The Canadian Journal of Higher Education La revue canadienne d'enseignement supérieur Volume XXXI, No. 1, 2001 pages 177-208 Family Income and Postsecondary Education In Canada LOUIS N. CHRISTOFIDESt, JIM CIRELLO*, & MICHAEL HOY* * tUniversity of Guelph, ÎBell Canada ABSTRACT We use data from the Surveys of Consumer Finance (1975-1993) to examine h o w postsecondary education participation rates have evolved over time and h o w certain variables may affect them. A number of socioe c o n o m i c i n f l u e n c e s are s h o w n to affect participation rates. B e y o n d these, particularly pronounced trend increases in postsecondary education attendance for children from low-income households have led to a conv e r g e n c e in the participation rates of children f r o m d i f f e r e n t i n c o m e groups and a consequent reduction in the regressivity associated with subsidies for postsecondary education. We consider possible reasons for this convergence. Conditioning on a number of other variables, w e are particularly interested in the possibility that increases in f a m i l y real income may have affected the demand for postsecondary education by * Drs. Christofides and Hoy are indebted to the SSHRC for financial support. Much of the work for this paper was done while L.N. Christofides was visiting the University of Cyprus and M. Hoy was visiting G.R.E.Q.A.M., Université d'Aix Marseille and CNRS; they thank them for their hospitality and financial support. The authors are indebted to M. Dooley, R. Finnie, B. Wandschneider and participants at the Canadian Economic Association Meetings at Brock University and at the faculty seminar at the Department of Economics, the University of Cyprus, for helpful discussions and suggestions. Constructive comments were also received from two anonymous referees. The views expressed in this paper are those of the authors and do not necessarily represent those of their institutions. 178 L.N. Christofides, J. Cirello, & M. Hoy children f r o m low-income families more than the demand by children from high-income households. We find that, although income does have a statistically significant non-linear influence which can explain much of the cross-sectional difference in attendance at postsecondary institutions, its quantitative effects are not sufficiently strong to account for the convergence over time in participation by children f r o m different family income groups. RÉSUMÉ Avec les informations fournies par les Sondages des finances des consommateurs (1975-1993), on y examine de quelle façon les taux de f r é q u e n t a t i o n o n t é v o l u é au fil des a n n é e s d a n s les é t a b l i s s e m e n t s d ' e n s e i g n e m e n t postsecondaire et de quelle façon certaines variables pourraient les affecter. Il est démontré que plusieurs influences socioéconomiques ont a f f e c t é les taux de f r é q u e n t a t i o n dans les établissements d ' e n s e i g n e m e n t postsecondaire. En plus, une tendance m a r q u é e à l ' a u g m e n t a t i o n de l ' i n s c r i p t i o n des e n f a n t s de f a m i l l e s à faible revenu a m e n é à une convergence dans les taux de fréquentation des enfants provenant de divers milieux économiques et ainsi une baisse d e la r é g r e s s i o n associée aux subventions pour l'éducation p o s t s e c o n d a i r e . O n y c o n s i d è r e les r a i s o n s p o s s i b l e s p o u r c e t t e convergence. Prenant en considération plusieurs variables, on s'intéresse particulièrement à la possibilité que les augmentations réelles dans les r e v e n u s f a m i l i a u x a u r a i e n t p u a f f e c t e r la d e m a n d e d ' é d u c a t i o n postsecondaire p o u r les enfants de familles à faible revenu davantage que pour ceux de familles à revenu élevé. On démontre que, m ê m e si le niveau de revenu exerce une influence non-linéaire statistiquement significative qui peut expliquer en grande partie la différence dans la f r é q u e n t a t i o n des é t a b l i s s e m e n t s d ' e n s e i g n e m e n t postsecondaire, les effets quantitatifs ne sont pas suffisamment importants pour expliquer la c o n v e r g e n c e , au fil des a n n é e s , des t a u x de f r é q u e n t a t i o n d a n s les é t a b l i s s e m e n t s d ' e n s e i g n e m e n t p o s t s e c o n d a i r e des e n f a n t s de divers milieux économiques. The Canadian Journal of Higher Education Volume XXXI, No. 1, 2001 Family Income and Postsecondary Education in Canada 179 INTRODUCTION Accessibility to postsecondary education is an important social issue on both efficiency and equity grounds. The existence of social and/or economic barriers which impede children f r o m lower income families f r o m obtaining a postsecondary education limits their potential p r o d u c t i v i t y and e a r n i n g s capabilities, h e n c e limiting g r o w t h in the economy, and also raises concerns about equality of opportunity and social mobility. Since p o s t s e c o n d a r y education is heavily subsidized f r o m tax revenues, higher attendance rates from higher income families will h a v e the effect of diminishing the degree of progressivity in the income tax system and possibly even making postsecondary education financing regressive. Highly educated individuals, w h o are disproportionately represented f r o m high income families, receive larger amounts of subsidized education than those who do not directly partake in its benefits but w h o also contribute to the funding of education. The result is that these government subsidies disproportionately favour high-income families and their children, who also tend to end up receiving increased future earnings generated by their postsecondary education (see Bar-Or, Burbidge, Magee, & Robb, 1995; Vaillancourt, 1995). One purpose of our paper is to examine any trends in the participation rates in postsecondary education for children from families with diff e r e n t i n c o m e l e v e l s in o r d e r to d e t e r m i n e w h e t h e r , f r o m a p u b l i c finance perspective, these subsidies are becoming relatively more or less regressive. Our analysis also sheds some light on the issue of the extent to which postsecondary education in Canada has the potential to increase social mobility and reduce inequality. In particular, we examine the possibly changing role of family income as a factor in these relationships. Since private returns to postsecondary education are substantial, social mobility will be enhanced if participation rates in postsecondary education are increasing more rapidly for children from lower income families. T h e r e l a t i o n s h i p b e t w e e n c u r r e n t e d u c a t i o n levels and f u t u r e earnings in the distribution of income is complex and so our analysis indicates only the potential role of changes in the relationship between f a m i l y i n c o m e and p o s t s e c o n d a r y e d u c a t i o n a t t e n d a n c e in r e d u c i n g The Canadian Journal of Higher Education Volume XXXI, No. 1, 2001 180 L.N. Christofides, J. Cirello, & M. Hoy inequality and enhancing social mobility. However, there is abundant evidence that there is a strong link between the level of education and a person's income. Thus, if the participation rates in postsecondary education for children f r o m lower income families increases relative to that of children f r o m higher income families, then one can expect, with a high degree of confidence, that w e will observe greater social mobility and less inequality of incomes than would otherwise be the case. 1 To address all of these issues it is important to separate the effects of various economic and non-economic factors which influence whether an individual attends a postsecondary educational institution, and this is what we do here. Studies for developed and underdeveloped countries generally show that children f r o m higher income families are more likely to obtain a postsecondary education. 2 M e h m e t (1978), w h o looks at this question using Ontario data for 1974, finds that even though lower income families contribute less towards the funding of postsecondary education due to lower income tax payments, the use of postsecondary education by children of high income families is sufficiently intense that the overall system is regressive. 3 Besides differing enrolment rates, he shows that a m o n g children w h o do attend postsecondary educational institutions, those f r o m higher income families are more likely to take more costly and higher return p r o g r a m s such as medicine, dentistry and law. T h e view that subsidized postsecondary education is regressive continues to receive w i d e s p r e a d acceptance. In a recent article in his university's m a g a z i n e , J a m e s D o w n e y ( 1 9 9 6 ) , P r e s i d e n t of the U n i v e r s i t y of Waterloo remarks that: D e s p i t e . . . h i g h p a r t i c i p a t i o n rates, w e h a v e s u c c e e d e d in a t t r a c t i n g too f e w w o m e n and m e n f r o m the l o w e r socioeconomic classes; university education is still largely a middleand upper-class preserve, subsidized by everyone, even those w h o do not participate. Thus, both the general economic and social-equity arguments for the very high level of public investment in universities and colleges have been losing force, (p. 13) In this paper w e use Canadian data over the period 1975 to 1993 to investigate whether the force of the D o w n e y criticism may have changed over time. We discover that, although attendance rates for postsecondary The Canadian Journal ofHigher Education Volume XXXI, No. 1, 2001 Family Income and Postsecondary Education in Canada 181 education continue to be higher for children from higher income families than f r o m lower income families, there has been a strong degree of convergence. F r o m 1975 to 1993 the overall percentage of children in the 18 to 24 year-old cohort attending postsecondary education rose f r o m 33% to 54%, with a substantially larger increase (18% to 4 4 % ) in the particip a t i o n rates of children f r o m f a m i l i e s in the p o o r e s t quintile of the income distribution relative to those from the highest quintile (53% to 71%). A l t h o u g h the participation rate in the highest quintiles has an upper ceiling, which may actually be lower than unity, 4 there is no necessary reason for the rate in the lower income quintiles to increase over time. In this paper w e explore possible reasons w h y this convergence m a y have occurred. One force which m a y account for this convergence is the growth of real incomes through time. Though quintile family income shares have r e m a i n e d relatively stable o v e r the period 1 9 7 5 - 1 9 9 3 , 5 average real incomes within each quintile have risen substantially. If the marginal e f f e c t on p o s t s e c o n d a r y s c h o o l a t t e n d a n c e of an i n c r e a s e in f a m i l y income is greater for lower income families, then a plausible explanation for the convergence in participation rates between high and low-income families is that generally rising real incomes may have led to a greater increase in attendance for relatively low-income families than for highincome families. We investigate this possibility by considering whether participation rates depend in a non-linear m a n n e r on absolute income levels. In a s s e s s i n g the role of i n c o m e , it is n e c e s s a r y to take into account the possible role of other influences such as parental educational attainment and the broad costs of and returns to postsecondary education on participation rates. Without these forces clearly accounted for, the role of real income cannot be reliably established. (That is, regression equations w h i c h omit relevant explanatory variables will measure the role of included variables, such as income, inappropriately.) We conclude that income is an independent and statistically significant determinant of postsecondary education attendance, but not a plausible cause of the observed c o n v e r g e n c e in relative participation rates. We identify trend increases in postsecondary education attendance which are above and beyond the influence of the explanatory variables that we have been The Canadian Journal ofHigher Education Volume XXXI, No. 1, 2001 182 L.N. Christofides, J. Cirello, & M. Hoy able to consider. W h i l e these f o r c e s are controlled for t h r o u g h t i m e effects, further research is needed in order to better appreciate the mechanisms that shape postsecondary education attendance in Canada. In the next section, w e p r e s e n t trends demonstrating the relative increase in accessibility of postsecondary education for children f r o m low i n c o m e families and the c o n c o m i t a n t reduction in the degree of regressivity in the system. In the third section, we discuss the data and sources u s e d in this study while, in the fourth section, w e present an econometric analysis of the role of income and other determinants of p o s t s e c o n d a r y attendance. We present concluding observations in the final section. REGRESSIVITY OF GOVERNMENT SUBSIDIES TO POSTSECONDARY EDUCATION In Table 1 w e present, for each income quintile and for selected years, the proportion of children f r o m the age group 18 to 24 years old who attend postsecondary education — we call this variable PROP. 6 A general increase in the proportion of children attending postsecondary education is evident over this period for all i n c o m e groups (see also Table 5). Dividing the proportion for the top quintile by the proportion in the bottom quintile for the same year, we see in Table 2 that in 1975 a child f r o m a family in the top quintile of the income distribution was 2.94 times more likely to be enrolled in a postsecondary education prog r a m t h a n a child f r o m a f a m i l y in the b o t t o m quintile. This f i g u r e shrank to 1.61 by 1993. From this relative perspective at least, there has been a reduction in the extent to which government funding for postsecondary education is regressive. A similar trend exists, in Table 3, for the number of children attending postsecondary programs — w e call this variable C A S for Children at School. W h y has this convergence occurred? One plausible explanation is that, u n d e r i m p e r f e c t capital markets, rising absolute incomes have a greater impact on postsecondary education attendance for the poor than for the rich. 7 We consider the possibility that rising incomes are more important for lower income families by dividing the sample into income The Canadian Journal of Higher Education Volume XXXI, No. 1, 2001 Family Income and Postsecondary Education in Canada 183 Table 1 Proportion of Children (PROP) in Postsecondary Education by Quintile Family Income Quintiles Year First Second Third Fourth Fifth 1975 0.18 0.26 0.33 0.46 0.53 1977 0.25 0.31 0.36 0.41 0.52 1981 0.26 0.34 0.38 0.43 0.54 1985 0.32 0.37 0.40 0.45 0.57 1989 0.35 0.41 0.45 0.53 0.62 1993 0.44 0.49 0.55 0.59 0.71 Source: Survey of Consumer Finance, various years. A number such as 0.18 for the first quintile in 1975 indicates that in the actual families of that quintile, the variable PROP (i.e., the proportion of children attending postseconary education) is on average equal to 0.18. See the next section for variable definitions. Table 2 The Relative Likelihood of Postsecondary Education Year Fifth Quintile Relative to First Quintile 1975 2.94 1977 2.08 1981 2.08 1985 1.78 1989 1.77 1993 1.61 Source: Survey of Consumer Finance, various years and Table 1. The Canadian Journal of Higher Education Volume XXXI, No. 1, 2001 184 L.N. Christofides, J. Cirello, & M. Hoy Table 3 Absolute Number of Children (CAS) in Postsecondary Education by Quintile Family Income Quintiles Year First Second Third Fourth Fifth 1975 0.25 0.34 0.45 0.58 0.70 1977 0.34 0.44 0.48 0.55 1981 0.34 0.44 0.52 0.61 0.70 0.74 1985 0.40 0.46 0.53 0.58 0.75 1989 0.43 0.52 0.56 0.69 0.80 1993 0.53 0.63 0.71 0.79 0.91 Source: Survey of Consumer Finance, various years. A number such as 0.25 for the first quintile in 1975 indicates that in the actual families of that quintile, the variable CAS(i.e., the absolute number of children in postseconary education) is on average equal to 0.25. See the next section for variable definitions. Table 4 Proportion of Children (PROP) in Postsecondary Education by Income Group (1986 constant dollars) Income Range ($) 1975 0-5,000 5,001-10,000 10,001-20,000 20,001-30,000 30,001-40,000 40,001-50,000 50,001-60,000 60,001-70,000 70,001-80,000 80,001-90,000 90,001-100,000 100,000+ 0.14 0.19 0.22 0.31 0.44 0.48 0.54 0.51 0.64 0.59 0.65 0.77 1977 Year 1981 1985 1989 1993 0.28 0.20 0.27 0.32 0.36 0.41 0.45 0.55 0.53 0.65 0.60 0.65 0.26 0.20 0.29 0.35 0.40 0.43 0.46 0.49 0.58 0.63 0.73 0.60 0.40 0.25 0.36 0.39 0.39 0.48 0.49 0.57 0.63 0.55 0.75 0.60 0.38 0.28 0.39 0.40 0.43 0.55 0.53 0.62 0.55 0.69 0.72 0.77 0.33 0.47 0.46 0.49 0.54 0.58 0.61 0.73 0.75 0.72 0.75 0.59 Source: Survey of Consumer Finance, various years and Table 1. The Canadian Journal ofHigher Education Volume XXXI, No. 1, 2001 Family Income and Postsecondary Education in Canada 185 categories based on absolute (1986 dollars) income levels, rather than the relative values in the quintiles. Using the variable P R O P examined in Tables 1 and 2, Table 4 shows that, regardless of year, the participation rates for the children of low-income families are much lower than those f o r the c h i l d r e n of h i g h - i n c o m e families. Within each S C F year, as i n c o m e rises, participation rates increase, albeit at a diminishing rate. Taken together, these e f f e c t s could m e a n that the l o w e s t quintile in Table 1, which contains higher absolute real income levels in 1993 than in 1975, could also entail an increase in the proportion of children in postsecondary education due to rising income which is much larger than that experienced in the highest quintile. If so, that might explain the convergence noted in Table 2. While this is a plausible argument, and one that has not been investigated in the education literature in Canada, Table 4 also indicates that this force may not be the only one at play. Long-term i n c r e a s e s in p a r t i c i p a t i o n rates are e v i d e n t even w h i l e h o l d i n g real income constant. Indeed, these increases are particularly clear for low income brackets. For instance, between 1975 and 1993 the participation rate increases from 0.22 to 0.46 in the $10,000-$20,000 income category while the increase in the $70,000-$80,000 income category is from 0.64 to 0.75. It would appear, therefore, that while the convergence noted in Tables 1 to 3 is consistent with the notion of imperfect capital markets and income-related effects, it m a y not be solely due to these forces. In the next two sections, w e investigate more fully the relationship between family income and postsecondary education attendance while, at the same time, controlling for a number of other variables that might be expected to influence postsecondary education decisions. DATA SOURCES AND VARIABLE DEFINITIONS T h e data for this study are d r a w n f r o m the available Surveys of Consumer Finance (SCF). These include the SCFs for 1975, 1977, 1979, 1981, 1982, and 1984 to 1993. Although a survey is available for 1983, it is not used because information on a critical variable, the number of children attending school, is presented in a manner which is not consistent with the fourteen other SCF surveys. 8 Each SCF tape was used to The Canadian Journal ofHigher Education Volume XXXI, No. 1, 2001 186 L.N. Christofides, J. Cirello, & M. Hoy construct the sub-sample of particular interest, namely that of families with children aged between 18 and 24. 9 (The SCF defines an economic family as a group of individuals living together and related by blood, marriage or adoption.) Since w e are interested in the forces that determine attendance at postsecondary institutions, we focus on the number of children attending school on a full-time or part-time basis. The variable Children at School (CAS), is the subject of study of a Poisson count data model. This model is suitable for the study of count variables such as the number of children at school (CAS). (Note that C A S is the vari- able u s e d in Table 3.) T h e p r o p e n s i t y f o r p o s t s e c o n d a r y e d u c a t i o n involves the variable C A S in relation to the total n u m b e r of children (Children) in the relevant age group (18 to 24) in the economic family. In exploratory Ordinary Least Squares (OLS) regressions, we study the variable P R O P that is the n u m b e r of children at school relative to the total number o f c h i l d r e n o f t h e r e l e v a n t a g e in t h e family (CAS/Children). This is the variable used in Tables 1, 2 and 4. In addition, w e report a Probit equation which focuses on the probability that a given family unit will h a v e at least one child at school. In this latter specification, the dependent variable (I) takes the value of 1 if a family has at least one child in postsecondary education and is equal to 0 otherwise. All three specifications take into account the influence of the number of children in the family on the dependent variable — i.e., on the variables PROP, C A S and the Probit index. The three approaches (OLS, Poisson regression and Probit) have different strengths and deal with slightly different aspects of the problem at hand. They are complementary and together they serve to produce some confidence about the statistical s i g n i f i c a n c e of the v a r i a b l e s u s e d to a c c o u n t f o r the o b s e r v e d patterns of postsecondary education. The statistical appropriateness and properties of these models are considered further in the next section. As noted in the second section, household income is likely to be an important force in decisions relating to postsecondary education and is, therefore, included as an explanatory variable in all three specifications. The variable Income is the sum of the head's and spouse's income and it, along with its square, are entered in our equations in real terms. A s a The Canadian Journal ofHigher Education Volume XXXI, No. 1, 2001 Family Income and Postsecondary Education in Canada 187 deflator, we use the All Items Consumer Price Index (CPI) for the major cities of Canada's provinces as reported in appendix Table A.l. 1 0 Further explanatory variables include the educational attainment of the h e a d of h o u s e h o l d . ( T h e e d u c a t i o n a t t a i n m e n t of the s p o u s e is highly co-linear with that of the head.) It is likely that heads with more education will encourage their children to also obtain more education. The following d u m m y variables are used: Grad equals 1 when the head has completed high school and has no further education; it equals 0 otherwise. S o m e postsecondary equals 1 when the head has some postseco n d a r y e d u c a t i o n but n o c e r t i f i c a t e , d i p l o m a or d e g r e e ; it e q u a l s 0 otherwise. Postsecondary equals 1 w h e n a certificate or d i p l o m a has been achieved and equals 0 otherwise. Finally, Degree equals 1 when a university degree has been achieved and equals 0 otherwise. The omitted c a t e g o r y is that of i n c o m p l e t e high school and the e f f e c t of the h e a d ' s education in the estimated equations is measured relative to this baseline case. The proximity to a postsecondary institution is an important element in the overall cost of obtaining further education. 11 Therefore, we include as an explanatory variable the d u m m y variable Urban which equals 1 when the family resides in an urban area and equals 0 otherwise. A further element in the cost of postsecondary education are real tuition fees. It is well-known that tuition fees in Canada are lower than those in elite institutions in the U.S. and that substantial increases in the Canadian fees did not occur until the latter part of the 1990s. However, this is not an a r g u m e n t for ignoring the relevance of tuition fees on postsecondary attendance in the period under study here. Doing so would, in general, bias the coefficient estimates of the included variables and would deprive us of any basis for estimating the possible reduction of attendance in postsecondary education following the recent, substantial, increases in tuition fees. 12 We construct the real tuition fee variable using nominal tuition fees in Arts programs at each province's largest university and deflating b y the CPI in each province's largest city — see A p p e n d i x Table A. 1. Tuition fees in Arts programs are very similar to the fees for programs in commerce, education, agriculture, science and music at these institutions. The square of this variable was also considered, but was not The Canadian Journal of Higher Education Volume XXXI, No. 1, 2001 188 L.N. Christofides, J. Cirello, & M. Hoy helpful and was, therefore, not included in the equations that follow. In view of the policy significance of this variable and possible future work in this area, we report real tuition fees in the Appendix Table A.2 and nominal tuition fees in Appendix Table A.3. 13 It is generally the case that real tuition has increased over time in each and every province and it is one of our purposes to see whether and to what extent these increases have discouraged attendance. This is an important consideration given that one of the main aims of the paper is to assess changes in the degree of regressivity associated with government subsidies for postsecondary education. Tuition increases shift the balance from government funding to private funding. The potential returns to postsecondary education may depend on the state o f l o c a l l a b o u r m a r k e t s . W i t h that in m i n d , b u t a l s o b e c a u s e regional differences in further costs of and tastes for postsecondary educ a t i o n m a y exist, w e also c o n d i t i o n on p r o v i n c i a l d u m m y variables which equal 1 if a family resides in a particular province and are equal to 0 otherwise. (Provincial effects are m e a s u r e d relative to B.C. — the omitted category.) The costs and returns to education are likely to vary over time as well as space. The full description of the returns to education and, in turn, the i n f l u e n c e of these on p o s t s e c o n d a r y education attendance are serious issues that cannot be addressed in their full complexity in this study. Indeed, they raise endogeneity issues (that is, the returns to education may depend on the number of individuals with postsecondary education qualifications) w h o s e resolution would considerably complicate the statistical requirements of our present effort. Yet, the problem of time-varying factors which affect the decision to attend postsecondary education cannot be ignored as doing so would bias the estimators for the variables that w e are able to include in this study. To deal with these issues in a relatively straightforward manner, w e introduce time effects in the pooled sample we study. 14 These year d u m m y variables m o p up the effect of any omitted variables with a time dimension and help define the role of our other variables more clearly. At the same time, they do not suffer f r o m possible simultaneity. Given that we condition on a variety of other variables, including income, it is likely that any The Canadian Journal ofHigher Education Volume XXXI, No. 1, 2001 Family Income and Postsecondary Education in Canada 189 remaining pattern of estimated time effects will reflect long-term trends in the expected net returns to education. Table 5 presents some sample statistics for each S C F year. Columns 1 and 2 report the size of the total and selected samples in each SCF. A s can be seen, the smallest and largest selected samples consist of 3,491 a n d 5 , 5 5 0 o b s e r v a t i o n s in t h e 1 9 7 5 a n d 1982 S C F s r e s p e c t i v e l y . Columns 4, 5 and 6 r e p o r t the m e a n v a l u e s of the v a r i a b l e s C A S , Children and PROP. The mean values of C A S and P R O P increase over time, while that of Children decreases. Column 3 shows the growth in real income that has occurred over time. It is reasonable to suppose that, as real income rises, liquidity constraints and capital market imperfections w e a k e n and the d e m a n d for postsecondary education increases. O n e i m p o r t a n t issue that w e w i s h to address is w h e t h e r the evident increase in postsecondary education is a reflection of a positive income effect, or whether there is a long-term increase over and above the real i n c o m e effect. The latter situation might arise because of an increase through time in the net returns to education, changes in demographic fundamentals and/or taste changes. These forces should be captured b y the time effects included in the pooled sample or by the constant terms in the equations for the separate SCFs. By incorporating squared income as an explanatory variable w e can also determine whether at least part of the convergence in postsecondary attendance rates between relatively high and relatively low income families is due to the generally rising absolute incomes across quintiles. ECONOMETRIC ANALYSIS We begin with an exploratory O L S regression of P R O P (proportion of children within a family out of the relevant age group w h o attend s o m e p o s t s e c o n d a r y educational p r o g r a m ) on I n c o m e , the Square of I n c o m e , t i m e e f f e c t s , and the other e x p l a n a t o r y variables d i s c u s s e d above. This econometric specification does not lend itself to standard hypothesis tests because of the obvious non-normality of the error term a n d P R O P . N e v e r t h e l e s s , the e s t i m a t e d e f f e c t s are s u g g e s t i v e . T h e results, which are not reported in detail here, indicate expected patterns The Canadian Journal of Higher Education Volume XXXI, No. 1, 2001 g is" £ Table 5 & a so o Basic Descriptive Statistics I s t-1 £ Number of Observations Mean Values s Year Total Sub-sample Real Income CAS Children PROP 1975 1977 26,569 39,782 3,491 0.4652 1.3191 1.3673 0.3529 1979 1981 1982 37,440 4,700 5,180 34,891.14 36,592.22 36,314.27 37,866 37,765 5,396 5,550 0.4649 0.5307 0.5503 1.3518 1.3638 0.3391 0.3889 0.4048 Se 1984 36,413 36,389 32,822 5,013 4,768 4,103 0.4063 0.4233 0.4389 o 43,710 38,027 41,406 45,580 42,804 5,428 4,478 4,775 5,231 & tJO o •Sg ST O' a 1985 1986 1987 1988 1989 1990 1991 1992 1993 40,007 39,489 4,801 4,319 4,395 37,031.58 36,918.18 34,914.83 35,473.43 37,185.50 37,688.32 38,643.81 39,731.90 40,182.37 39,514.92 39,212.27 39,767.93 0.5054 0.5387 0.5436 0.5623 0.5990 0.6053 0.6019 0.6570 0.6856 0.7297 0.7102 1.3766 1.3363 1.2836 1.2713 1.2826 1.2737 1.2597 1.2859 1.2713 1.2725 1.2760 0.3708 0.4643 0.4773 0.4741 0.5144 0.5354 0.5679 0.5530 Source: Survey of Consumer Finance, various years. The variables PROP and CAS are defined in Tables 1 and 3 respectively. The variable Children is the total number of children ages 18-24 in the family. A number such as 1.3191 represents the average number of such children in the families of our sample in 1975. For further details, see the third section. fio I Family Income and Postsecondary Education in Canada 191 of behaviour. ( O L S equations w e r e estimated with T S P 4 . 2 b . ) P R O P depends on Income and Income squared with coefficients (t-statistics in b r a c k e t s ) of 0 . 4 2 9 2 6 E - 5 ( 2 4 . 3 5 ) a n d - 0 . 1 5 9 4 2 E - 1 0 ( - 1 0 . 7 3 ) . T h e income effect is positive for most levels of income, but because of the negative coefficient on the income squared term, it diminishes as income rises. 15 The implications of this particular pattern of income effects for the convergence in participation rates, noted in the second section, are not obvious without a further quantitative assessment. A simple calculation involves e v a l u a t i n g the c h a n g e in P R O P w h i c h occurs b e t w e e n 1975 and 1993 for selected quintiles due solely to changes in f a m i l y incomes between those time periods. In 1975, the lowest quintile average real income was $8,336 and it grew to $11,101 by 1993, increasing P R O P by about 0.011. The highest quintile average real income increased f r o m $66,403 in 1975 to $74,558 in 1993, increasing P R O P by a b o u t 0.016. Such i n c o m e changes have minor effects on P R O P and would actually increase the proportion of children attending school more for the high-income than for the low-income group. These calculations suggest, therefore, that while the qualitative income effects are consistent with convergence, the quantitative effects of income are essentially negligible and cannot account for the effects noted in Table l. 16 The H e a d ' s educational achievement is associated positively with P R O P : A university degree, the educational variable with the highest effect relative to the omitted class, increases P R O P by 0.270 (41.68). P R O P is 0.042 (10.95) higher for urban families than rural ones. The real tuition variable is significant at the 5% level in a two-sided test and has a coefficient o f - 0 . 3 2 1 E - 4 (-2.30). The variable Children has a coefficient of 0.747E-2 (0.58), with Children Squared carrying a coefficient - 0 . 4 6 5 E - 2 ( - 1 . 3 9 ) and neither variable is u s e f u l in this e x p l o r a t o r y regression. Finally, the coefficients on the provincial d u m m i e s range, relative to British Columbia, f r o m - 0 . 0 1 0 ( - 1 . 1 9 ) in Alberta to 0.110 (9.67) in Prince Edward Island. The time effects in the O L S equation increase more or less monotonically both in size and significance from 0.005 (0.53) in 1977 to 0.159 (14.59) in 1993. (The 1977 intercept is not significantly different from that for 1975, the base year.) Thus, an increase through time in P R O P The Canadian Journal ofHigher Education Volume XXXI, No. 1, 2001 192 L.N. Christofides, J. Cirello, & M. Hoy across all income groups is suggested. This conclusion also holds in separate O L S regressions for each SCF survey year. Here, the intercept of the estimated equation for each SCF survey year increases over time f r o m 0.075 (1.67) in the 1977 sample to 0.161 (2.29) in 1993. C o n c e i v a b l y , d i f f e r e n t t i m e e f f e c t s f o r d i f f e r e n t quintile g r o u p s might be supported by the data, a suggestion that would be consistent with the raw data in Table 1. With such effects in mind, the pooled O L S regression w a s re-estimated, allowing for interactions between year and quintile effects. We treat all base year (1975) quintiles as having the same m e a n value of P R O P once explanatory variables are taken into account. Thereafter, different quintiles are allowed to have a different c o e f f i c i e n t b o t h across quintiles and SCF years. Until the 1984 SCF, there is no consistent pattern of quintile/time effects and the coefficients on the quintile/time effects are, in general, not significantly different f r o m zero. Thus, in Table 1, the increases in P R O P from the low to the high quintiles m a y be the result of differences in the average values of explanatory variables in the different quintiles. In addition, until 1984, the differences across years in the value of P R O P for given quintiles are not significant. However, for 1984 and 1985 the first quintiles have coefficients (t ratios) equal to 0.063 (3.41) and 0.086 (4.61) respectively, while the s e c o n d quintiles h a v e coefficients (t ratios) equal to 0.046 (2.71) and 0.070 (4.00), respectively. Thus, after 1983 and relative to the b a s e year, the lowest t w o quintiles begin to display higher values of P R O P w i t h the greatest e f f e c t occurring in the lowest quintile. F r o m 1986 onwards, all quintiles show consistent increases in P R O P with the highest effects occurring in the lowest quintiles. By 1993, for example, the five quintiles have coefficients (t ratios) equal to 0.168 (8.63), 0.194 (10.65), 0.150 (8.66), 0.137 (7.59) and 0.154 (7.53). These effects are reasonably representative of the intermediate years as well. These results suggest that there is indeed a tendency for P R O P to increase over time and that this increase is larger for lower quintiles. It should be noted, however, that the quintile effects for each SCF year are often not significantly d i f f e r e n t f r o m each other so that a simple year effect with no quintile interactions is often sufficient. The Canadian Journal of Higher Education Volume XXXI, No. 1, 2001 Family Income and Postsecondary Education in Canada 193 Other explanatory variables in this O L S equation have coefficients (t ratios) w h i c h are very similar to those in the simpler specification which just has year effects with no quintile interactions. T h e O L S r e s u l t s are b a s e d on the m o s t w i d e l y u s e d m e t h o d o f assessing the relation between a variable such as P R O P and possible e x p l a n a t o r y v a r i a b l e s a n d c o n s t i t u t e a f i r s t p a s s at t h e p r o b l e m . However, they suffer from permitting the predicted values of the dependent variable to lie outside the 0 to 1 interval characterizing P R O P and standard hypothesis tests assume that the additive error term is normally distributed. This last assumption implies that values for P R O P such as plus and minus infinity are possible. For these reasons it is necessary to check that the variables used in the O L S approach continue to be important in statistically better defined specifications. It would be disturbing, for instance, if income and income squared were not significant variables in alternative specifications. In the alternative specifications considered below, P R O P is no longer the dependent variable. Instead, we use (1) the Poisson model for count data which explains integers such as the n u m b e r of children in postsecondary education (CAS) and (2) the Probit model which describes the probability of having at least one child in p o s t s e c o n d a r y education (see Greene, 2000). T h e f o r m e r seeks to explain the actual n u m b e r of children at university using: Prob (CAS = casj = e -\Xfasn) / casn\ casn = 0,1,2... (1) where the subscripts n and i index count outcomes and observations respectively and Xj is specified as: ln^P'X;. The vector (2) contains the explanatory variables described above for the ith observation and the vector P the constant coefficients. The marginal effects of changes in variables on the conditional expectation of C A S are given by: dE (CAS\Xi)/dXi = d (k^/dXi = e?'*, (3 (3) The Canadian Journal ofHigher Education Volume XXXI, No. 1, 2001 194 L.N. Christofides, J. Cirello, & M. Hoy a n d a r e a n a l o g o u s to t h e v e c t o r (3 in t h e O L S c o n t e x t . T h e P r o b i t m o d e l c o n c e r n s itself w i t h the latent v a r i a b l e I * w h i c h d e t e r m i n e s whether at least one child should attend postsecondary education: (4) where i indexes the z'th observation, e;- is a standard normal variable, the vector X contains the values for the zth observation of the explanatory variables discussed earlier and y is a vector of constant parameters. W h a t w e do observe is the variable /, that is, whether at least one child did attend postsecondary education and w e assume that: 7=1 if I* >0 (5) 1=0 if I* <0 (6) The conditional expectation of / * is given by F (y 'X) and the marginal effects b y f (y ' X ) y , where F is the cumulative standard normal and f is the standard normal density function. C o l u m n s 1 - 3 , Table 6, report estimates of the coefficients in the Poisson model, the implied t-statistics and marginal effects, respectively. C o l u m n 3 is obtained f r o m column 1 b y multiplying by X = 0.4766, where A, has been evaluated at the mean values of Columns 4—6 of Table 6 r e p o r t s i m i l a r i n f o r m a t i o n f o r the Probit model. 1 7 M a r g i n a l e f f e c t s are p r e s e n t e d o n l y f o r the c o n t i n u o u s v a r i a b l e s in Table 6. The results in this table are qualitatively similar to the O L S results reported above. Additional children first increase and, beyond a certain number, decrease the variable C A S and the probability of having at least one child in postsecondary schooling. Residing in urban areas is associated with increases in both C A S and the probability of having at least one child in postsecondary schooling. Higher educational attainment for the family head increases C A S as well as the probability of having at least one child in postsecondary schooling, this effect being most pronounced w h e n the head holds a university degree. The real tuition fee variable, which w a s only marginally useful in the O L S results, has no significant effect on C A S and is only significant at the 5% level in the Probit equation. Significant d i f f e r e n c e s b e t w e e n other provinces and British Columbia are present in both specifications (see Table 6). The Canadian Journal of Higher Education Volume XXXI, No. 1, 2001 Family Income and Postsecondary Education in Canada 195 However, it is the effects of Income, Income Squared and Time that are of particular interest. Real income continues to be a significant nonlinear influence on both C A S and the probability of having at least one child in p o s t s e c o n d a r y education. In the Poisson model, real i n c o m e increases C A S until real income equals $115,582 while, in the Probit model, the probability of having at least one child in school rises until real income equals $126,503 which, in both cases, accounts for virtually all observed income levels. The year effects in successive SCF surveys increase in both the Poisson and Probit specifications, indicating growth over time in attendance at postsecondary institutions. It is instructive to use the estimates in these alternative approaches to see whether the rise in real income over time can explain the convergence of interest in postsecondary education attendance across quintiles. In the probit estimates, for instance, the 1975 probability of having at least one child in school is 0.295 for the first and 0.496 for the fifth quintile respectively. 1 8 B y 1993 these p r o b a b i l i t i e s are 0 . 3 0 8 and 0 . 5 1 6 respectively if the time effect is ignored. That is, the growth in income alone cannot account for a much higher probability of at least one child at school for first (the lowest) quintile families in 1993 relative to 1975. O n c e the 1993 t i m e e f f e c t (0.45 in c o l u m n 4, Table 6) is taken into account, these probabilities become 0.48 and 0.688 respectively and the considerably heightened interest in postsecondary education is captured by the time dummy. In light of the current policy concern about the possible effects of increases in tuition fees on university attendance, the weak performance of the variable Tuition m a y come as a surprise. It must be remembered, however, that given the strong time element in this study it is real tuition fees that should be of interest and, as Table A.2 in the appendix shows, these were constant or even declining in many provinces until 1991. In 1991 nominal tuition fees in Quebec were increased for the first time in our sample and by 1993 real tuition fees increase in all provinces above their 1991 levels. It is conceivable that these increases in the cost of education are n o t given a c h a n c e to appear in the equations of Table 6 because the provincial and time effects m o p up most of the information in the variable Tuition. In order to explore this possibility we conduct The CanadianJournalofHigher Education Volume XXXI, No. 1, 2001 196 L.N. Christofides, J. Cirello, & M. Hoy NO O o w w WW m ci cn "c3 NO c ' — ' NO oo CN o o o '5b C I S u •a o N OU " 1• — ,1 « a -m ^ O NO Op C N •«t O NO NC N 1C N7 1 X) o C 0) 'o S < u o U (N <—| O C N O O Ww w C N t^ i/"> en <n O N en ci o oo en ^ O • — i oo iri o o o 1 1 O NO NC NC N N O O N C N m en O O O O N O o o o WW w w W cn N OC N < NO cn « a «—< r- — < C Np N x-i O N iri C 1 ca < u S T3 O S +-> oo NO c ON ^ 3 ^ o O ON H ci U en 1 a 7 NO < T h o N OO N O i/-i K C N cn O i/-> cn N O oo o cn C NC N N ci O NO C NO N^ C < S ^ 1 O cn m O ^ C NO <o C NO N O NO ON o en en C NC N (N ci ci ci O O O N ON O in cn O oO O o ci C) o 1 C N O W o NO — 1 NO 1 o ^ ON OC C NN N ^ o ^ O oo' N O m' C N C N en >/-> ON NO" ON 7 NO C No O O w > O NO NO C No •t p Tf p N O r-' NO' oo' O ci CÏ o 1 o OH en W-I F — H a o in O V 1 w cn ON o WW oo ON C N (N H < + h p p NO p V C N O O " ' o 1 t 1 U NO en u-i C N cn O © O i W oo t en <ri © NO O ON O o i C N ON I/-1 en ON C NC N C NC NO O O O ci O O T3 g O O 00 o o o o 1 T3 •2 C ° -«•a « x> •5 'G ca > a .2 ti '3 H « e o g £ 2 3 C 2 / T3 C/3 c C c O o I u u Oh H M U « 2 â « "2 § S o U U P te Ô £ £ The Canadian Journal ofHigher Education Volume XXXI, No. 1, 2001 « C g» Q •o I 'o s U 3 K .O • - j U-, s g a; z o C ca £ ( U o 1 0 -O ca < L >_ 3 C o o o ca ^ ca -e cn u ca C Z > Family Income and Postsecondary Education in Canada 197 w G < u O 2 O O N in O O (N TF O © ^f F"; m O SS O t— in O Os in — • Os O Cos m <N rn • ^ - s o o s O O s O s m > n m OS cn OH c < D 'o S ( U C N m 00 •«f 1 fNm^Hso-H*fossor-<soooossomo ©OOO^H^^cNrncNCNOTl-^foo O O O O O O O O O O O O O O " o U o W n! G < U T3 O S « » G 3 O O § oo cn o cn in _ S O H •n Os i n S O © 1 © cn O S cn in in oo o CN O O cn cn p oo Os oo o -H 00 © — ! o oo cn 1 so Os S O S O o a* G .2 S t+H < u o U a •c C S > m c N O s S O S O O O s O O S O O S IT) O C NT T m os ^ n c n ^ i n o o m o o c NN s o r o N C N c n so cncosq O p O O O ^ ~ c " cNC " O © © © O © O O O O O O O O C N I C — Os " H C N ^t" in S O t — 00 Os © C N C Ow t^-r-OOOOOOOOOOOOOOOOOSOSOSOS c OSOSOSOSOSOSOSOSOSOSOSOSOSOS o u T3 o o •G "u M M o The Canadian Journal ofHigher Education Volume XXXI, No. 1, 2001 198 L.N. Christofides, J. Cirello, & M. Hoy two sensitivity analyses. To begin with, we respecify the equations of Table 6 b y removing the time effects and including a time trend (1975 o b s e r v a t i o n s are coded as Is, 1976 as 2s, and so on) and time trend squared. If Tuition has a role to play it n o w has a better chance to fulfill it and, of course, w e continue to have an interest in the role of long-term trends. In the C o u n t m o d e l , Tuition has a c o e f f i c i e n t (t statistic) of 0.36E-03 (12.95); the counter-intuitive positive sign suggests that this variable m a y be picking u p some of the long-term trends in the number of children in postsecondary education. In the Probit equation the coefficient (t statistic) on Tuition is - 0 . 6 1 E - 0 4 (-1.60) and it is not as welldefined as its counterpart in Table 6. Both specifications produce strong trend e f f e c t s : In the C o u n t e q u a t i o n the results f o r trend and trendsquared are 0.0179 (7.98) a n d - 0 . 0 0 0 5 ( - 5 . 5 7 ) respectively; in the Probit m o d e l t h e y are 0 . 0 0 2 2 (0.45) and 0 . 0 0 1 3 (5.19) respectively. T h u s , Tuition does not appear to have a useful role, while the time trend variables continue to be important. It is p o s s i b l e that the sensitivity analysis a b o v e does not go far enough in the sense that it still allows much of the provincial variation in Tuition to b e c a p t u r e d b y the provincial d u m m y variables. Separate provincial equations with a trend and trend-squared term offer another w a y to evaluate the impact of Tuition. At the same time this extension deals with an issue which was noted in footnote 13, that is, the provincial CPI information allows for no cross-sectional variation for the base year and hence does not provide adequate cross-sectional deflation of nominal variables, including Income and Income Squared (denoted as Income 2 in the tables). Separate provincial equations deal with this concern as well as the appropriate role for tuition. Accordingly, we re-estim a t e o u r e q u a t i o n s u s i n g provincial sub-samples. In the interests of brevity, w e do not report these results in detail. It is noteworthy that Tuition never has the anticipated negative and significant coefficient; i n d e e d , in a l l C o u n t e q u a t i o n s a n d in t h e P r o b i t e q u a t i o n s f o r N e w f o u n d l a n d , Prince Edward Island and British Columbia it has a sign i f i c a n t , p o s i t i v e , c o e f f i c i e n t w h i c h , in all likelihood, p r o x i e s t i m e effects. The trend and trend-squared variables continue to be important The Canadian Journal of Higher Education Volume XXXI, No. 1, 2001 Family Income and Postsecondary Education in Canada 199 except in Prairie provinces where they are not significant in either specification. All other variables continue to perform as indicated above. To check for the possibility that the variable Tuition does have an effect on postsecondary attendance for low income families, but that this effect is essentially swamped by using the sample based on all families, regardless of income level, we ran the same econometric models as in Table 6 (and O L S as well) for the subsamples defined by the poorest 2 0 % of families and also for the poorest 4 0 % of families of the entire sample. 19 The result was that the variable Tuition continues not to be statistically significant in explaining the dependent variable. Further work using as yet unavailable data for the high-tuition period of the late 1990s would b e desirable. CONCLUSION Using econometric analysis based on Survey Consumer Finance data f r o m 1975 to 1993 we have been able to isolate some of the important socio-economic variables which have affected the pattern of attendance at p o s t s e c o n d a r y e d u c a t i o n a l i n s t i t u t i o n s in C a n a d a o v e r this t i m e period. Parents' income and education level are important independent explanatory variables, as expected. Proximity to a postsecondary institut i o n , as c a p t u r e d b y o u r U r b a n d u m m y v a r i a b l e , is a l s o a f a c t o r . Provincial d u m m i e s are significant as well and reflect regional differences in interest for postsecondary education which are not explained by d i f f e r e n c e s in t h e o t h e r s o c i o - e c o n o m i c v a r i a b l e s t h a t h a v e b e e n included. Surprisingly, the level of tuition fees does not turn out to be a relevant factor. Although this m a y be due to the fact that variation in real tuition fees over this time period was limited, all efforts to allow the variable Tuition to express s o m e e f f e c t on postsecondary attendance f a i l e d . D e s p i t e t h e i n c l u s i o n of all of the a b o v e - m e n t i o n e d s o c i o economic and regional variables, a persistent and increasing trend in part i c i p a t i o n in p o s t s e c o n d a r y e d u c a t i o n is c a p t u r e d by t i m e d u m m i e s included in our econometric equations. Thus, we have demonstrated that, although differentials in family incomes can explain a substantial degree of observed differences in attendance at postsecondary institutions in The Canadian Journal of Higher Education Volume XXXI, No. 1, 2001 200 L.N. Christofides, J. Cirello, & M. Hoy any given year, trends in income levels over time do not explain the relative convergence over time of attendance at postsecondary institutions across quintile groups. 20 These results shed light on a number of important issues concerning equity and efficiency in the financing of postsecondary education. It is clear that, whatever the reason, the time period 1975 to 1993 has seen a larger increase in p o s t s e c o n d a r y education for individuals f r o m relatively lower income families. Although individuals from higher income f a m i l i e s are still m o r e likely to attend p o s t s e c o n d a r y education, the extent to which the benefits of government subsidies for postsecondary education are enjoyed disproportionately by higher income individuals and families has been reduced and so the regressive impact of governm e n t s u b s i d i z a t i o n of p o s t s e c o n d a r y e d u c a t i o n has f a l l e n o v e r this period. Our results suggest that, although the expected positive effect of increasing f a m i l y i n c o m e on postsecondary education participation is stronger at lower income levels, this property in conjunction with overall increasing family income over this period is not strong enough to explain the higher rate of growth of postsecondary participation rates of children f r o m lower income families. Alternatively, long-term trends in postsecondary education have been very important and relatively more important for low income families in explaining increasing rates of participation in postsecondary education. Income, however, continues to exert a strong influence on participation rates for any given year. This suggests that imperfect capital markets may continue to play a role in determining the decision to attend postsecondary education. Finally, to the extent that there has been significant convergence in participation rates in postsecondary education between income classes, which is independent of trends in income levels, there is reason to believe that trends in postsecondary education attendance will exert a positive influence on social mobility and equality of incomes in the future. To understand more fully the reasons for the trends suggested by the results of this paper, continued work will be required."^ The Canadian Journal of Higher Education Volume XXXI, No. 1, 2001 Family Income and Postsecondary Education in Canada 201 Notes 1 Other economic factors may be at work to increase inequality over time. However, any narrowing of the differences in postsecondary education levels between children from families of different income levels should at least limit any increases in inequality that would otherwise be observed. 2 Studies which support this claim include Hansen & Weisbrod (1969), Radner & Miller (1970), Peltzman (1973), Jackson & Weathersby (1975) and Bishop (1977). Psacharopoulos (1986) documents studies for several developing countries. For Canada, see Mehmet (1978) and Meng & Sentance (1982). Also, see Anisef, et al. (1985) for a summary of other Canadian studies which show consistently that individuals from families of higher socio-economic status are more likely to enter postsecondary educations. For a wide-ranging set of references on education in Canada, see Guppy & Davies (1998). J He shows that the lowest income class (less than $2000 income in 1970 dollars) receives benefits from postsecondary education which exceed their tax contributions. This result occurs since this income group contributes almost nothing to tax revenues. However, the next three income groups ($2000 to $10,000) all contribute more than they receive in benefits from the education system while the opposite holds for those earning in excess of $10,000. 4 The SCF category of 18-24 year olds will inevitably include individuals who have no interest in further education as well as those who have already graduated from university but are still captured in this category. ^ Osberg (1996), for example, shows that, except for the effect of recessions, there has been little change in inequality in Canada over the period 1975 to 1994. See also Wolfson (1986). 6 Data from the 1975-1993 Surveys of Consumer Finance (selected years as available) are used in this study because this information is available for many more years than is the case with data from other sources such as the census. In accordance with standard procedures, we use the sampling weights provided by the Surveys in determining the means of variables. Not to do so would generate biased estimates due to the fact that the surveys do not sample households of different types with equal probability. The age group 18-24 years of age represents the age group which has traditionally been most interested in postsecondary education — see the third section for a more detailed discussion of the data used in this study. Guppy and Davies (1998, pp. 90-92) show that, over this period, the participation rate for females has increased more dramatiThe Canadian Journal ofHigher Education Volume XXXI, No. 1, 2001 202 L.N. Christofides, J. Cirello, & M. Hoy cally than that for males, suggesting that separate analyses by gender would be desirable. Unfortunately, the SCF data do not identify the gender of the children in the 18-24 year bracket. ^ Although students can be expected to earn substantially higher incomes as a result of their education, this "human capital" is embodied in the person and cannot be used as collateral for a loan as is the case for financial and physical assets. This makes it difficult for students to borrow funds from private lenders. This constraint is especially binding for children from low income families who have greater difficulty directly providing funds for their children or helping them secure loans from the private sector. ^ For 1983, this data is provided for only two categories (1) one child and (2) two or more within the single age grouping of 18 to 24, while other SCFs report the actual number of children in school. It is also the case that restrictions such as for the 1983 data set apply to the 1984 and 1985 data sets, but the age groupings are split into two, 18 to 21 and 22 to 24, and so these restrictions are not likely to be binding in many cases. 9 We note that this SCF group may include some individuals who are still at high school and may exclude some individuals who are engaged in postgraduate studies. It may also exclude some young adults who have set up households on their own. In order to ascertain the magnitude of this problem, we examined the Individual SCF files, isolating all 18-24 year olds who are in fulltime college or university attendance. In 1993 for example, only 4.83% of the 18 year olds in this group described themselves as household heads. Naturally, this figure increases as age increases and by the age of twenty-two, this figure is 17.52%. We assume that household formation is dependent on whether parents are still alive, whether they live together in a single household, and other factors which we treat as exogenous. Subject to these caveats, we refer to the schooling undertaken by the 18-24 year olds in the families of our sample as postsecondary education. It should be noted that, as Mitchell (1994) has shown, females are likely to leave the family nest earlier than males. Unfortunately, we are not able to take gender effects into account using the SCF data. 10 Note that these indices set 1986 = 100. See Statistics Canada, The Consumer Price Index (62-001). 11 Card (1995) examines the relevance of this variable for estimates of the return to education. The Canadian Journal ofHigher Education Volume XXXI, No. 1, 2001 Family Income and Postsecondary Education in Canada 203 We note, however, that the variance of real tuition fees may have been too small to allow us to reliably estimate the relevance of this variable. This is a matter that we cannot prejudge. We return to this issue below. Because, as indicated in Appendix Table A.l, the CPI in 1986 = 100 in all provinces, the reader is cautioned against comparisons of real tuition across provinces. We return to this issue below. Effects are measured relative to 1975 — the omitted category. For computational convenience and ease of reporting and interpretation, we report in detail only pooled results where the intercept terms are assumed to differ across province and the fourteen SCFs but include no interactions between time and province-specific effects. We do, however, also discuss results based on separate equations in exploratory OLS equations. As noted below, these suggest similar conclusions as the pooled data with time effects. The quadratic term results in a negative derivative for levels of real income beyond $134,632. It should be noted, however, that family income (in constant 1986 dollars) exceeds $100,000 for only 1.5% of the families in the sample so that the income effect is positive for most families in the sample. This does not mean that income is unimportant. The difference in average incomes between the highest and lowest quintiles explains a good deal of the cross-sectional variation in postsecondary education attendance. For instance, this difference is 0.18 for 1975 and 0.17 for 1993. The effect of 0.18 for 1975 is evaluated as (0.42926E-5 times the 1975 fifth quintile average income of $66,403 plus 0.15942E-10 times $66,403 squared) minus (0.42926E-5 times the 1975 first quintile average income of $8,336 plus -0.15942E-10 times $8,336 squared). A similar calculation explains the figure for 1993 keeping in mind that the first quintile average real income is by then $11,101 while that for the fifth quintile is $74,558. The Poisson count model was estimated with LIMDEP6.0 while the Probit model was estimated using TSP4.2b. 1 ^ To calculate these probabilities we multiply the estimated coefficients in the probit column of Table 6 by the variable means and add these up. We then evaluate the income and income squared terms times their respective coefficients for each quintile. The overall sum of all these terms is the value of the argument in the probit approach. The estimated probability is given by the value of the cumulative standard normal distribution at the value of the argument. The cut-off income level (in 1986 dollars) for the poorest 20% in the entire sample is $15,575 and for the poorest 40% is $26,333. The Canadian Journal of Higher Education Volume XXXI, No. 1, 2001 204 L.N. Christofides, J. Cirello, & M. Hoy It is conceivable that, by including the time effects, the hypothesis that higher absolute levels of real income can explain the increased interest in postsecondary education has been subjected to far too stringent a test. Further work in this area, which unbundles the effects captured by the time dummies into the influence of relevant variables such as exogenous measures of the returns to education, would be very desirable. References A n i s e f , P., B e r t r a n d , M . - A . , H o r t i a n , U., & James, C.E. (1985). Accessibility to postsecondary education in Canada: A review of the literature. Toronto, ON: Ministry of Education. Bar-Or, Y., Burbidge, J., Magee, L., & Robb, A.L. (1995). The wage premium to a university education in Canada, 1971-1991. Journal of Labor Economics, 73(4), 762-794. Bishop, J. (1977). The effect of public policies on the demand for higher education. Journal of Human Resources, 12(3), 285-307. Card, D. (1995). Using geographic variation in college proximity to estimate the return to schooling. In L.N. Christofides, E.K. Grant, & R. Swidinsky (Eds.), Aspects of labour market behaviour: Essays in honour of John Vanderkamp (pp. 201-221). Toronto, ON: University of Toronto Press. Downey, J. (1996). Turning adventure into advantage. University of Waterloo Magazine, (Winter), 12-14. Greene, W.H. (2000). Econometric analysis, 4th ed. Englewood Cliffs, NJ: Prentice Hall. Guppy, N., & Davies, S. (1998). Education in Canada: Recent trends and future challenges. Ottawa, ON: Statistics Canada. Hansen, W.L., & Weisbrod, B.A. (1969). The distribution of costs and direct benefits of public higher education: The case of California. Journal of Human Resources, 4(2), 176-191. Jackson, G.A., & Weathersby, G.B. (1975). Individual demand for higher education: A review and analysis of recent empirical studies. Journal of Higher Education, 46(6), 623-652. Meng, R., & Sentance, J. (1982). Canadian universities: Who benefits and who pays? The Canadian Journal of Higher Education, 12(3), 45-58. The Canadian Journal ofHigher Education Volume XXXI, No. 1, 2001 Family Income and Postsecondary Education in Canada 205 Mehmet, O. (1978). Who benefits from the Ontario university system? Toronto, ON: Ontario Economic Council. Mitchell, B. (1994). Family structure and leaving the nest: A social resource perspective. Sociological Perspectives, 37(4), 651-671. Osberg, L. (1996). Economic growth, income distribution, and economic welfare in Canada, 1975-1994. Halifax, NS: Dalhousie University. Peltzman, S. (1973). The effect of government subsidies-in-kind on private expenditures: The case of higher education. The Journal of Political Economy, £7(1), 1-27. Psacharopoulos, G. (1986). Financing education in developing countries. Washington, DC: World Bank. Radner, R., & Miller, L. (1970). Demand and supply in U.S. higher education: A progress report. American Economic Review, 60(2), 326-334. Vaillancourt, F. (1985). The private and total returns to education in Canada, 1985. Canadian Journal of Economics, 28(3), 532-554. Wolfson, M. (1986). Stasis amid change: Income inequality in Canada, 1965-1983. The Review of Income and Wealth, 52(4), 337-369. The Canadian Journal ofHigher Education Volume XXXI, No. 1, 2001 L.N. Christofides, BC 206 B W SK •a AB O 00 in S oo oo o O r-; en en Os m o i/i en en S O O en sd r^ en r ^ C N r^ (N C en S O o o • < 3 - m S r-- oo Os O N p G J. Cirello, & M. Hoy «ci S O S O o C N p oo oo p Os p en Os S O t^ en C N oo sà en sd o «ci so r - oo O C N C N N C S os o o o « u-l •Si- so en en oo N IO en C C N O oo Os sd m S O S o o o oo l/"> rtOs O en C N C N S ici S so t'- oo O o o o MB p S O en O 1/1 o o SO Os O oo o £ O en r-; «ci os r^ Os V) C N ici oo Os os O S o C N „ en en Os Os •ci sà Os Os O ICI o C N C N N C t-; Os p Os en 00 en O O ici sd O o C N C N en o o S 00 SO sq Os O en oo Os ici o N en C N C N C o o IO o o 't o o H O SO SO QC o lO ^ r- in o SO NB en Tl- r- p en en en LO 00 o s O S SO r- rN sd C N C «ci Os roo O S 00 oo en en 2; C N "Cl so Os >fi t-- 00 CN SO r-; oo CN sd oo ici Os p oo OS so so o o o <n so p sd so CN en os os 00 OS >—1 ICI oo Os '—1 m o sd CM sq en ici C N "O r en C N sd oo o s o s o o o o o o en Os en 00 en oo sd Os o N en (N C ICI C N SO en sd o SO o r- en C N os ici sd sd C N C N C N in en in C C N N en C N 00 ici sd O N o C N C N C SO ^ o en o o o os CN O en «ci o oo Os oo oo os U-l r- O O O o* a m t^ vi w o\ -h M PI —i Os O 00 OS en O CN CN (N CN OS 00 os o Os OS ,—1 OS Os CN os Os — '—' M -S u o H c d U > H m Os Os Os rOs .—i T—1 en oo — ,, oo Os —t CN 00 OS —t The Canadian Journal ofHigher Education Volume XXXI, No. 1, 2001 so 00 os 1 en Os Os 1 Table A.2 Real Tuition Fees for Full-time Students at Canadian Universities Memorial C O 5 S 5 » 6 a oss a » I <3 UofPEI Dalhousie U of N B U of Qucbec U of T U of Man. UofSask. U of Alberta UBC Year NF PEI NS NB QC ON MB SK AB BC 1975 1977 1979 1981 1982 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1147 988 1050 829 825 957 964 1006 1026 1052 1067 1125 1112 1264 1368 1304 1231 1194 1099 1102 1270 1296 1350 1429 1453 1471 1469 1461 1671 1763 1451 1243 1248 1206 1210 1427 1458 1466 1473 1477 1467 1447 1415 1739 1896 1303 1440 1219 1126 1132 1348 1370 1400 1526 1571 1591 1607 1589 1677 1852 1144 986 835 672 600 548 525 500 478 461 441 423 670 1021 1080 1276 1294 1133 1124 1106 1198 1210 1215 1197 1217 1196 1229 1274 1365 1437 944 852 864 805 806 767 811 822 852 899 1064 1120 1174 1384 1577 1011 974 998 893 819 938 978 1015 1025 1080 1122 1129 1180 1449 1912 889 943 874 776 702 820 856 852 843 903 890 907 988 1116 1262 945 803 866 763 760 940 1193 1275 1280 1292 1305 1365 1358 1460 1409 Nominal tuition fees for Arts programs (Table A.3) deflated by CPI (Table A. 1). University fees are used as a proxy for postsecondary education tuition fees. ^ re o S re a a ». o s? re re 0 a 1 re a 5" s ? a a to o — i 5= r & a » S- to o 00 Table A.3 Nominal Tuition Fees for Full-time Students at Canadian Universities t- r Memorial UofPEI Dalhousie U of NB U of Québec U of T U of Man. UofSask. U of Alberta UBC Year NF PEI NS NB QC ON MB SK AB BC tsj a 1975 1977 1979 1981 1982 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 500 500 630 630 690 892 936 1006 1056 1108 1164 1280 1344 1544 1700 600 660 750 865 950 1200 1270 1350 1480 1560 1640 1720 1840 2120 2280 650 650 765 915 1007 1320 1410 1466 1525 1585 1650 1710 1770 2195 2415 581 740 740 850 935 1250 1325 1400 1575 1675 1775 1875 1975 2100 2350 500 500 500 500 500 500 500 500 500 500 500 500 850 1320 1416 559 655 680 835 915 1101 1156 1215 1264 1350 1410 1516 1638 1770 1894 425 450 540 615 670 705 776 822 888 975 1210 1332 1467 1756 2055 460 520 625 690 690 870 940 1015 1075 1185 1280 1344 1478 1830 2484 400 500 550 605 606 770 828 852 878 966 995 1069 1229 1413 1610 428 428 536 590 650 882 1155 1275 1320 1380 1455 1605 1680 1860 1860 Î5isr Source: Statistics Canada, Tuition and living for postsecondary education tuition fees. accommodation costs at Canadian universities (81-219). University fees are used as a proxy £ s W 4 5 0 a' p* R» £ 1