College attendance, tuition and family income

College Attendance, Tuition and Family Income∗ Olive Sweetman NUI Maynooth, Maynooth, Co. Kildare. PreliminaryPlease do not quote October 1, 2002 ∗I am grateful to Arnaud Chevalier, Paul Devereux, Aedin Doris, Donal O’Neill and seminar participants at NUI Maynooth and the Irish Economic Association conference in Mullingar for helpful comments regarding this work. I would also like to thank the Irish Social Science Data archive at ISSC for providing me with the data. 1 1Introduction There is broad agreement in the literature about the fact that there is a positive relationship between parental income and college attendance. However there is less agreement about why this relationship exists. The explanations for this relationship fall broadly into two camps. The Þrst explanation is that richer parents Þnd it less costly to send their children to college. Cameron and Heckman distinguish between what they call long-term credit constraints and short-term credit constraints. A short term credit constraint means that parents cannot afford to send their children to college. Long term credit constraints refer to the notion that poorer parents have less resources to spend on their children’s education throughout their life and thus they are less likely to be in a position to attend college later on in life. The alternative explanation is that children from richer parents have a lower distaste for education and thus acquire more education. It is important from a policy point of view to distinguish between these explanations. If children were short-term credit constrained then the government might want to introduce a system of loans or grants to encourage children from lower income backgrounds to attend college. The problem with being credit constrained is that children will have money once they graduate but they do not have the funds before they go to college. If it was due to taste factors then access programs for example might be more beneÞcial. To distinguish between these two factors we would ideally like to conduct an experiment. This might involve taking a group that is identical in all respects and giving one group increased loans to attend college. This is not really feasible. However in 1995 the Minister for Education in Ireland announced that undergraduate fees would be abolished. In 1995/96 students paid half fees and in 1996/97 undergraduate fees were completely abolished. The press release from the Department of Education on February 8 1995 stated: ’Today’s decision on abolishing undergraduate fees aims at providing universal access to third level education. The psychological impact of today’s decision will encourage and allow people to consider pursuing a third level education as a very realisable option in their life choice... The abolition of third level fees is a major step forward in improving access to higher education - fees are no longer a barrier’1 1In conjunction with this removal, the Minister also announced changes in the tax relief 2 This policy will certainly relax the budget constraint. 2.Howeverthis policy alone does not affect the disutility associated with attending college. In this paper I examine the effect of this policy on college attendance by social class. In the Section 1, I outline a simple model which examines the theoretical predictions of the effect of such a change in fees. In Section 2, I discuss the data set and the methodology used for the empirical work. Section 3 provides preliminary results and discussion. 2Model Consider a model of educational attainment, similar to Dynarski (2000) and Card (2000) in a world where there are no means tested grants and everyone pays fees. Individuals differ by parental income and tastes for education whichiscorrelatedwithparentalincome. V(S, c(t)) = Rs 0(U(c(t)) −γ(t))e−ρtdt +R∞ s(U(c(t))e−ρtdt C is consumption. γreßects disutility of schooling which depends on parental income. We assume that dγ dyp<0.As income increases disutility falls. γalso depends on an individual effect uiwhere uiis iid Normal (0,1). Students face a given interest rate, r(yp),whereris the opportunity cost of acquiring funds. It depends on parental income. dr dyp<0.It is assumed that wealthier parents have easier access to capital markets and face a lower interest rate. A student also faces direct costs of schooling T(1 −A(yp)) where Tis tuition costs and A(yp)is the proportion of aid which the student gets from the state. 0≤A≤1.We assume that aid is means tested. Let us consider a simple system.We assume that children who’s parents earn below a certain arrangements for covenants. 2Ideally we would like to maintain lifetime incomes constant and simply give them a loan so that we could distinguish between wealth effects and credit constraints. 3 threshold value of income get more aid than those above the threshold.We assume that the relationship between A and ypis such that for yp<y t(some threshold value) A=Ahand for yp>y tA=Alwhere Ah>A l.This implies that starting with a ypbelow the threshold, for small changes in yp dA dyp=0.Fory pabove the threshold, dA dyp=0for all changes in yp.For changes in ypthat cross the threshold then dA dyp<0.This implies overall that dA dyp≤0.A student will invest in schooling until the marginal cost of acquiring funds=marginal rate of return. Let y(s, t)denote earnings by an individual in period t with s years of schooling. Then intertemporal budget constraint is: R∞ 0(c(t))e−rtdt =−Rs 0(T(t)(1 −A(yp))e−rtdt +R∞ s(y(s, t)e−rtdt MB(S)=R∞ 0 δy(s,s+τ) dS e−rτdτ MC(S)=y(s, s)+T(s)(1 −A(yp)) +1 λe−(ρ−r)sγ(s) If we assume that post-school earnings do not change over the life-cycle then so that y(s,t) = f(s) then MB(S)=f0(s)/r An individual’s optimal level of school is where the MB(S) = MC or re-written: f0(s) f(s)=r{1+T(1−A(yp) f(s)+1 λe−(ρ−r)sγ(s) f(s)} The left hand side measures the proportional increase in earnings per year associated with a change in schooling. The right hand side is the annuitized marginal cost of the Sth unit of schooling expressed as a fraction of foregone earnings. Using Card (2001), if we assume that u(c(t))=log c(t), that tuition costs are constant over the time in school, that the disutility of schooling does not change over time and that tuition costs are small relative to lifetime earnings then the right hand side is approximately equal to: r(yp){1+T(1−A(yp)) f(s)+e−ρsγ(yp,u i)} This implies that optimal schooling s∗is a function of: s∗=f(T,A,ρ,γ(yp),r(yp),u i) 4 dS dA =−rT f00(s)−rf0(s)−rγf0(s)e−ρs+rγρf(s)e−ρs>0(1) This implies that as aid increases optimal schooling increases. Appendix 2 provides more detail. When there is no disutility associated with schooling , i.e. γ=0,then dS dA =−rT f00(s)−rf0(s)>0(2) Examining the effect of parental income on schooling: dS dyp =−g0(yp) g0(s)(3) where: g0(s)=f00(s)−rf0(s)−rγf0(s)e−ρs+rγρf(s)e−ρs(4) and g0(yp)=−dr dyp [f(s)+T(1 −A)+e−ρsγf(s)] −dγ dyp re−ρsf(s)+rT dA dyp (5) Since dr dypand dγ dyp<0,the Þrst two terms are positive. The Þrst term reßects credit constraints. Wealthier parents can borrow at lower rates. The 5 second term reßects the disutility of schooling, children of wealthier parents have a lower distaste for schooling. The third term however is less than or equal to zero. It is negative if the changes in ypcross the threshold, otherwiseitisequaltozero. Thisimpliesthatthesignofg0(yp)>0unless the negative sign on the third term in the above equation outweighs the positive effect of the other two terms. With increases in parental income, schooling will generally increase as both rwill fall and γwill fall. However if by increasing parental income, government aid is cut there is some chance that these children which are just above the threshold value of income have lower schooling than those below the threshold assuming that the decrease in aid is substantial and outweighs any credit constraint or disutility effect. That is dS dyp=−g0(yp) g0(s)>0if g0(yp)>0 Under the above assumptions, as parental income increases, optimal schooling increases. Theexpressionfortheterm dS dypdA is more complicated. If we take the simple case where we assume that A is exogenous, γ=0,f00(s)<0,f 000(s)= 0,then of dS dypdA is: dS dypdA =−dr dypT[(f00(s))2−rf0(s)f00(s)+r2f00 (s)[(f(s)+T(1−A)] [f00(s)−rf0(s)]3<0 dS dypdA <0. As aid increases, the gap in optimal schooling levels by parental income falls. It becomes more difficult to sign this term with the added assumptions that γ>0and dA dyp6=0. Next, we want to examine the proportions attending college. The signs on this will depend on what we got above. Letusassumethatwecanwrites ∗as s∗=f(T,A,ρ,γ(yp),r(yp)) −ui 6 We assume that attending college involves achieving at least a level of s, sc. Therefore: P(s∗>sc)=P(s ∗=f(T,A,ρ,γ(yp),r(yp)) −ui>s c) P(ui<f(T,A,ρ,γ(yp)−sc)=Φ(uc) How does income affect the proportion of people attending college? dΦ(uc) δyp=φ(uc)δuc δyp>0if δs∗ dyp>0 As income increases, the proportion of people going to college increases. The cutoffucincreases with income (δuc δyp>0if δs∗ dyp>0) .Underthese assumptions, the model predicts that a larger proportion of people attend college from higher income groups for two reasons. Firstly they have a lower cost of paying tuition and also they have a lower distaste for college. What happens the gap in the proportions, attending college by income group,as A increases? What is the sign of d2Φ(uc) δypδA?For example does the difference in the proportion going to college by income group narrow or widen? d2Φ(uc) δypδA=+φ(uc)δuc δypδA+φ0(uc)δuc δyp δuc δA If we assume that δs∗ dyp>0δs∗ dA >0and δs∗ dypδA<0. The Þrst term ( term 1) in this expression, is negative. The term δuc δypδA shows what happens the gap in the cutoffsbetweenthelowandhighincome people as A increases. In this case, this has a negative sign which says that the gap narrows as A increases. The sign of the second term(term2) φ0(uc)δuc δyp δuc δAis determined by the sign of φ0(uc).If φ0(uc)<0(>0) then term 2 is negative(positive). If φ0(uc)<0(>0),thenucis located to the right ( left) of zero. This would mean that the gap the between the lower and higher income group in the proportion going to college should narrow as aid increases. However if φ0(uc)>0then the result is ambiguous. From this model we cannot predict exactly whether a higher proportion of low or high income people 7 will go to college as result of the policy change. The introduction of free fees coincided with the abolition of tax relief for covenants. If as the department’s press release stated ’covenants beneÞtthebetteroffdisproportionately’, then this suggests that the introduction of free fees for the better offwas likely to be offset by the changes in tax regulations so their budget constraint may be unaffected. In Ireland, there are some students who always had their tuition paid by the state based on their family income or on what speciÞccoursetheywere taken. I am going to ignore the second group for the moment. Let us suppose that there are three income groups, low middle and high. We can assume that A=1 for the low income group and that A<1 for the other two groups. With the introduction of free fees for everyone, we would expect no change in the lower income group and the proportion attending college in both of the other two groups to increase. However as we said already, it is not clear whether the gap in the proportions attending college between the group 2 and 3 actually widens or narrows. 3 ProposedMethodologyandData Since the predictions from the theoretical model are ambiguous. To examine the impact of the policy, I propose to use the data on school leavers and the difference-in-difference estimator to examine the impact of the policy. This can be calculated using a limited dependent variable model such as a probit or logit model. cit=β0+β1(ypmed)+β2(Yphigh)+β3free+β4(free∗ypmed)+β5(free∗ yphigh)+δ(X) Where cit is a dummy variable which equals 1 if the person igoes to college from cohort t, zero otherwise. Let us assume for convenience that there are three levels of parental income, low, medium and high. We will assume that individuals from the lower level of income are already entitled to free fees. Free is a dummy variable =1 if free fees have been introduced for everyone,zero otherwise. Xreßects other control variables. 8 The coefficients β1(β2)reßects the difference in average attendance rates between the low and medium(high) income levels before the free fees was introduced. The coefficient β3reßects average changes in attendance rates for the lower income group before and after the policy was initiated. β4(β5) measures the change in attendance by the medium(high) income group over and above the low income group. This is a difference in difference estimator. If we assume 1) that this change in policy did not affect lower-socioeconomic groups and 2) this was the only policy change that took place over this time period then we can interpret this as the true effect of the policy change. There may be some problems with assumption 2). It is possible over this time period that there were other policies aimed speciÞcally at increasing attendance from lower socio-economic groups.3We may also have to control for changes in the quality of students over time. Students begin second level education in Ireland at about the age of 12. Second level education consists of a junior cycle which lasts 3 years and a senior cycle which lasts for 2 to 3 years. At the end of the senior cycle, students take a state exam called the Leaving CertiÞcate. Access to third level courses depends on the results obtained. If a student gets the required number of points for a particular course in their Leaving CertiÞcate, they are automatically entitled to enter the course.The data set which I use is the School Leavers survey available annually from 1980-19994.Itsurveys about 2000 students each year about one year after leaving school and has information about their school experience, what they did after school, information on college attended, course taken , employment record etc. One of the drawback of the data set is that it does not provide information on parental earnings. However there is information on parental occupation. I use this occupational coding information to form 7 social classes. I have a separate category for farmers. These are described in the Appendix. I do not know whether a given student would have been entitled to a grant. I only know for those who attended whether they received a grant or not. The probability of receiving a grant increases with social class number. Farmers have quite a high probability of receiving a grant also.(See Appendix table A1 for details). I limit my sample to those who left with their Leaving Cert completed. 3For instance the targeted initiative was launched by the HEA in 1996/1997 see Osborne and Leith(2000) 4I do not have the 1997 and 1999 data yet. 9 Table 3 Proportion of Students Leaving School with Completed Leaving Certs by Social Class. 1994 1995 1996 1998 total .79 .82 .81 .81 sc1 .89 .92 .91 sc2 .88 .90 .89 sc3 .87 .89 .85 sc4 .75 .76 .76 sc5 .66 .72 .68 sc6 .52 .66 .61 sc7 .89 .87 .90 16 5 Appendix 1 Key for Social Class sc1 higher professional, managerial, proprietors sc2 lower professional, lower managerial sc3 other non-manual sc4 skilled manual sc5 semi-skilled manual sc6 unskilled manual sc7 farmers 17 Table A1 Proportion Attending College who Receive Grants by Social Class 1994 & 1995 total sc1 .25(.03) sc2 .39(.02) sc3 .55(.03) sc4 .78(.02) sc5 .75(.05) sc6 .92(.04) sc7 .67(.03) Table A2 Average Total Points of Those who did Leaving Cert by Social Class 1994 1995 1996 1998(?) total 284 287 291 310 sc1 352 343 378 sc2 321 327 327 sc3 280 288 299 sc4 235 250 274 sc5 228 232 264 sc6 227 217 257 sc7 303 293 330 Table A3 Proportion Attending College by Social Class 1994 1995 1996 1998 total .47 .48 .44 .46 sc1 .67 .67 .68 sc2 .62 .58 .53 sc3 .47 .49 .47 sc4 .29 .38 .30 sc5 .30 .31 .27 sc6 .29 .21 .27 sc7 .55 .53 .56 18 6 Appendix 2 The First order condition is: f0(s) f(s)=r{1+T(1−A) f(s)+e−ρsγ(yp,u i)} This can be re-written as: g(s, A, γ,y p)=f0(s)−rf(s)−rT(1 −A)−re−ρsγf(s)=0 The 2nd order condition for a maximum requires that g0(s)<0. This implies that g0(s)=f00(s)−rf0(s)−rγf0(s)e−ρs+rγρf(s)e−ρs<0 g0(A)=rT To Þnd the relationship between aid and schooling. dS dA =−g0(A) g0(s)=−rT f00(s)−rf0(s)−rγf0(s)e−ρs+rγρf(s)e−ρs This is positive since g0(s)<0. As aid increases, optimal schooling increases. When γ=0,that is, there is no disutility of schooling then the relationshipbetweenSandAis: dS dA =−g0(a) g0(s)=−rT f00(s)−rf0(s) Now we examine the relationship between parental income and optimal schooling. Remember that γ,r and Adepend on parental income. dr dyp< 0,dγ dyp<0. We assume that children who’s parents earn below a certain threshold value of income get more aid than those above the threshold.We assume that the relationship between A and ypis such that for yp<y t(some threshold value) A=Ahand for yp>y tA=Alwhere Ah>A l.This implies that starting with a ypbelow the threshold, for small changes in ypthat dA dyp=0.Fory pabove the threshold, dA dyp=0for all changes in A. For changes in ypthat cross the threshold then dA dyp>0 19 g(s, A, γ,y p)=f0(s)−rf(s)−rT(1 −A)−re−ρsγf(s)=0 g0(yp)=−dr dypf(s)−dr dypT(1 −A)+rT dA dyp−dr dype−ρsγf(s)−dγ dypre−ρsf(s) g0(yp)=−dr dyp[f(s)+T(1 −A)+e−ρsγf(s)]−dγ dypre−ρsf(s)+rT dA dyp Since dr dypand dγ dyp<0,the Þrst two terms are positive. The Þrst term reßects credit constraints. Wealthier parents can borrow at lower rates. The second term reßects the disutility of schooling, children of wealthier parents have a lower distaste for schooling. The third term however is less than or equal to zero. It is negative if the changes in ypcross the threshold, otherwise it is equal to zero. This implies that the sign of g0(yp)>0unless the negativesignonthethirdtermintheaboveequationoutweightsthepositive effect of the other two terms. With increases in parental income, schooling will generally increase as both rwill fall and γwill fall. However if by increasing parental income, government aid is cut there is some chance that that these children which are just above the threshold value of income have lower schooling than those below the threshold assuming that the decrease in aid is substantial and outweighs any credit constraint or disutility effect. dS dyp=−g0(yp) g0(s)>0if g0(yp)>0 The expression for the term dS dypdA is more complicated. Even if we take the simple case where we assume that A is exogenous, γ=0,f00(s)<0, f000(s)=0,then the sign of dS dypdA is ambiguous. In this case it is equal to: dS dypdA =−dr dypT[(f00(s))2−rf0(s)f00(s)+r2f00 (s)[(f(s)+T(1−A)] [f00(s)−rf0(s)]3 −dr dypT>0since dr dyp<0and [f00(s)−rf0(s)]3<0 Taking what is inside the square bracket of the numerator: We have:[(f00(s))2−rf0(s)f00(s)+r2f00(s)[(f(s)+T(1 −A)] 20 collecting terms we have: f00(s){f00(s)−rf0(s)+r2(f(s)+T(1 −A)} f00(s){f00(s)−r(f0(s)−rf(s)−rT(1 −A)} From the Þrst order condition we know that (f0(s)−rf(s)+rT(1−A)=0 so we are left with( f00(s))2which is positive. The numerator is positive and the denominator is negative so we have, dS dypdA <0. The terms become more complicated with the added assumptions of γ>0 and dA dyp6=0. 21