Introduction There is considerable debate on whether schools can actually improve student outcomes. The con-troversy remains despite large volumes of research on schools and students. Much of this research was conducted in response to the Coleman Report (1966), which suggested that schools did not matter. Measurable school inputs, such as spending per student, pupil-teacher ratios, and the ed-ucation and experience of teachers, had no significant effect on student outcomes once individual family background and peer effects were controlled for. Although the subsequent research has been considerable, the debate on whether schools matter has yet to be resolved. Many conflicting pieces of empirical evidence have been found. Rivkin, Hanushek and Kain (2005) make a significant contribution to this literature by showing that individual teachers can systematically affect student achievement. These estimated effects may not be related to the usual measurable quality of teachers, such as education levels and experience, so prior research may have missed these effects by only searching on those dimensions. These au-thors take considerable care to identify teacher quality while allowing for potential problems from missing or mis-measured variables, in addition to school and student self-selection. We continue on this line of research by estimating the effects of school leadership, particularly individual school principals, on student outcomes. We identify the effect of individual high school principals on high school graduation probabil-ities. Encouraging youth to complete high school confers benefits to the individual and potentially to society. High school completion has been related to better employment outcomes of individuals, 112 higher worker productivity, lower reliance on welfare payments, reduced probabilities of individu-als committing crime, and higher involvement in democratic institutions. Identifying the effect of school leadership on school effectiveness in terms of school retention rates provides useful direc-tion for education policy-makers. School principals can affect student outcomes in many ways. As school leaders, they have in-fluence on many aspects of the school, including teacher supervision, introducing new curriculum and teaching techniques, student discipline, student allocation to teachers and classes, etcetera. They may motivate both teachers and students more effectively, or create an environment in the school that promotes staying in school that fits the particular student body better. See Appendix F for a list of duties and responsibilities of school principals in the jurisdiction we study. We employ a unique administrative data-set from the Canadian Province of British Columbia in the 1990s. High school principals in British Columbia were regularly rotated between schools over this period, so the principal's effect on student graduation probabilities can be separated from individual school and neighbourhood characteristics. We use administrative information on all students entering grade 12 in that province over the 1991 to 1996 period, observing high school graduation and the particular principal leading the school. Education scholars have highlighted several school conditions through which school leader-ship may influence student outcomes. These main school conditions are: (1) purposes and goals, (2) structure and social networks, (3) people, and (4) organizational culture (Hallinger and Heck (1998)). Much of this research was conducted within the wider agenda attempting to identify the particular attributes of high achieving or effective schools. In Hallinger and Heck's (1998) re-view of empirical studies of principal leadership, they conclude that the evidence on the effect of principals on student outcomes is mixed, and that detection of effects often required sophisticated techniques involving mediating variables (often the school conditions listed above). This line of research mostly employed survey data of individual teacher perceptions of various components of leadership and school conditions. For example, teachers may be asked to rate how strongly they agree with a statement such as "Our school administrators have a strong presence in the school" to measure school leadership. They may be asked to rate their agreement with the statement "I easily understand our school's mission/outcomes statement(s)" to measure school purposes and goals (Leithwood and Jantzi (1999)). A typical concern of economists with this type of research is that survey measures of perception may be endogenous or suffer from considerable 113 mis-measurement, biasing any results. Our analysis does not rely on such measures of perception. Instead we employ turnover of school principals within schools over time to identify their effects on graduation probabilities, purged of any fixed school, neighbourhood and stable peer group effects. This strategy comes at the expense of not being able to identify the particular pathways by which principals affect student outcomes, nor the strategies of principals that are effective. Our empirical strategy has two main components. First, we employ a semi-parametric tech-nique to identify a lower bound estimate of the variance in the quality of individual school princi-pals. This technique involves removal of fixed school effects, thus only within school variation in school principal quality is employed in identification. Unlike Rivkin, Hanushek and Kain (2005), we cannot remove individual student fixed effects in this study, as we only observe individual students once, the year they enter grade 12. Thus identification requires that principals were not rotated across schools in response to changes in the quality of students, and that students do not sort themselves across schools in response to principal changes. The second component of the empirical strategy is more parametric in nature. We estimate the effects of a number of individual, peer and neighbourhood characteristics on individual high school graduation probabilities, along with the fixed effects of schools and individual school principals. We matched the administrative data on individual grade 12 students to social services adminis-trative data on the students themselves and their families. This matching provides information on prior welfare receipt of the student's family and indicators of Social Service interventions in the home while the youth resided there. These measures provide useful information on family background but we do not have direct continuous measures of either parental income or education. Instead, average levels (taken from the Census) for the neighbourhood surrounding each school are included to proxy for these missing variables. Neighbourhood quality may also have an effect on graduation rates directly, so these variables may pick up these influences too. We also control for student peer effects using several measures of the quality of a student's peers in their school and grade. School principals may have more potential to influence the school completion behaviour of certain groups of youth, such as those youth who are more at risk of dropping out. We focus par-ticularly on the effect of school principals on the graduation rates of youth from families that have relied on welfare payments in the past. The overall graduation rate of these youth is considerably 114 lower than that of youth who are not from welfare backgrounds. The database includes indicators of whether a student has failed a prior grade in school, and has test scores from exams undertaken at the end of grade 11. We employ these measures in the parametric part of the analysis. Such measures also reflect prior inputs into the school achievement of individuals, as schooling is a cumulative process, plus innate academic ability. The main contribution of this analysis over the previous economic literature is the ability to measure the effect of individual school principals on the graduation probability of students. The idiosyncratic (unobservable) quality of school principals is one input into the education production function that, to our knowledge, has not previously been investigated.1 Our results suggest that there is sizable heterogeneity in school principal quality, as observed in high school graduation rate differences. The statistical significance of our semi-parametric results is, however, low. The outline of this chapter is as follows. A brief review of the related literature is provided in Section 4.2. Both parametric and semi-parametric models of high school graduation are outlined in Section 4.3. The administrative data we employ is described in Section 4.4. Semi-parametric lower bound estimates of the variance of principal quality are provided in Section 4.5. Estimates from our parametric model of high school graduation and of the distribution of school principal quality are given in Section 4.6. Section 4.7 has some concluding remarks. 4.2 The Literature The literature on the determinants of education outcomes in the United States is vast. Hanushek (2003) claims that the literature has failed to find a consistently significant relationship between school inputs and outcomes. Krueger (2003) argues that the literature can be interpreted as finding a significant relationship between pupil-teacher ratios and student outcomes. In Krueger's meta-analysis, the prior empirical research was weighted in a different, and he argues more consistent, manner to the weighting scheme employed by Hanushek. The literature on peer effects and student outcomes is also growing. Hanushek et al (2003) found significant peer effects on student outcomes in Texas elementary schools. As noted in the introduction to this chapter, Rivkin, Hanushek and Kain (2005) find that in-1 We employed school principals as instruments for high school graduation in a related study on the effect of high school graduation on subsequent welfare use for youth from welfare backgrounds. See Coelli, Green and Warburton (2003) for details. 115 dividual teachers do have significant effects on student outcomes. The measurable characteristics of teachers (experience, educational qualifications, salary) employed in most prior analyses may not reflect the intrinsic quality of certain teachers in producing better student outcomes. In this study, the authors employed a semi-parametric fixed effects (of teachers) estimator to uncover the effect of these intrinsic qualities of teachers on elementary school student test scores, and found that teachers (and thus schools) do have significant effects. Hallinger and Heck (1998) reviewed a large number of empirical studies of principal leadership conducted over the period from 1980 to 1995. The vast majority of these studies were from the Education literature, and mostly employed survey data of individual teacher perceptions of various components of leadership and school conditions. The authors conclude that the evidence on the impact of principals on student outcomes is mixed, and that detection of effects often required so-phisticated techniques involving mediating variables. Much of this research was conducted within the wider agenda attempting to identify the particular attributes of high achieving or effective schools. The effect of certain school principal measures on elementary school achievement in Canada has been analyzed in a handful of studies.2 Montmarquette and Mahseredjian (1989) estimated an education production function of elementary school achievement that included school principal characteristics, along with individual, teacher and other school characteristics. Student background variables (parental education, income, entering IQ, etcetera) were the most significant predictors of achievement. School principal characteristics (education, experience) did have a statistically significant effect on outcomes while teacher characteristics did not. Unobserved school character-istics (estimated using an error components technique) explained a little of the remaining variance in achievement. Lytton and Pyryt (1998) analyzed the effect of various neighbourhood, student and school characteristics on test score outcomes of elementary school children. This study was part of the education literature on school effectiveness, as discussed above. A variable indicating whether the school principal thought achievement tests were worthwhile had a small but significant effect on outcomes. The most significant determinants of test scores were not school-based measures, 2There is a growing number of Canadian empirical studies of education outcomes generally. Several studies are collected in the volume Towards Evidence-Based Policy for Canadian Education, edited by de Brouker and Sweet-man (2002). Many of these studies employ data from a number of Canadian and international examinations of school students.-' Other Canadian studies of elementary school student outcomes include Johnson (2005), Hender-son, Mieszkowski and Sauvageau (1976, 1978), Cartwright and Allen (2002), and Worswick (2003), among others. The effect of school principals in particular was not analyzed in these studies. 116 however. Neighbourhood mean income in particular was a significant and large predictor of test scores. Leithwood and Jantzi (1999) analyzed the effect of both principal and teacher leadership on student engagement in the school. This study employed a survey of teacher perceptions of lead-ership and school conditions in one large Eastern Canadian school district. The authors found a link from principal leadership perceptions, through school conditions, to student engagement. 4.3 Models of High School Graduation 4.3.1 Parametric Model An individual will graduate from high school if she or he both stays in school and surpasses some threshold level of achievement. Both are the result of decisions made by the individual, including the effort expended while in school. These choices result from utility maximization decisions of the individual. The individual will weigh the expected benefits of graduation - the increased lifetime flow of utility from graduation - against the costs, including the time spent in school. The net benefit of graduation from high school, denoted by the unobserved latent variable I*cs, can be represented by equation 4.1. This net benefit calculation will include the effort each youth must expend to graduate, given their prior academic preparation and innate academic ability. Individuals with better prior preparation and ability will not need to expend as much effort as others to graduate. lies = Pics'*! + NICSTT2 + SCS1T3 + AICST;± + P(_i) c s 7T 5 + G(_i) c s7T 6 + 6 I C S (4.1) Individual i in cohort c is observed to graduate from high school s (represented by Gics = 1) if I*cs > 0, i.e. if the net benefit of graduating is positive. An individual is observed to drop out (Gics = 0)itl*cs<0. The matrices F, N and S denote family inputs, neighbourhood influences and school inputs respectively. Prior academic preparation and ability may be proxied by measured achievement via the term Aics. Here G(_j)C5 denotes the percentage of an individual's classmates who graduate high school. The subscript (—i) denotes averages are calculated over all students in school s and cohort c except student i. This term captures purely endogenous peer effects in the graduation decision. The benefits of graduation may depend directly on the number of one's peers who choose to graduate. This is in addition to any impact that the background or predetermined characteristics 117 of one's peers have on the net benefit (including the effort required while in school) of graduating high school. The predetermined characteristics of peers enter the net benefit calculation in the term P(-i)cs- These exogenous (contextual) characteristics, such as gender, race and family background, are not affected by the current endogenous behaviour of students. School peers can influence outcomes of individual youth in several ways. In terms of school achievement, peers can be a source of motivation and competition, they may learn more easily so the class can do more in a given amount of time, they may be less disruptive, and so on. Peers may also influence an individual's expectations of the benefits of high school graduation, by being a source of information regarding the benefits of school success. They may also directly raise the utility from graduation via "belonging" to the peer group. The impact of peers on education out-comes has received considerable attention in the economics literature, although empirical evidence of peer effects is not prevalent. Neighbourhoods N may also have their own separate influence on the graduation probabilities of youth. The expected benefits of graduation, in terms of better job and post-secondary education prospects, and in terms of expected higher utility, will depend on the surroundings of the individ-ual. If more role models exist in the local community who have obviously benefited from further education, the more likely the individual will decide to graduate. Each student will have an equivalent equation to 4.1 determining their net benefit of high school graduation. If the current behaviour of peers does affect an individual's net benefit of graduation (the parameter 7r 6 is non-zero), there will be a reciprocal impact of one's own graduation GiCS on the achievement of others in the school and grade, affecting G(_i)C 5 directly. This reciprocal effect then induces a correlation between G(_j) c s and the error term eics. This correlation leads to a bias in regression estimates of equation 4.1 if measures such as G(_i) c s are included. This potential bias is commonly known as the reflection problem in estimating social interactions such as peer effects (Manski (1993), Brock & Durlauf (2001)). Taking expectations of equation 4.1 conditional on the predetermined variables, one can solve for the endogenous peer group measure G(-i)cs. A reduced-form version of equation 4.1 can then be written as follows. tics ~ Fics(f>l + Nics(j)2 + 5CS03 + Aics(f)4 + P(-i)cs05 + Vies (4.2) Here the 0 parameters are combinations of the w parameters in equation 4.1. To recover the 118 underlying structural parameters (the 7r's) requires strong identifying assumptions. The objective of this analysis is to identify the overall effect of school principals on graduation probabilities. Separating out the direct effect of school principals on graduation from any potential indirect effect of school principals on the individual's probability of graduation via peer effects is not crucial. If students can move or self-select to schools where certain principals are in charge, it is im-portant to control for all individual attributes that affect graduation, including measures of prior academic preparation and ability. Obtaining unbiased estimates of the parameters in equation 4.2 requires a zero correlation between the included regressors and the error term rjics. This requires the assumption that there is no unobserved individual ability or motivation factor that affects both prior achievement (the Aics term) and the net benefits of graduation via the error term rjics. In-cluding family background and neighbourhood characteristics should pick up most of the factors driving individual motivation to graduate high school. Including prior measures of high school achievement Aics in our estimates comes at a cost. School principals may have an effect on these prior student achievement levels if they were present at the school in the prior year, so by including these measures, we are removing one path by which principals may affect high school graduation probabilities. In light of this, we construct estimates of the effect of school principals on graduation rates both including and excluding these prior achievement measures. Unbiased estimation of equation 4.2 also requires that there are no missing measures of school inputs in particular, but also neighbourhood and family background measures. Such missing mea-sures are likely to be correlated across students in the same school and grade, which will bias any estimates of peer group effects in particular. This is called the "correlated effects" problem identi-fied by Manski (1983) and others. Such missing measures may also bias estimates of the effect of school principals here, which is the direct concern of this analysis. Including school fixed effects in the regression estimation is necessary to control for any non-time varying school characteristics. This identification strategy then attributes changes over time in individual school characteristics to the school principal, if there is variation in school principals in a particular school. This analysis is related to the literature on Education Production Functions (EPFs). Under this approach, schooling outcomes such as graduation are a function of various family, school and peer group inputs. See Appendix E for a description of this related approach. 119 4.3.2 Semi-parametric Model Here we follow as far as we can the semi-parametric estimation strategy of Rivkin, Hanushek and Kain (2005), with some notable differences. We begin by assuming the following linear equation for the school graduation probability of an individual youth. Instead of positing individual inputs into the graduation decision equation, we focus on the total systematic effect of schools, school principals and individuals on graduation. Gics - Ss + Qcs + 7; + vics (4.3) The probability that an individual i in cohort c of school s graduates from high school is written as a linear function of school (<5), principal (6) and individual (7) fixed effects, plus a random error term (v). The fixed student effect is the composite of all individual and family factors that affect graduation, such as parental education and permanent income, individual student ability, etcetera. The fixed school effect is the composite of all stable elements of schools that affect graduation, such as resources, neighbourhood, peer quality, school district hiring practices, infrastructure, etcetera. The principal component captures the average quality of a particular principal over time. The random error term is a composite of all time varying factors affecting graduation. In equation 4.3, the variance of 9 will measure the variance in the quality of school principals. We use information on principal turnover and graduation rates by school and cohort to generate a lower bound estimate of the within-school variance in principal quality. Equation 4.4 represents the mean graduation rate of students in cohort c of school s as a linear function of average student quality in the cohort and school, fixed school and principal effects, and the cohort average random error. G~Z = 6S + 6CS + 7^ 7 + vZ (4.4) The school principal may vary across cohorts in the school, but all students in the same cohort and school (subscripted by cs) will have the same principal effect (9CS). We can then compare the graduation rate of an individual cohort to the average graduation rate of the school over our observation period. (GZ- G~a) = [6CS -Ts) + ^us-%) + (vTs-v;) (4.5) In equation 4.5, all fixed school effects have been removed by subtracting school average grad-uation rates. Thus deviations in the graduation rate of a particular cohort from the school average is 120 a function of deviations in average student quality from the school average student quality, devia-tions in principal quality from the school average principal quality, and an average error component made up of all time varying individual, family, neighbourhood and school factors. Squaring both sides of equation 4.5 yields equation 4.6. (GTs - G~a)2 = {9CS - ~9~s)2 + (%-s - Ts)2 + 2 (TcAs +TA- TsOcs - + ecs (4.6) Equation 4.6 characterizes the squared deviations in graduation rates as a sum of terms denoting the within school variance in principal quality, within school variation in average student quality, the covariance between average student quality deviations and principal quality deviations within a school, and a final component denoted e. This final component e encompasses all random error variances and cross product terms between our random error and principal and student quality deviations. To identify the variance of school principal quality, we make the following assumption. Devi-ations in the cohort average quality of students within a school are not correlated with deviations in individual principal quality within that school. This assumption does not imply that the overall average quality of students in a school must be unrelated to the overall average quality of principals in a school. It merely requires that changes in student quality are not related to changes in prin-cipal quality within a school. If we think that there is positive self-selection of students over time (good students move to schools where good principals move to) or positive movement of principals across schools over time (good principals move to schools with improving student quality), it will tend to bias up our estimate of the variance of principal quality. We calculate the arithmetic average of these squared deviations in graduation rates within each school to form a measure of the within school variance in graduation rates. The average is taken over n, the total number of years we observe the school in our sample. Taking expectations of this measure of the within school variance in graduation rates, employing equation 4.6, and imposing the assumption stated above yields equation 4.7. E j n 1 n ~ / X^ cs — Gs)2 = E —} (9CS — 9S) n c=l c=l + o^- + £[e7] (4.7) We observe the same principal in a school for more than one cohort. To reflect this, we use the subscript j to indicate the particular principal in school s when cohort c entered grade 12. Thus principal j has a principal effect of By Equation 4.8 defines the expectation of our term of interest, 121 the term capturing the within school variance of school principal quality. The term crja denotes the within school variance of principal quality, where E[6f\ = o2es. We assume that each principal is a random draw from a common distribution, such that E[9j9k] = 0 where j ^ k. E n c=l nz *—' n fc=i (4.8) The large term on the right hand side of equation 4.8 after ajs is a deterministic number denot-ing the amount of school principal turnover within the school. The number qj denotes the number of years that principal j is in the school, while J denotes the total number of different principals in the school over the period. While this turnover term looks quite complicated, it collapses to easily understood numbers in most cases. If the same principal leads the school for the entire sample period, this term will equal zero. The variation in principal quality in a school that has the same principal over the period must be zero. If there are multiple principals in charge over the period, the turnover term will be positive and increasing in the number of principals (the amount of principal turnover). For example, if there are two principals in the school over the period, each one for the same number of years, then the turnover term equals one half. If there are three principals for equal numbers of years, the term equals two thirds. The intuition behind this equation is that the within school variance in school graduation rates should be higher in schools with more than one principal, and it should be increasing in the amount of principal turnover. Details of the construction of this turnover term, including a simple example, is provided in Appendix G. The term denotes the variance of cohort average quality of students in a school over time. To identify the variance of principal quality using principal turnover, we assume that principal turnover is not related to this within school variance in cohort average student quality. Note that this does not imply that turnover is unrelated to the average quality of students in a school, just its within school variance. Our primary estimating equation in the semi-parametric estimator is 4.7, after substituting in equation 4.8. The regressand is the school mean squared deviation of graduation rates in each year from the school average graduation rate. We regress this on the term we construct to denote principal turnover (the summation term on the right hand side of equation 4.8). Ignoring any confounding factors and imposing the assumptions discussed in this section, the coefficient on this term will provide a consistent estimator of the within school variance of principal quality ajs. 122 Our estimator removes all across school variation in school principal quality, so we are gener-ating a lower bound estimate of the overall variance in principal quality. If all schools hired from a common pool of potential school principals, across school variation in school principal quality would be zero. If, however, certain schools can hire from a larger pool of applicants, by offering say more advantageous living and working conditions, average quality of those hired should be higher. Thus there may be considerable across school variation in principal quality that we do not use. Another source of downward bias in our estimate of the variance in principal quality is the violation of the assumption that the quality of leadership does not change when principals do not change. Principals may take a number of years to make their mark on a school after joining it, changing the culture and instruction over time. The effect of quality will therefore also change over time. We investigate this particular issue further in the empirical analysis to follow. One reason that may bias up our estimate of principal quality variance is if there is non-random attrition of principals. We observe principal turnover from both rotation of principals across schools and from principals leaving the sector. If only good or bad principals leave, and new hires are drawn randomly from the distribution, turnover will be related to quality. For exam-ple, say a school gets a good draw from the principal distribution, raising graduation rates. Then that principal leaves, and the next principal is drawn randomly. Thus turnover and quality devia-tions will be related. More turnover will be observed in schools that have a larger distribution in principal quality. We also need to assume that principal turnover is not related to other exogenous changes in the school environment. If there are teacher or instructional changes in a school that coincide with principal turnover, the effect of these changes on graduation rates are attributed to the principal. There are two important differences between our estimator of the within school variance of principal quality and the estimator of the variance of teacher quality developed by Rivkin, Hanushek and Kain (2005). To begin, we cannot difference out the individual fixed effect as we only observe individuals once in our data - the year they enter grade 12. Secondly, we employ a within school estimator constructed by calculating the within-school variance in graduation rates, and use the school as the unit of observation. The Rivkin et al (2005) estimator uses first differences in student achievement within a school and grade, and uses individual cohorts within a school as the unit of observation. This was a purposeful choice here as principals may take some time before making 123 noticeable differences to a school. A first differencing technique will only identify the immediate effects of a new principal on a school, missing more important medium term effects. 4.4 The Data The data we employ in our investigation is constructed from a linkage of three data sources. The first source is British Columbia Ministry of Education records on all youth enrolled at the start of November in grade 12 of a B.C high school from 1991 to 1996. For each grade 12 student we observe whether they graduated from high school. We also observe the high school the individual attended, from which we can identify the principal at the school when the student was in grade 12. These records can also be used to calculate graduation rates for each school in each year. This data source also has information on each individual's grades in up to five courses in grade 11 and, if they complete grade 12, their final high school Grade Point Average (GPA), which is a weighted average of their course marks. We also know whether the youth failed a previous year of school. We keep only observations on individuals who either graduated from high school by age 19.5 or never graduated in our sample period. This gives individuals on average about a year to complete high school even if they did not complete it on the regular schedule with their cohort. Few drop-outs complete high school after age 19.5 in British Columbia. We link this high school data to administrative data from the British Columbia Income Assis-tance (IA) programme. The link is constructed by matching name and birth date between the two sets of files. There are stringent rules for identification of applicants for IA, with three pieces of identification required. Given a successful link, we know whether the individual came into contact with the IA system as a child (i.e., at any time before grade 12), in particular as a member of a family receiving IA payments. We also know whether they came into contact with other parts of the child welfare system, in particular, interventions of Social Services in the family home. We also link the data on individual students to the 1996 Census tract records through the home location as identified by the postal zone of the individual. Individual home postal zone information is only available from 1996 in the school records. Prior to 1996, the link to Census tract records is made with the location of the high school attended in grade 12. With this link, we can use Census data on characteristics of the surrounding population to control for neighbourhood effects. Since we do not have direct information on the income or education level of the individuals' parents, 124 the Census tract data provide an indirect means of controlling for family background effects on graduation. Our neighbourhood characteristics may also proxy peer quality, as many youth attend the school nearest them. Our neighbourhood characteristics, however, are measured at one point in time (1996 Census) so they will not capture any movements in peer quality within a school over time. 4.4.1 Data Description We focus on public high schools in British Columbia, as schools in many school districts were subject to the program where principals were regularly rotated from one school to another by the school board for the district. This focus will also minimize resource differences across schools, with funding levels for public schools set by the British Columbia Provincial government. In some cases, the school principal could not always be identified from Ministry of Education records, so our final sample covered 147 public high schools out of a potential sample of 160. We observe the school principal in all six years (1991 to 1996) in 98 cases, and observe the school principal for five years in the remaining 49 cases (mostly the 1996 data was missing). We observe approximately 125,000 grade twelve students in the data set we employ in estimation. Of the 147 schools in our final sample, 39 had the same school principal for the entire period observed. The remaining 108 schools had more than one principal over the period. Of these 108 schools, 74 had two principals, 32 had three principals, and 2 even had four different principals over the six year period. In 35 of these 108 schools, one of the principals observed was also observed in another school during the period. In all but two of these cases, the principal was seen in another school within the same school district. Thus we observe significant rotation of principals across schools. There is also significant principal turnover unrelated to rotation, due to new principals entering and others leaving the British Columbia public high school principal pool. In all, we observe 267 different principals leading the 147 high schools over this six year period. Our semi-parametric estimator of the variance of principal quality uses information on school principal turnover from rotation, entry and attrition equally. The parametric estimator employs the extra information provided by observing some principals in more than one school. On average over this period in British Columbia, eighty-one percent of entering grade 12 stu-dents graduate from high school. Average graduation rates varied significantly across these public 125 high schools, from a low of forty-five to a high of ninety-two percent. The distribution of mean school graduation rates over the 1991 to 1996 period is presented in Figure 4.1 at the end of this chapter. 4.5 Semi-parametric Estimates of Principal Quality Variance Our semi-parametric estimator of the variance in principal quality works off the hypothesis that the within-school variation in graduation rates should be higher in schools that have several principals over a period than in schools with only one principal over the same length of time. We do observe such a difference in our data. The within school variance in graduation rates (in percentage points) is 30.0 in schools that have only one principal, and 32.7 in schools that have multiple principals, over our period of analysis. This difference is small (nine percent higher variance), but is affected by the fact that average school size is much smaller in schools that had only one principal over the period.4 Year to year variation in graduation rates in a school will be larger if the graduation rates are constructed using a smaller number of observations (students here). If we control for school size when calculating the difference in the within school variance in graduation rates, a much larger difference (twenty-two percent higher variance) is observed in schools with multiple principals. The difference is still not statistically significant, however, with a probability value for the difference of only 0.38. We now turn to estimates employing the semi-parametric technique developed in Section 4.3.2. This estimator involves regressing the within school variance in graduation rates on our indicator of principal turnover within the school. The coefficient on this turnover indicator is our estimate of within school variance in principal quality. We also include the inverse of grade 12 enrolment in the particular school in the estimated regression equation to control for sampling variability in our estimates of the within school variance in graduation rates. Including this term will control for differences in the within school variance of student quality over time across different sized schools (the term in equation 4.7) and the final error component e~s. As discussed above, principals may only make an impact on a school they are put in charge of over several years. Our estimator here will find difficulty in picking up such effects. To investigate 4Schools with multiple principals had on average 160 entering grade 12 students per year, while schools with only one principal had 125 students. The average graduation rate was a little higher in schools with only one principal, at 81.6%, with a graduation rate of 79.7% in schools with multiple principals. 126 Table 4.1: Variance in Principal Quality: Semi-parametric Estimates Schools All < 3 principals < 2 principals A l l Students Turnover indicator 3.5 5.2 10.1 (14.1) (14.4) (19.6) Observations 147 145 113 Welfare Students Turnover indicator 9.7 12.9 9.0 (39.4) (40.2) (45.7) Observations 88 87 68 Notes: Parameters are converted into percentage points. Regressions also include the inverse of school grade 12 enrolment, or grade 12 enrolment of welfare students in the bottom panel. Standard errors are in parentheses. this issue, we construct our estimates of the variance of within school principal quality for the whole sample, and for sub-samples where we include only those schools with small numbers of principals. By focussing on schools with fewer principals over the period, each principal has on average longer to make an impact on the school, thus making it easier for our estimator to identify the true variance in principal quality. Estimates of the within-school variance in principal quality are presented in Table 4.1. Esti-mates for all students are presented in the top panel of the table. Including all schools (the first column) yields a small and insignificant estimate of the within school variance of principal quality (3.5 percentage points). If we include only schools where we observe three or less principals over the period (second column), our variance estimate increases considerably but is still statistically insignificant. Only two schools were dropped from the estimates here. These schools had four different principals over the six year period. In column three, we only include schools where we observe one or two principals over the period. In this case, our estimate of the variance in princi-pal quality jumps to 10.1 percentage points, but is again statistically insignificant. This last point estimate is reasonably large, implying a one standard deviation increase in principal quality raises the probability of a student graduating high school by 3.2 percentage points. As noted in the introduction, certain school principals may have more success in assisting 127 particular student types to graduate, such as those youth who are more at risk of dropping out of high school. We now look at the effect of school principals on the graduation rates of youth from families that have relied on welfare payments (Income Assistance). The overall graduation rate of these youth is much lower (69 percent) than for youth who are not from welfare backgrounds (82 percent). These youth are most likely from low income backgrounds, given the family's prior dependence on welfare. Estimates of the within-school variance in principal quality based on welfare youth only are presented in the bottom panel of Table 4.1. In this case we observe positive and large estimates of the within school variance in principal quality for all three samples, but the estimates are not statistically significantly different from zero. The smaller number of observations (students) being used within each school has meant an increase in the standard errors of our estimates. Note that we employed only those schools that had at least seventy five students from welfare backgrounds in these estimates. This reduced the number of schools employed during estimation, but was necessary to reduce volatility in our calculations of within school variances in graduation rates for this subset of youth. Our estimates imply that a one standard deviation increase in principal quality raises the probability of high school graduation of between three and four percentage points. We also constructed semi-parametric estimates of the variance of principal quality using a within school estimator that employed changes in graduation rates year to year in identification, rather than annual deviations in graduation rates from school averages. This alternative estimator is closer to that constructed by Rivkin, Hanushek and Kain (2005). It identifies principal quality differences using the immediate effect of principal turnover (first year in a new school) on gradua-tion rates. Estimates of the variance in principal quality calculated using this alternative estimator were statistically insignificant and even negative. This result may again reflect the hypothesis that principals take a number of years before having their full impact on a school, with graduation rates taking time to adjust to reflect the true quality of a new principal. 4.6 Parametric Model Estimates We now turn to estimating the parametric model of high school graduation described in Sec-tion 4.3.1 above. One advantage of this estimator over the semi-parametric estimator of the pre-vious section is the ability to control for some of the observable characteristics of individuals that 128 affect graduation. A second advantage is the ability to map out the entire distribution of estimated principal effects, rather than just identifying the variance of principal quality. A third advantage is that this estimator can employ the extra information provided by observing many principals in more than one school over the period (principal rotation). The drawbacks of this parametric model estimator is that the results will reflect the particular functional form chosen, and no direct test of the statistical significance of our estimate of the variance of principal effects is available. Our goal here is to estimate the importance of school principals on the graduation probabil-ities of British Columbia youth. We estimate several versions of equation 4.2, adding sets of explanatory variables in stages to identify their effect in explaining graduation rates. We include several measures of student family background as proxies for family inputs into school achieve-ment and beliefs about the benefits of high school graduation. These variables include indicators of gender (FEMALE), quarter of birth, native status (NATIVE), non-english language spoken at home (NONENG), and separate indicators if a CHINESE or EAST INDIAN language is spoken at home. There is an indicator of whether the family the child belonged to ever received Provincial welfare payments or Income Assistance in British Columbia (WELFARE), when the child lived in the home. There are also indicators of whether Social Services had to assess the home for poten-tial problems related to the children residing there (ASSESS), whether the assessment led to the Province providing counseling or other services (FAMSERV), and whether the Province put the child into alternative care (CARE). We also have available direct measures of the prior school achievement of our observed youth. Individual grade 11 exam results are available for all our observed youth, and final grade 12 grade point average, or GPA, information is available for those youth who graduated high school. We use this information to construct a single measure (GPA type scale) of grade 11 achievement (GRADES 11) from the information we have. This measure is built on a scale from zero to four. The number of grade 11 exam results we have in the data-set varies by individuals and there is no one grade (e.g., math) present for all individuals. Thus, we have to aggregate the grade data in a way that makes use of the varied individual data. We also adjust the constructed measure to eliminate differentia] grade inflation across schools. The details on the construction of this variable are given in Appendix H. We also construct indicators of whether an individual failed one previous grade (PFAIL1), failed more than one grade (PFAIL2), or was advanced a grade (PADV1), using the age of the student. 129 High school principals may have an effect on prior measures of student achievement if they have been at the school for a number of years. This may be reflected in the average grade 11 exam results of students entering grade 12, and on the prevalence of failing previous grades of school. As a result, including this information in our estimated equations may tend to reduce the potential effect of principals on graduation rates. On the other hand, including such measures allows greater control for student ability levels. We present estimates both including and excluding these achievement measures, for the individuals themselves and peer averages. Seven particular neighbourhood characteristics are included as predictors of high school grad-uation in our analysis. These characteristics may proxy missing family characteristics in our esti-mates, as well as control for the effect of neighbourhoods on graduation probabilities. The seven neighbourhood characteristics are: the proportion of population who have taken up welfare or Income Assistance (IAPERCAP), the proportion of dwellings occupier-owned (DWELL), the pro-portion of the population born in Canada (CANBORN), the proportion of adults with less than a grade 9 education (PLTG9E), the proportion of families with a single parent (LONEPAR), the median family income (FAMINC), and the proportion of 25 to 64 year old individuals employed (EMPRATE). We construct peer quality measures for each individual student by calculating the average of the individual characteristics for all other students in the same school and cohort (year).5 For example, we calculate the proportion of a student's classmates that came from a welfare background, but do not include the individual student themselves in the calculation. These are the exogenous peer measures P(-i)cs described in Section 4.3.1 above. Summary statistics for these peer measures, for the individual characteristics, and for our seven neighbourhood characteristics, are provided in Table 4.2. Cohort indicators are also included in all the estimating equations. These will absorb any changes in Provincial government policy in schools, in British Columbia labour market conditions (high unemployment rates may keep youth in school), in Income Assistance rules, and in aggregate post-secondary education possibilities. Rather that present all the estimated coefficients of our models, we begin by presenting R-squared values for our various model specifications in Table 4.3. The models were estimated using the probit technique. We first report the Psuedo R-squared measure suggested by McFadden 5Peer measures were not included for quarter of birth indicators. 130 Table 4.2: Summary Statistics for Explanatory Variables A l l students Mean s.d. Welfare students Mean s.d. GRADUATE 0.805 0.688 Individual characteristics FEMALE 0.516 0.551 NATIVE 0.022 0.053 CARE 0.009 0.041 FAMSERV 0.046 0.175 ASSESS 0.080 0.269 NONENG 0.201 0.148 INDIAN 0.060 0.049 CHINESE 0.123 0.052 WELFARE 0.134 1 GRADES 11 2.442 0.845 2.140 0.809 PFAIL1 0.182 0.255 PFAIL2 0.006 0.008 PADV1 0.019 0.016 Neighbourhood chars. IAPERCAP 0.037 0.060 0.049 0.068 DWELL 0.682 0.164 0.631 0.177 CANBORN 0.753 0.132 0.768 0.130 PLTG9E 0.089 0.051 0.102 0.050 LONEPAR 0.125 0.042 0.141 0.046 FAMINC ($000s) 24.81 6.37 22.57 4.223 EMPRATE 0.604 0.077 0.589 0.073 Peer measures FEMALE 0.516 0.048 0.516 0.045 NATIVE 0.022 0.048 0.026 0.032 CARE 0.009 0.011 0.011 0.010 FAMSERV 0.046 0.028 0.053 0.028 ASSESS 0.080 0.043 0.094 0.041 NONENG 0.201 0.202 0.200 0.211 INDIAN 0.060 0.065 0.063 0.069 CHINESE 0.123 0.142 0.110 0.138 WELFARE 0.134 0.071 0.170 0.070 GRADES 11 2.442 0.185 2.403 0.165 PFAIL1 0.182 0.060 0.197 0.058 PFAIL2 0.006 0.007 0.007 0.007 PADV1 0.019 0.013 0.018 0.012 School graduation rate 0.805 0.061 0.688 0.082 Observations 125,321 13,752 Notes: The mean graduation rate in the school for welfare students is calculated using welfare students only. Sources - British Columbia ministries and the 1996 Canadian Census. 131 (1974). It is calculated as 1 - LUR/LQ where LUR is the likelihood function value for the unrestricted model (including all the regressors), while L A is the value for a model including a constant only (no regressors). The observed versus predicted R-squared values are constructed as the R-squared from ordinary least squares regressions of the graduation indicator (our binary choice variable) on the individual predicted values from the appropriate probit model. These R-squared measures provide the reader with a perspective on the contribution of our various sets of regressors in predicting graduation rates. We present more complete information on our preferred model specification below. The top panel of Table 4.3 presents results for specifications that exclude our measures of prior school achievement (GRADES11, PFAIL1, etcetera). The first column in Table 4.3 is based on a model specification that includes only individual student characteristics and year indicators. In the second column, neighbourhood characteristics are added, while in the third, peer measures are added. We observe small but highly statistically significant increases in explanatory power as we add each set of additional characteristics. The probability value for likelihood ratio tests of each added set of explanatory values is essentially zero in all cases. Adding school fixed effects in column 4 increases the explanatory power of the model consider-ably. This suggests either schools are very important, or that these school fixed effects are picking up unmeasured differences across schools in student quality or neighbourhood influences. The fixed effect of schools on graduation probabilities are vastly captured by including one variable of school mean graduation rates (column 5) rather than the 146 individual school fixed effects of col-umn 4. The R-squared values are almost as high for this alternative and much more parsimonious specification of school effects. Columns 6 and 7 add individual school principal indicators to the estimated regressions. In column 6, we control for school effects using individual school indicators, as in column 4. In column 7, school effects are controlled for simply with the school mean graduation rate, as in column 5. The benefit of the specification in column 7 is that individual principal effects can be estimated for all principals. These principal effects are the impact of individual school principals on graduation rates relative to the mean graduation rate for the school over our sample period. Only indicators of principals that are not at the same school for the entire sample period are included, as it is not possible to separately identify principal effects from school effects if the principal is at the same school for the entire observed period. There are 228 such principals out of the total of 132 Table 4.3: School Graduation Probit Estimates: A l l Students Explanatory variables (1) (2) (3) (4) (5) (6) (7) NO achievement measures Student characteristics yes yes yes yes yes yes yes Neighbourhood chars. - yes yes yes yes yes yes Peer measures - - yes yes yes yes yes School fixed effects - - - yes - yes -School mean grad. rates - - - - yes - yes Principal fixed effects - - - - - yes yes Psuedo R-squared .0358 .0396 .0408 .0584 .0570 .0614 .0605 Obs. vs predicted R-squared .0377 .0413 .0425 .0599 .0586 .0629 .0621 LR test p-value 0.00 0.00 0.00 0.00 0.00 0.00 0.00 WITH achievement measures Student characteristics yes yes yes yes yes yes yes Neighbourhood chars. - yes yes yes yes yes yes Peer measures - - yes yes yes yes yes School fixed effects - - - yes - yes -School mean grad. rates - - - - yes - yes Principal fixed effects - - - - - yes yes Psuedo R-squared .2457 .2483 .2501 .2628 .2606 .2661 .2647 Obs. vs predicted R-squared .2474 .2500 .2517 .2654 .2634 .2688 .2677 LR test p-value 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Notes: 125,321 observations. Al l specifications include year fixed effects. The Psuedo R-squared values equal 1 - Lur/L0, where Lur is the likelihood function value for the unrestricted model (including all the regressors), while L0 is the value for a model including a constant only (no regressors). The observed versus predicted R-squared values are the R-squared from OLS regres-sions of the graduation indicator on the individual predicted values from the appropriate probit model. The Likelihood Ratio (LR) test p-value tests the joint statistical significance of the added set of regressors only (the lowest "yes" term). 133 267 principals observed in our data. Thus 228 principal indicators are added to the specification of column 7. Only 142 principal indicators are separately identified in the specification of column 6, as only differences in principal quality within a school can be identified when school fixed effects are employed. We see the explanatory power increase again when these principal indicators are added, and the increases are highly statistically significant. The lower half of table 4.3 presents results for model specifications that include our measures of individual prior school achievement, plus peer measures of prior school achievement. As could be expected, the explanatory power of our graduation probability regressions increases markedly when we include these individual measures of school achievement. The additional explanatory power of schools is a little lower than when we exclude measures of prior achievement. The addi-tional explanatory power of school principals in predicting school graduation in these regressions is, however, the same regardless of whether we include these individual prior achievement mea-sures or not. The specification in column 7 is our preferred model of high school graduation. It includes all the individual, neighbourhood and peer characteristics, controls for school effects with the mean graduation rate, and includes our principal indicators. The marginal effects of each individual, neighbourhood and peer characteristic on the probability of high school graduation estimated us-ing this specification are presented in Table 4.4. Al l our individual characteristics have significant effects on high school graduation, and generally in the directions that we would expect. An ex-ception may be the large negative effect of speaking Chinese in the home on graduation. The only neighbourhood characteristic that has a significant and expected effect on graduation is the the proportion of homes that are owned.6 The higher the proportion, the higher the probability of graduation. The proportion of the population with less than a grade nine education (PLTG9E) has an unexpected positive impact on graduation. Of the peer measures, being in a cohort with more females raises the probability of graduation, as does being in a cohort with more students speaking a non-english language at home. Being in a cohort with higher grade 11 grades actually reduces the probability of graduation. 6Given that for all but 1996, neighbourhood characteristics were linked to students using the location of the school rather than the individual student, variability within schools in our neighbourhood measures is essentially zero. Thus including school effects will soak up all the potential contribution of our neighbourhood measures to predicting gradu-ation probabilities. Neighbourhood characteristics were significant predictors of graduation when school effects were excluded, as in columns (2) and (3) of Table 4.3. 134 Table 4.4: Marginal Effects for Graduation Probabilities Al l students Effect s.e. Welfare students Effect s.e. Individual characteristics FEMALE 1 2*** 0.26 0.6 0.89 NATIVE 0.94 _(j 3*** 2.05 CARE -6.0*** 1.41 -3.6 2.40 FAMSERV _\ g*** 0.66 _2.7** 1.31 ASSESS _7 4*** 0.59 1.13 NONENG -1.4** 0.58 4.3** 1.68 INDIAN _2 5*** 0.67 -2.4 2.85 CHINESE 1 2*** 0.73 -11.8*** 3.05 WELFARE 4 j * * * 0.42 GRADES 11 144*** 0.60 194*** 1.47 PFAIL1 _3 9*** 0.35 4 g*** 1.05 PFAIL2 _7 5*** 1.68 -11 7** 5.10 PADV1 _5 9*** 1.21 -4.9 4.02 Neighbourhood chars. IAPERCAP -0.1 0.19 -0.3 0.73 DWELL 0.22 0.2 0.78 CANBORN -0.1 0.33 1.2 1.11 PLTG9E 0.7** 0.27 0.7 0.93 LONEPAR -0.2 0.22 0.1 0.75 FAMINC ($000s) 0.0 0.27 0.4 0.80 EMPRATE 0.2 0.21 -0.3 0.75 Peer measures FEMALE 0.5*** 0.16 0.1 0.53 NATIVE -0.1 0.24 -0.6 0.71 CARE -0.6*** 0.19 0.6 0.65 FAMSERV 0.0 0.24 -1.1 0.83 ASSESS 0.5* 0.30 32*** 0.99 NONENG 2 7*** 0.74 5.8** 2.65 INDIAN -0.4 0.32 -1.7 1.24 CHINESE 2 o*** 0.76 -4.2 2.59 WELFARE 0.0 0.31 -0.8 1.15 GRADES 11 _2 5*** 0.29 -1.6** 0.80 PFAIL1 -0.2 0.23 -1.2 0.82 PFAIL2 0.1 0.16 -0.2 0.58 PAD VI -0.3 0.17 0.3 0.56 School graduation rate 5.8*** 0.40 g_2*** 1.08 Observations 125,321 13,752 Notes: One, two and three asterisks (*s) denote statistical significance at the 10%, 5% and 1% levels respectively. These marginal effects reflect turning indicator variables from zero to one, and increasing continuous variables from sample mean levels to one standard deviation above the mean levels. Probit regressions also include quarter of birth dummies, year dummies and school principal dummies. 135 The estimates from our preferred specification are now employed to map out the distribution of within school principal quality, based on this particular functional form. To do this, we begin by calculating predicted school graduation rates for each principal Pj, holding all other variables con-stant (individual, neighbourhood, and peer characteristics, and the school mean graduation rate). We are thus removing the effect of student body quality facing each principal. The distribution of these predicted graduation rates by principal is presented in Figure 4.2. The standard deviation of these predicted school graduation rates by school principal is 4.9 percentage points. These princi-pal effects were calculated using the model in the bottom half of Table 4.3, including our measures of prior school achievement. The principal effect distribution is essentially the same if these prior measures of achievement are excluded. Note that there will be variation in these estimated principal effects even if there is no quality differences across principals. This is because of sampling variability due to our estimation of con-ditional mean graduation rates by school principal from our data. We can adjust the estimate of the variance in principal effects due to this sampling variability to arrive at a "true" variance of princi-pal effects. This involves subtracting an estimate of the sampling variance from the raw variance of the distribution in Figure 4.2. If we assume that sampling error and true heterogeneity in principal quality are independent, the variance of our estimated principal effects can be written as the sum of the variance of the true heterogeneity and the sampling error variance. For a principal with a true graduation rate of Pj and with whom there is associated Nj students in our sample, the sampling variance is Pj(l — Pj)/Ny We estimate Pj for each principal using the fitted graduation effect Pj described above. We then average over the calculated sampling variances for each principal to get an overall sampling variance estimate. Finally, we subtract that sampling variance estimate from the variance of our estimated principal effects to obtain our estimate of the variance of the "true" heterogeneity. Using this adjustment technique, our estimate of the "true" standard deviation in principal effects is 4.0 percentage points. If a student has a school principal that is one standard deviation higher in the quality distribution, it raises their probability of graduation by 4.0 percentage points. This estimate is roughly in line with our semi-parametric estimates of the within school variance in principal quality. As discussed above, school principals may be more able to affect the graduation probabilities of youth who are more at risk of dropping out of high school, such as youth from welfare back-136 grounds. As with the semi-parametric estimates of the previous section, we analyzed the effect of school principals on the graduation probabilities of the sub-sample of youth from welfare families using the parametric model of this section. As in the semi-parametric estimates of the previous section, we employed observations from those schools that had at least seventy five students from welfare backgrounds here. This reduced the number of principal effects that could be separately identified also, from 228 to 141.7 The marginal effects of our explanatory variables on graduation probabilities for our youth from welfare backgrounds only are presented in the right hand side of Table 4.4. These marginal effects were constructed from estimates of a model specification including all the individual, neighbour-hood and peer characteristics, the school mean graduation rate for welfare youth, and principal fixed effects. This is the same specification as in column 7 of Table 4.3, but was estimated us-ing youth from welfare backgrounds only. The more parsimonious specification including school mean graduation rates rather than school fixed effects does not perform quite as well in this case, but it still captures the vast majority of the school effects. Note that the mean graduation rate of welfare youth only was employed here. This measure of school effects had much higher explana-tory power than the mean graduation rate of all students in the school in these regressions. Some schools appear to be better at encouraging welfare youth to graduate over and above what would be predicted by their ability to encourage non-welfare youth to graduate. The additional explanatory power from including principal fixed effects was larger here for welfare youth than for the whole sample. This increase in explanatory power is the same whether we control for school effects using individual school indicators or the school mean graduation rate for welfare youth. Thus it appears that school principals (and schools) may vary more considerably in their ability to encourage these welfare youth to graduate. We can again map out the distribution of principal effects on the graduation probabilities of welfare youth using these model estimates. The distribution of predicted principal effects, holding all other explanatory variables constant, are presented in Figure 4.3. The standard deviation of these estimated principal effects was 9.3 percentage points. After adjusting for sampling variation, our estimate of the "true" standard deviation of principal effects is a sizable 6.4 percentage points. The smaller numbers of students per principal employed in these estimates raised our calculation 7 We could not identify one additional principal effect in our reduced sample as it was a perfect predictor of gradu-ation status. 137 of the variance of the estimated principal effects due purely to sampling variation, but the estimated variance of the "true" heterogeneity in principal quality is still larger for welfare youth than for all youth. Welfare youth who attend a school that has a principal one standard deviation higher on the quality distribution have a 6.4 percentage point higher probability of graduating. This estimate is slightly higher than our semi-parametric estimates of the previous section. 4.7 Conclusions We have found evidence that school principals do matter in terms of affecting high school gradua-tion rates. Both semi-parametric and parametric estimates of the within school variance in principal quality suggest that there is sizable quality heterogeneity. There is also some evidence of a slightly larger effect of school principal quality on the graduation probabilities of youth from low income backgrounds, as indicated by the youth's family receiving welfare in the past. Our evidence sug-gests that school policies that can raise the quality of high school principals may improve high school retention and graduation rates. Intrinsic school leadership quality appears to be an impor-tant component in determining the ultimate effectiveness of schools. Our identification strategy employed observed turnover of principals within schools. It is not reliant on particular observable characteristics of school principals such as their education levels or experience, nor on subjective measures of the school environment or principal effectiveness. A considerable amount of principal turnover that we observe stems from school principals quitting this type of career. Being a school principal is a stressful job, and many school districts are finding it difficult to attract quality applicants and to keep quality principals in their jobs. Given the importance of school principals found in this research, there may be a role for public policy in increasing efforts to retain good school principals, via increased salaries or other measures to improve the desirability of working as a school principal. Our evidence of heterogeneity in principal quality is not entirely conclusive, however, as the statistical significance of our semi-parametric estimates of the within school variance in principal quality is low. The imprecision of our results may reflect a sample size that is not large enough to capture statistically significant principal effects. More years of administrative school data, covering the 1997 to 2001 period, will be available soon and may assist us to improve the precision of our estimates. Low statistical significance may also reflect the hypothesis that school principals take 138 several years to affect the schools they are hired to lead. Improving our estimation techniques to better account for such phenomena is an area for future research. 139 Figure 4.1: School Mean Graduation Rate Distribution Figure 4.2: Principal Effect Distribution - AH Students 12 10 8 0 11111. i < 111111; r; 111. i r 0.4 0.5 0.6 0.7 0.8 0.9 1 Figure 4.3: Principal Effect Distribution - Welfare Students 0.4 0.5 0.6 0.7 0.8 0.9 1 Sources - British Columbia Ministry of Education and authors' calculations. 140 CHAPTER 5 Concluding Remarks My main objective in this dissertation was to analyze more closely the role that family back-ground, and particularly parental income, plays in determining the education attainment of youth. If parental income is a significant causal determinant of the education outcomes of youth, there may be a role for government intervention. Such intervention can be supported on both equity and efficiency grounds, to minimize the intergenerational transmission of inequality and to encourage an efficient supply of educated workers for the economy. • In Chapter 2,1 found that persistent shocks to parental income, indicated by parental job loss, have considerable negative effects on the education attendance of youth. Youth of high school leaving age whose parents lose their jobs are more likely to drop out of high school and are much less likely to attend university. This provides strong evidence of the causal effect of parental income on education attainment. In Chapter 3, I found that increases in the cost of attending university (tuition fees) negatively affected the university attendance probabilities of youth from low income backgrounds much more than it affected middle and high income youth. This also provides evidence of the importance of parental income in determining education attainment. The two pieces of research are thus complementary and reach the same conclusion. Parental income is a significant determinant of education attainment. Most previous research on the causal effect of parental income on education attainment have found only small or no causal effect, whereas I find large effects. I attribute at least part of this difference in findings to the observation that some of the previous literature used changes in in-come within families over time to identify effects. Such changes may be dominated by temporary movements, whereas I find that it is only persistent negative income shocks related to parental job 141 loss that have a significant negative effect on youth education outcomes. The main contribution of my work to the literature is the identification of these persistent negative income shocks and estimating the large effect of these shocks on youth's education attendance. The negative effect of parental income on education attendance I identify suggests that a sig-nificant proportion of the observed raw correlation between parental income and the education attendance of youth is causal. It may be the case, however, that such negative shocks to income have larger effects on youth than if the youth came from a family that had lower income levels throughout their lives. Parents who have low income levels throughout their working lives may be prepared to provide for their children's education. Parents with initially higher incomes may not feel the need to save as much for their children's education, so a negative income shock may have a larger effect on transfers to children given the consumption lifestyle of the family. Analyzing the effect of parental job loss on how family resources are divided between family members is an area for future research, including whether youth contribute to family resources in response to parental job loss. Student loans were available to low income youth during the period I examine. Despite this, large effects of parental income shocks on university attendance were identified. The evidence points to considerable financial constraints of some form on education attendance, but suggests that borrowing constraints alone may not be the only form that these financial constraints may take. Individual investments in higher education are risky, and individual preferences for assuming large debt loads at young ages may be quite heterogeneous across the population. A proportion of youth may be averse to borrowing to invest in their own human capital even if the average expected financial payoff appears large. Individual youth generally cannot insure against the individual risk of their human capital investments. There are several risks involved, including course completion risk and income return risk. Provision of student loans overcomes loan market incompleteness, but does not overcome insurance market incompleteness. Parental transfers are one way that parents assume some of the risk of youth's education investments. Several countries have initiated in-come contingent student loan repayment schemes to provide a particular kind of insurance.1 Such schemes are attracting attention in North America also. Identifying the causal effect of parental income on education attendance in these jurisdictions, perhaps using parental job loss shocks, is an area of future research that may bear some light on the expected benefits of such student loan 'The countries include the United Kingdom, Australia and New Zealand. 142 schemes. The large negative effect of tuition increases on the university attendance of low income youth may suggest that Canada's student loan program has not kept pace with these increases in tuition. Student loan limits were essentially constant over the 1995 to 2001 period, the period I analyzed. Student loan limits have been increased recently. Estimating the effect of this increase on education attendance may also be a fruitful area for future research. The effect of student loan changes on education attendance has been analyzed in the United States but not, to my knowledge, in Canada. I estimated the effect of persistent parental income shocks following job loss on the education attendance of Canadian youth with the Survey of Labour and Income Dynamics (SLID) data set. This particular data set has the information necessary for this analysis, whereas the main United States data sets used to analyze education outcomes of individual youth do not. The Panel Study of Income and Dynamics (PSID) does not have detailed year to year education enrolment information for young adults. The National Longitudinal Study of Youth (NLSY) does not collect annual parental income and labour market outcome information for all youth of school-leaving age, as no parental information is collected for youth who leave the parental home. This situation may, however, be changing. Recent waves of the Survey of Income and Program Participation (SIPP) have been conducted over a four year panel, rather than just over the two to three years that the earlier SIPP waves covered. This Survey does collect the information necessary to conduct the type of analysis I conduct in Chapter 2, and these longer more recent panels may also be long enough. Once the second of these longer waves of the SIPP is available for analysis, I should be able to undertake a parallel analysis for US youth. One of the main contributions of Chapter 3 to the literature is the identification of the impact of potential rationing of post-secondary education places on the attendance of youth from different parental income backgrounds. I estimated the effect of cohort size and provincial funding of post-secondary education institutions on the education attendance of Canadian youth. These variables will affect the probability of being accepted at a post-secondary education institution if there is excess demand for places at government-subsidized tuition levels. These variables have vastly been excluded from prior research of the determinants of individual education outcomes. I find that cohort size significantly affected the probability of attendance at the university level for Canadian youth, implying that there may be significant rationing of places at the university level. Youth from larger cohorts were less likely to attend university even after controlling for 143 many individual characteristics, tuition and provincial spending on universities and community colleges. This suggests that the higher level of competition for university places resulting from larger cohorts is binding on youth. There was a larger negative effect of cohort size on the univer-sity attendance of youth from low income backgrounds. Low income youth may be being rationed out of university because they have lower measured achievement during high school, reducing their probability of acceptance at university. Rationing may thus be causing some of the observed inequality in university attendance in Canada. This again suggests a role for government inter-vention, via increased funding of universities in growing areas, to minimize the intergenerational transmission of inequality. It also suggests that tuition reduction policies alone may not have the desired effect on equality of access to education opportunities if it results in less spaces being available for prospective students. In Chapter 4, my co-authors and I found evidence that school principals do matter in terms of affecting high school graduation rates. There is also some evidence of a slightly larger effect of school principal quality on the graduation probabilities of youth from low income backgrounds, as measured by family welfare receipt. Our evidence suggests that school policies that can raise the quality of high school principals may improve high school retention and graduation rates. In-trinsic school leadership quality appears to be an important component in determining the ultimate effectiveness of schools. My co-authors and I are currently considering several areas of future research related to the analysis of Chapter 4. An extension of the data set to include the years from 1997 to 2001 is currently being constructed. This longer sample period will allow us to identify the changing effect of school principals over the period the school principal is in a school. Good principals may take several years to have their full influence on a school. In addition, we plan to analyze the effect of school principals on the test scores of students, rather than just on their graduation probabilities. 144 Bibliography Acemoglu, Daron & J.-S. Pischke (2001) "Changes in the wage structure, family income, and children's education", European Economic Review, 45(4-6), 890-904, May. Beaudry, Paul, Thomas Lemieux and Daniel Parent (2000) "What is Happening in the Youth Labour Market in Canada?", Canadian Public Policy, 26(Supplement 1), S59-S83, July. 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Worswick, Christopher (2003) "School Program Choice and Streaming: Evidence from French Immersion Programs", Carleton University, Canada, Paper presented to the Canadian Em-ployment Research Forum Conference in Ottawa, June. 150 Appendices Appendix A: Final SLID Sample Construction and Panel Attrition The first two panels of the SLID data set include 2,909 longitudinal respondents of the ap-propriate age for inclusion in the analyses of Chapters 2 and 3. Appropriate observations include youth aged 15 or 16 at the start of each panel from Quebec and Ontario, and youth aged 14, 15 or 16 from the remaining provinces. Many of the potential observations were not able to be em-ployed in the analyses for a variety of reasons, including panel attrition and item non-response. In total, 1,035 observations could not be used in the analysis of Chapter 3, representing 36% of the potential sample. This left 1,874 usable observations. Less data could be employed in the analysis of Chapter 2 due to stronger information requirements. In total, 1,574 observations could not be used in this case, representing 54% of the potential sample. This left 1,335 usable observations. The following is a list of sequential removal of observations and the reasons why they were removed. The first six items in this list are relevant to the data sets employed in the analyses of both Chapters 2 and 3. The final two items refer to the data set employed in Chapter 2 only. 1. Youth not observed at age 16' - 4% (of the 2,909 eligible respondents). 2. Youth not residing at parental home at age 16, so no parental information available - 3%. 3. The family household the youth belonged to fell out of the sample - 11%. 4. The youth left the family household after age 16 and could not be contacted by Statistics Canada staff-6%. 5. Youth did not answer education attendance questions for each year required even when con-tacted - 8%. 6. At least one covariate was not defined for the youth, e.g. average parental income, number of siblings, parental education - 4%. 7. Annual information on the employment outcomes of the main income earner of the family were not available for each year required - 14%. ' A small percentage of youth were not observed at age 16. This occurs when the household the youth belonged to fell out of the longitudinal survey prior to the youth turning 16. 152 8. The annual education transitions reported by the youth suggested errors in reporting - 4%. Attendance information was imputed for a small number of survey respondents where missing observations were encountered. This was undertaken to minimize sample attrition, and was only followed for youth at ages 16 and 17 where subsequent annual attendance reports justified impu-tation. Imputation involved attributing high school attendance to youth at age 16 or 17 who were subsequently enrolled at high school at the next annual survey. Tables A . l and A.2 provide summary information on the sample employed and on the observa-tions that could not be employed (where possible) for Chapters 2 and 3 respectively. The parental income measure here is for the one year (rather than a three year average) when the youth was aged 16, or the nearest younger age if no details were available at age 16. The characteristics of youth not employed in the analysis is only different to the characteristics of those included in some dimensions. They are more likely to be from a lone parent family, to have less educated parents, and less likely to be city residents. Their exclusion from the analyses should only result in biased estimates if there is some unmeasured characteristics of these youth related to their exclusion from the sample, their education attendance, and to their individual characteristics or background. One check on the representativeness of the final samples employed in the analysis is to compare the outcomes of these youth with the outcomes of a separate sample of youth of the same age. The Canadian Census was employed for this purpose. Some summary statistics for the SLID samples employed in my analyses and equivalently aged youth from the 1996 Census Public Use file are provided in Table A.3. The SLID samples were more likely to be students, particularly at other PSE institutions. They are also more likely to live at home, which is most likely due to it being easier to track youth who remain in the family home when undertaking annual SLID questionnaires. SLID final sample youth are also more likely to have worked in the previous year. Care must be taken here as the work questions are much more detailed in the SLID than in the Census, and thus more likely to pick up small amounts of part-time work. 153 Table A . l : Statistical Comparison: Sample for Chapter 2 Variable Ch. 2 Sample Mean s.d. Dropped obs. Mean s.d. Observations Female 0.488 0.485 1,574 French mother tongue 0.203 0.205 1,574 Aboriginal descent 0.028 0.030 1,574 Visible minority 0.087 0.109 1,574 Parent immigrant 0.236 0.246 1,574 Lone parent 0.151 0.224 1,498 Parents not graduate HS 0.119 0.169 1,500 Parents other PSE only 0.448 0.409 1,500 Parent completed university 0.1.90 0.167 1,500 Real parental income 64,700 42,765 62,771 45,710 1,498 Children in family 2.79 1.56 2.80 1.41 1,435 City resident (> 100,000) 0.533 0.628 1,574 Rural resident 0.169 0.121 1,574 University > 80 km 0.190 0.158 1,574 College > 40 km 0.137 0.112 1,574 Atlantic Canada 0.132 0.093 1,574 Quebec 0.194 0.244 1,574 Ontario 0.282 0.319 1,574 Prairies 0.224 0.209 1,574 British Columbia 0.168 0.134 1,574 Observations 1,335 Source: Survey of Labour and Income Dynamics. 154 Table A.2: Statistical Comparison: Sample for Chapter 3 Variable Ch. 3 Sample Mean s.d. Dropped obs. Mean s.d. Observations Female 0.484 0.492 1,035 French mother tongue 0.222 0.178 1,035 Aboriginal descent 0.024 0.037 1,035 Visible minority 0.239 0.247 1,035 Parent immigrant 0.091 0.117 1,035 Lone parent 0.166 0.243 959 Parents not graduate HS 0.114 0.206 961 Parents other PSE only 0.445 0.388 961 Parent completed university 0.203 0.134 961 Real parental income 65,421 41,481 60,090 49,050 959 Children in family 2.781 1.441 2.811 1.547 896 City resident ( > 100,000) 0.569 0.624 1,035 Rural resident 0.152 0.119 . 1,035 University > 80 km 0.177 0.162 1,035 College > 40 km 0.128 0.111 1,035 Atlantic Canada 0.120 0.089 1,035 Quebec 0.227 0.220 1,035 Ontario 0.282 0.336 1,035 Prairies 0.209 0.222 1,035 British Columbia 0.162 0.133 1,035 Observations 1,874 Source: Survey of Labour and Income Dynamics. 155 Table A.3: Statistic Comparison: Final Samples Employed and 1996 Census Chapter 2 Chapter 3 Census Attended PSE University 0.30 0.32 0.28 Other PSE 0.35 0.36 0.26 Any PSE 0.65 0.68 0.54 Living with parents A l l 0.83 0.75 University student 0.90 0.88 Other PSE student 0.87 0.80 Non-student 0.69 0.61 Worked past year A l l 0.85 0.77 University student 0.83 0.82 Other PSE student 0.85 0.79 Non-student 0.90 0.78 Observations 1,335 1,874 10,535 Source: Survey of Labour and Income Dynamics and 1996 Canadian Census. 156 Appendix B: Covariates and Data Sources Covariates Here is a description of the various covariates included in the analyses of Chapters 2 and 3. Summary statistics were provided in Tables 2.4 and 3.3 respectively. The Female indicator is self-explanatory. The French Mother Tongue variable indicates whether the youth's first language spoken is French. This is common in Quebec and New Brunswick, and there are French speakers in certain parts of Ontario also. The aboriginal descent indicator is a self-report of belonging to one of the several indigenous populations in Canada. If either parent was not born in Canada, the parent immigrant indicator was set to one. Visible minority status is a self report. The lone parent indicator is set to one if the youth lived with only one parent at age 16. The majority of lone parents were female. The children in family variable measures the number of children ever born or raised by the female parent. If the youth belonged to a single parent family headed by a male, then the number of children ever raised by the male parent was employed. The first parental education indicator denotes that neither parent (or the one parent if a single parent family) graduated from high school. The second denotes that at least one parent completed some kind of post-secondary degree, but neither completed a university bachelors degree or higher. The third indicator denotes that at least one parent completed a university bachelors degree or higher. Parental income was calculated as the average annual real parental income after tax over the three years when the youth was aged 16, 17 and 18.2 The parentage of youth was determined by the family structure of the household when the youth was aged 16, i.e. whether the youth lived with both parents or only one. Living costs vary considerably across Canada. For example, rent is much higher in the city of Vancouver than in rural Saskatchewan. Statistics Canada constructs annual measures of Low Income Cut-offs (LICOs). These measures vary by family size and size of the area of residence. Differences in these LICO measures between rural and urban areas reflect differences in costs of living. These measures were employed to adjust parental income for living cost differences prior to splitting youth into parental income quantiles. Youth were divided into three equal groups (high, middle and low) by average real after tax parental income in excess of the 2Nominal income measures were deflated by the Canada-wide CPI index. 157 appropriate LICO measure for the household. This procedure resulted in denoting youth with real (2001 dollar) unadjusted pre-tax parental income below approximately $40,000 as low income. High income youth are those with parental income above approximately $70,000. The city and rural area indicators refer to the size of the area of residence when the youth is 16. The remainder of youth reside in small urban areas, i.e. cities and towns with less than 100,000 residents. There are three indicators for whether the residence of the youth at age 16 was further than 40 and 80 kilometres (25 and 50 miles) from the nearest university or college (community college or CEGEP). Very few individuals live beyond 80 kilometres of a community college in Canada. The measures of real community college and university tuition are averages across institutions within each province in the year that the youth would normally enter community college or univer-sity respectively. The university provided financial aid variable captures the impact of scholarships and bursaries on the demand for university education in certain provinces. Separate measures of scholarship (merit-based) and bursary (need-based) funding were unavailable. This variable is calculated as the annual total amount of financial aid (in 2000/01 dollars) provided directly by uni-versities in a province divided by the total number of full-time university students in that province and year. It thus measures the average expected amount of such financial aid for a youth attend-ing university. The unemployment rate refers to the provincial rate in the year the youth would normally enter community college. Data Sources The vast majority of variables employed in this analysis were constructed directly from the SLID internal use data sets made available via the British Columbia Inter-University Research Data Centre (BCIRDC) at the University of British Columbia. The sources employed during con-struction of variables not taken from the SLID are listed below. 1. Parental income measures were adjusted using Low Income Cutoff (LICO) measures by size of area of residence and family size taken from the Statistics Canada publication authored by Paquet (2002). 2. Distances to closest post-secondary institutions (universities and community colleges) were constructed using the latitude and longitude of the place of residence of each youth at age 16 taken from the SLID. The latitude and longitude of PSE institutions was constructed 158 using a database of the postal code of each institution in Canada compiled by Marc Frenette of Statistics Canada (see Frenette (2004) for details). Postal codes were transformed into latitude and longitude measures using the Postal Code Conversion File (PCCF) database from Statistics Canada. Straight line distances were constructed using the following formula: Distance = 6,370.997 * cos_1[sin(/at2 /) * sm(lati)+ cos(laty) * cos(lati) * cos(longy — longi)) (A.l) In this equation, the latitude (lot) and longitude (long) numbers were measured in radi-ans by dividing the original latitude and longitude measures in degrees and decimals by 57.29577951. The subscripts y and i refer to the locations of youths and PSE institutions respectively. 3. Annual average community college tuition by province were obtained from statistics re-ported by the Manitoba Council on Post-Secondary Education. These provincial averages were not weighted within each province, but tuition at publicly funded community colleges varied little within provinces. See the following website for the data. http://www.copse.mb.ca/en/documents/statistics/index.htm 4. Annual average university tuition by province was constructed from individual university tu-ition fees for undergraduate arts programs (within-province students) collected by Statistics Canada. Data from 1994/95 onwards were provided directly by Statistics Canada's Centre for Education Statistics. Prior to 1994/95, information was taken from the release entitled "Tuition and living accommodation costs for full-time students at Canadian degree granting institutions". Averages within each province were calculated using 1997/98 total full-time enrolment numbers as weights. University enrolment numbers were also sourced from Sta-tistics Canada, using Cansim cross-tabulation 580701. 5. Annual Provincial unemployment rates were taken from Statistics Canada's Cansim II table 282-0002. 6. Annual aggregate university-provided financial aid by university was provided by Statistics Canada's Centre for Education Statistics. These numbers were aggregated within provinces then divided by aggregate full-time enrolment at universities within each province. 159 7. Cohort size indices were constructed using Statistics Canada's annual estimates of popula-tion by age and province, obtained from the Cansim II table 51-0001. 8. Data on provincial spending on universities and community colleges wereobtained from the Cansim II tables 478-0007 and 478-0004 respectively. These aggregate numbers were divided by the provincial population aged 18 to 24 (see source above). 9. A l l variables that were constructed in real terms used the Canada-wide Consumer Price Index, sourced from Cansim II table 326-0001. 10. Neighbourhood characteristics were taken from the 1996 Canadian Census using the 20/20 package from Statistics Canada. These characteristics are for the census tract (where avail-able in cities), census subdivision (where available) or division if both tract and subdivision data are unavailable, where the youth resided at age 16. The 1991 geography enumeration area identifiers available in the SLID were transformed into 1996 Census geography enu-meration areas using an electronic file provided by Statistics Canada. The 1996 enumeration area identifiers were then linked to 1996 Census tract, division and subdivision identifiers us-ing information from the GeoSuite package from Statistics Canada. These tract, division and subdivision identifiers were then used to link characteristics of neighbourhoods to individual youth. Adjustment of parental income measures The method of adjustment of parental income chosen here deserves further consideration. Prior research in this area employed alternative procedures for adjusting family income. Some re-searchers did not adjust parental income at all, such as Corak, Lipps & Zhao (2004) and Knighton & Mirza (2002). Researchers have also normalized family income by dividing it by the square root of family size prior to analysis. This procedure was not followed here. I control for differences in family composition more flexibly in my analyses by including indicators of lone parents and measures of the number of children directly in estimation. In response to observed differences in costs of living by the size of the place of residence, researchers have constructed their indicators of parental income quantiles separately by size of area of residence. For example, quantiles are constructed first for families from rural areas, then for families from small urban areas, etcetera. This method may yield unexpected results if, for 160 example, the vast majority of families in rural areas are actually low income, but one third will be identified as high income and another third as middle income. The method of adjustment chosen here (income in excess of LICOs) will avoid such outcomes. The method of parental income adjustment I employ will not account for observed differences in living costs between large cities such as high cost Vancouver and lower cost Montreal. However, adjusting income by city of residence may again yield unexpected results. Cost differences may reflect an individual's desire of more people to live in Vancouver rather than in Montreal. High income individuals may use part of their higher income to live in the city of their choice, resulting in a correlation between living costs and income levels. Living in a large city may be required to obtain certain high income jobs, as certain workers may be more productive in cities, rationalizing the higher wages. Controlling for city versus rural differences in costs of living appears warranted. Controlling for differences between large cities is not justified if firms and individuals are free to make rational choices of where to locate.3 3There would be justification if workers are much more productive in Vancouver than Montreal based on locality alone. This seems unlikely. 161 Appendix C: Grade Transition Model Details The Likelihood Function and Estimation The likelihood function I estimate in Section 2.7 is described here. It is taken directly from Appendix B in Cameron and Heckman (2001). The notation set out in Section 2.7 is followed. Denote dajatC as the realized value of DajaiC. Abbreviate the initial condition to da,c- Note that the schooling status at age a (denoted ja) is equal to the choice made at age a — 1, which is denoted c 0 _i . Define a history H of education outcomes for an individual as follows. H = (-Da,c <^ a,o LJa+ltca,c ~ <^a+l,Ca,cj - D a , C a _ i , c = ^ a , C a - i , c ) (A.2) Conditioning on the observables Z and a particular value for the unobservable rji, the probabil-ity of observing the above history can be defined as follows. PT(H\Z,7H) = Y[[Pr{Da,c = da,c\Za,Vi)}da-": • J[ [Pr(L>a+l,ca,c = da+l,caJ Za+l, Vl)]d^-• • • f j [Pr(/J s,C s_ 1, c = 4 , C ; r _ 1 , c | ^ , ^ ) ] ^ - 1 ' c (A.3) At each age after the initial condition (a € {a + 1 , a } ) there is a separate probability product term for each schooling status c a _ i . The superscript variables (daiC, etcetera) are indicators that pick out the appropriate elements of the education history H for a particular observation. The probability of each education transition and the initial condition are modeled using the functional form in equation 2.13. The log-likelihood function L that is maximized during estimation is: L = In J3Pr(i)-Pr(£r|Z,^) ,i=l (A.4) Here probability Pr(i) > 0 is associated with mass point rji, and 2\Zi=i Pr(*) = 1 is imposed. Estimation revealed that two mass points (I = 2) were sufficient to characterize the data. This find-ing is consistent with other studies employing this random effects estimation technique. Estimation involved setting 771 = 0 and 772 = 1. I estimated the probability Pr(l), setting Pr(2) = 1 — Pr(l). The distribution of 77 was estimated recursively, identifying Pr(l) from estimation of the initial condition at age 16. To identify the variable coefficients (the /3's) and the factor loadings on the unobservable (the a's), one choice within each choice set must have its coefficient and factor loading values normal-ized in order to identify the remaining parameters. Denote the choice c* as the normalization. The 162 parameters /?a,ca-i,c* and factor loading a Q ] C o _i ] C * were then constrained to zero within each choice set. As a result of this normalization, the remaining estimated coefficients and factor loadings are defined relative to those for the normalization case. Estimation of the model parameters involved searching among a set of starting values for the probability and the factor loadings (the a's). This was necessary as the log likelihood function L is not guaranteed to be globally concave. Forming the Transitions and Estimation Details Here are some specific details about how I constructed the education transitions undertaken by youth, and more details on how transitions were modeled. A number of youth in the sample reported completion of eight years or less of school by age 16. These youth were re-classified as completing nine years with little loss to the model's ability to capture attendance outcomes while considerably savings in model parsimony. A larger number of youth reported completion of eleven years of school by age 16. These reports were generally at odds with other information in the SLID provided by the parents on the grade the youth was attending at age 15. This information was not reported for all youth during all years of the SLID so could not be used in estimation. These reports were also at odds with the normal education path of Canadian youth, who generally begin the first grade of school at age 6. It suggests that some youth may have considered the kindergarten year as a year of elementary school, leading to an overestimation of the number of years of school completed at age 16 by one. These youth were re-classified as completing ten years of school. A very small number of youth reported completion of twelve or thirteen years of school, or reported attendance at community college and university, at age 16. These youth were excluded from the analysis. A small number of youth also reported subsequent education transitions that did not accord with a normal education progression. For example, some youth reported completion of grade nine at age 16, and university attendance at age 17. Such unusual transitions were deemed reporting error, so those observations were also excluded from the analysis of Chapter 2. Reporting of high school graduation status in the SLID did not appear accurate. Graduation rates were much lower than in other Canadian surveys such as the Census. Not all youth are asked if they graduate high school each year in the SLID. They are only asked this question if they answered prior questions on high school attendance in a particular way. This may have resulted in this under-reporting of graduation status, particularly for youth who attend some type of post-163 secondary education directly after completing high school. High school graduation status was not used as a pre-requisite for university attendance during model estimation. High school graduation information was used in the model for youth who did not go on immediately to post-secondary education. For example, youth who reported attending grade twelve at age 18 but no receipt of a high school graduation certificate were modeled separately from those reporting such receipt. The third transitions of these two groups were quite different, with the latter much more likely to attend university for the first time at age 19. Given the different schooling structure in Quebec, grade transitions were modeled separately for youth from that province. The majority of youth in Quebec often choose to enter a CEGEP after completion of the 11th grade of school. They can then complete two years of CEGEP to gain the prerequisites for university entrance. Studies at a CEGEP are generally broken into two streams: the academic stream and the vocational stream. Those youth undertaking the former can gain the prerequisites for university entry. Those undertaking the latter gain vocational (for example a trade) skills but do not gain the university entrance requirements. The choice of stream is not reported in the SLID micro data. Youth in grade 11 in Ontario at age 17 are much less likely to go to university after only 12 years of school. The majority of universities in that province required a thirteenth year of study at school for gaining university entrance pre-requisites. To allow for this, this transition was modeled separately for Ontarian youth at this age and grade. Simulation Details The grade transition model parameter estimates were employed to construct treatment on the treated effects in response to parental income shocks. Construction of these effects involved sim-ulating the impact of the parental shock on the predicted probability of each annual education outcome for each youth in the sub-sample of those who suffered from the parental income shock. I simulate the model in a sequence of steps. First, I calculate a fitted probability of being in grade nine or grade ten at age 16 for each youth in the sub-sample, given their characteristics and the estimates from the initial condition equation. This calculated probability is compared with a random draw from a uniform distribution on [0, 1] to assign an appropriate initial grade status to each sub-sample member. Those youth assigned to grade ten status are then used to calculate a fitted probability of making each possible education transition (to dropout, grade 11 or to other 164 PSE) again employing their individual characteristics and using the parameter estimates from the appropriate multinomial logit equation for grade ten youth at age 16. Those fitted probabilities are compared to another random draw from U[0, 1] in order to assign an appropriate age 17 status for those individuals. The same procedure is used to simulate education transitions for youth assigned to grade nine status at age 16. The process continues for each education transition in a similar manner, where assigned edu-cation status at one age determines which transition probabilities are simulated at the next age for that individual. These simulations are conducted 200 times for each individual in the sub-sample. The average of the simulated probabilities across all individuals and across these 200 repetitions are then calculated, for each possible education status at each age. The simulations were all constructed twice. First, simulations were constructed setting the parental shock indicator to zero for all youth in the sub-sample. Simulations were then constructed again setting the parental shock indicator back to one. The difference in the simulated probabilities of each annual education outcome is the measure of the treatment on the treated effect. To construct standard errors on these simulated treatment on the treated effects, the same sim-ulation exercise was followed for five hundred random draws from the estimated distribution of the parameters. The inverse hessian was employed as the appropriate variance-covariance matrix of the estimated grade transition model parameters following Cameron and Heckman (2001). The parameter estimates were assumed to be normally distributed when taking these random draws. In particular, a Choleski decomposition was taken of the estimated variance-covariance matrix. This decomposition matrix was multiplied by a vector of independent draws from a standard normal distribution, then added to the vector of parameter estimates to form one random draw from the estimated distribution of parameters. 165 Appendix D: Financial Aid Eligibility Indicators Financial aid eligibility indicators were constructed using the financial aid eligibility rules em-ployed by each provincial student financial aid body and using each youth's individual circum-stances as reported in the SLID survey. Eligibility rules were originally developed by each province separately, but considerable effort was made in the middle of the 1990s to form consistent rules for all jurisdictions that were part of the federal government's Canadian Student Loan Program (CSLP).4 This group included all provinces except Quebec.5 Quebec has its own program and eligibility rules.6 Under the CSLP program, financial aid is primarily in the form of loans. British Columbia did offer the provincial portion of funding (40%) in the form of grants to first and sec-ond year undergraduate students, but this has recently been converted into loans also.7 Under the Quebec program, the first $2,000 to $3,000 is in the form of loans, with bursaries provided for need above those amounts. The student financial aid eligibility rules, although differing in details between the Quebec and CSLP systems, follow a similar structure. First the expenses of studying at university or community college are calculated, including tuition, books, living expenses and travel. Living expense allowances vary across provinces, and there is a considerably higher allowance given to youth who must live away from home while studying. Living away from home is defined as living beyond 25 kilometres of the PSE institution attended, plus living in an area without public transport. Youth with children of their own also have higher living expense allowances. The second step in determining eligibility involves calculation of each student's income sources. A minimum amount is assumed for income from summer employment. For most youth, a contribu-tion from each youth's parents is assumed.8 This contribution is calculated as a certain percentage 4Many thanks to Leesha Lin and Gerd Reicker of Human Resources Development Canada (HRDC), and to Dara-lynn of the British Columbia Student Aid Program (BCSAP) for provision of the historical eligibility parameters for this program. 5The Northwest Territories also have their own student financial aid program, but the SLID survey does not sample outside the 10 provinces of Canada. 6Many thanks to Maryse Bergevin of McGill University for providing historical tables of Quebec's financial aid rules. 7Several other provinces provided the provincial portion of funding in the form of grants prior to the mid-1990s also. 8 Youth who are married and/or have children of their own are considered independent of their own parents, and thus no parental contribution is attributable. 166 of parental income (verified using the previous year's tax return) above some amount allowed for the "moderate standard of living" of the family. This minimum depends on both the province of residence and the number of dependent children (usually those under 18 still living at home) in the family. The percentage of parental income used in calculating the parental contribution rises as in-come rises. Once expenses and income have been calculated, any excess of expenses over income is the amount of financial aid (loans and possibly grants) that each youth is eligible to receive. Financial aid eligibility indicators were constructed to denote youth eligible for aid covering at least half of the calculated expenses of studying. Separate indicators were calculated for study at university and community college levels. A slightly larger percentage of youth are eligible for aid covering at least half of university expenses as those expenses were larger on average. University tuition is higher in all provinces, and more youth must move away from home (at greater expense) to attend university than to attend college. Financial aid eligibility is strongly related to average parental income, as expected. Around 88% of low income youth, 45% of middle income youth and only 5% of high income youth are eligible for student financial aid that would cover at least half of their expenses if they attend university. Youth from high income backgrounds may be eligible if parental income in the year preceding normal university entrance was unusually low, but average income remained high. Also, if youth from high income families have children of their own or are married then their parental income is not relevant in the determination of financial aid eligibility. Several alternative measures of financial aid eligibility were included (along with all the other co-variates listed in Table 3.3) in preliminary estimates of PSE attendance decisions. These in-cluded the financial aid eligibility indicators discussed above, indicators denoting eligibility cov-ering at least tuition costs, and measures of the real dollar value of financial aid eligibility. In all cases, the estimated relationship between financial aid eligibility and PSE attendance was negative, and for the real dollar value measure, statistically significant. Those eligible for financial aid were less likely to attend PSE than those who did not. This does not suggest a causal relationship from eligibility to lower attendance. Rather, financial aid is only available to youth who historically are least likely to attend: those from low income families with many siblings and living far from PSE institutions. Inclusion of these eligibility indicators lowered slightly the impact of these other variables included in the analysis which determine eligibility. Financial aid eligibility indicators were not included in final versions of the estimates due to this direct relationship. 167 Appendix E: School Achievement Production Function School achievement can be represented as a function of several inputs, including family inputs, own ability, peer effects and school inputs (teachers, other resources, curricula, discipline levels, etc).9 School achievement is a cumulative process, with past inputs affecting achievement as well as current inputs. Current inputs will determine any gains (or losses) in achievement from prior levels. The cumulative nature of school achievement can be seen clearly in the following regression analog of some true EPF for the achievement AiGs of student i in grade G of school s. AGs = XiGsa>G + P(-i)GsPG + A(_i)CslG G - l G - l G - l + ^ 2 Xigsag + ^ 2 P(-i)gsPg + */2 A{-i)9^9 + Vi^G + £iGs (A.5) 9=1 9=1 9=1 The matrix X denotes all family, school and neighbourhood inputs in the EPF. Peer group measures are separated into exogenous (contextual) variables in P(-i)Gs a n d the endogenous or behavioural variable in A^Qs- The term fiis denotes endowed ability. The endogenous peer group measure here is the actual contemporaneous average achievement level of other students in the class (A^Gs)- If students are doing better in class, it may lift the achievement of all other students in the class, over and above the measurable exogenous characteristics of those students. If historical input measures are not included in the estimated equation, their impact will be subsumed into the error term. In this case, the identification of peer effects is difficult. Many of the missing historic variables (especially school input variables) will be common to peers and to current included input measures, yielding significant omitted variable bias. The error will be corre-lated to our peer measure, potentially biasing up the estimated impact of peers on own achievement. Manski (1983) denoted these potential biases as correlation effects. Taking first differences of equation A.5 yields a value added model of achievement. AAiGs = XiGsaG + NiGspG + SGsjG + P{_i)Gs5G + A^csVc + CiGs (A.6) This achievement growth specification is not the only one employed in the literature. Often past achievement A^G_^S is included as a regressor without imposing a coefficient of one on it. ''Note that individual motivation does not enter the EPF in the standard version of the model in the literature. 168 Researchers support such a specification by claiming that past achievement is a sufficient statis-tic for all past inputs and for individual ability. Todd and Wolpin (2003) discuss the identifying restrictions inherent in these value-added models. In our study, we are not directly estimating an EPF for achievement, such as equation A.5. However, certain estimation problems highlighted by Todd and Wolpin are common to our study estimating an equation such as 4.2. School principals can influence the school inputs in this production function, but further, they may be able to alter the function itself. They may be able to bring in a better technology for the production of individual school outcomes given the inputs at hand. 169 Appendix F: School Principal Duties and Responsibilities The following school principal powers and duties were taken from the British Columbia Reg-ulation concerning School Regulation (BC Reg. 265/89, amended by BC Reg. 1114/04), made under the authority of the B.C. School Act. (6) The principal or, if so authorized by the principal, the vice principal of a school shall, (a) perform the supervisory, management and other duties required or assigned by the board, (b) confer with the board on matters of educational policy and, where appropriate, attend board meetings for that purpose, (c) evaluate teachers under his or her supervision and report to the board as to his or her evalu-ation, (d) assist in making the Act and this regulation effective and in carrying out a system of edu-cation in conformity with the orders of the minister, (e) advise and assist the superintendent of schools in exercising his or her powers under the Act, (f) recommend to the superintendent of schools the assignment or reassignment of teachers to positions on the teaching staff of the school board, [SCHOOL REGULATION BC Ministry of Education Governance and Legislation Unit D-64 September 15, 2004] (g) recommend to the superintendent of schools the dismissal or discipline of a teacher, (h) perform teaching duties assigned by the board, (h.l) administer and grade, as required by the minister, Required Graduation Program Ex-aminations, (h.2) ensure the security of Provincial examinations, including retaining completed Provin-cial examinations for any period of time set by the minister, and (i) represent the board when meeting with the public in the capacity of principal or vice princi-pal of a school. (7) The principal of a school is responsible for administering and supervising the school including (a) the implementation of educational programs, (b) the placing and programming of students in the school, 170 (c) the timetables of teachers, (d) the program of teaching and learning activities, (e) the program of student evaluation and assessment and reporting to parents, (f) the maintenance of school records, and (g) the general conduct of students, both on school premises and during activities that are off school premises and that are organized or sponsored by the school, and shall, in accordance with the policies of the board, exercise paramount authority within the school in matters concerning the discipline of students. (8) Principals shall ensure that parents or guardians are regularly provided with reports in respect of the student's school progress in intellectual development, human and social development and career development and the student's attendance and punctuality. These regulations also include duties related to providing reports on teachers, the details of student reports, and holding of school assemblies. 171 Appendix G: School Principal Turnover Term Construction Here is a simple example of the construction of the principal turnover term in equation 4.8. E 1 n n c=l = E - E(C + 0S2 - 28CS9S) c=l (A.7) In this example, there are two principals in our school (with principal effects 9j and 9k), and each is leading the school for three years, giving a total number of years of six (n = 6). To begin, take the expectation of one term (cohort or year) within the school average, where the principal in charge is principal j (thus 9CS = 9j). E[9] + d8 - 29j9s] = E [9]] + E :(9j + 9j + 9J + 9k + 9k + 9k) 8) - 2 E 6j Q(0,- + 9j + 9j + 9k + 8k + 9k)^j (A. Using our definition of E[92} = ajs and our assumption that E[9j9k] = 0, this equation can be written as follows. E\9) + 8S2 - 20,6.] = al + i (32 + 32) < - 2 \ (3) < 6 1 rr* (A.9) In the turnover term for this particular school, we have six equivalent terms to that above in the school average. So, our turnover term here is also simply one half. Now, we can follow the same method to show how we develop the turnover term for the general case. Again let us look at one element of the school average term, where principal j is again in charge. There are a total of J principals in the school over the sample period, each in charge for qk years, where k = 1 , J , and Yit=i Qk = n - m t r n s general case, principal j is in charge for qj years. 1 E\9] + 9S - 2939s\ = E [8j] + — E 2 - E n 9j ^ 9 C c=l i 1 \— v 2 2 1 + — qk Qj (A. 10) fc=i 172 Averaging this term over the n years that school s is in our sample yields equation 4.8, our turnover term for the general case. This average in equation 4.8 uses the fact that for each principal j, there are qj equivalent terms to equation A. 10 in the school average. 173 Appendix H: Grade 11 Achievement Measure As discussed in the paper, we have data for each individual on grades from a series of grade 11 exams, and we need a way to aggregate the grade data in a way that makes use of the varied individual data. To do this, we make use of the grade 12 Grade Point Average (GPA), which is calculated in a standard way across the province. We have the grade 12 GPA only for individuals who graduated from grade 12 since the province only calculates it for that group. We regress the grade 12 GPA on a large set of dummy variables corresponding to five grade ranges for each of the five types of grade 11 exams upon which we have data. The regression is specified in such a way that we can construct a predicted GPA whether the individual has information on only one exam or on up to five. The exercise is complicated by the fact that the grade 12 GPA is only observed for individuals who graduated from grade 12 and because the GPA has a maximum value of 4. Thus, we estimate a doubly censored (at zero, for those individuals for whom we do not have a GPA value, and four) Tobit model relating GPA to grade 11 grades. Using the estimated coefficients from this regression we construct a fitted GPA score for every individual in our data-set based on their grade 11 grades. The second stage of our construction addresses potential grade inflation in some schools rel-ative to others. To address this, we use data on school specific average marks on province wide exams administered to evaluate relative school performance. Since these exams are the same across all schools, they provide a standard, independent of school specific grade inflation. To estimate the extent of school grade inflation we regress the average fitted GPA score for the school (constructed as just described) on the school's province-wide exam grade average. The residual from this re-gression, which we will call RESIDM, represents the extent to which a given school tends to give high or low grades relative to the average across schools. We next reestimate the censored Tobit GPA regression including the same exam mark dummy variables as before plus the RESIDM value corresponding to the individual's high school. We then create a new fitted GPA score based on the coefficients from this newest Tobit estimation and the individual's grade 11 exam results, with the RESIDM variable set to zero. This provides an average grade for each individual, GRADES11, which is purged of relative grade inflation across schools. 174 

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