The Australian National University
Centre for Economic Policy Research DISCUSSION PAPER
Repayment Burdens with US College Loans Bruce Chapman and Kiatanantha Lounkaewa
DISCUSSION PAPER NO. 647 November 2010
ISSN: 1442-8636 ISBN: 978-1-921693-28-1
1
Repayment Burdens with US College Loans Bruce Chapmana,* and Kiatanantha Lounkaewa,b
Abstract There is a significant and on-going unease with, and debate concerning, the state of US college loans. One of the most important questions relates to so-called “repayment burdens”, the financial difficulties associated with repayments. This paper examines the issue from both theoretical and empirical perspectives, the major goal being to understand the interaction between loan design and occupational choices. We find compelling original evidence that the design of US loans imposes severe expected hardships for many borrowers, especially those with very high debts, such as lawyers. The case for policy reform towards graduates’ capacity to repay seems incontestable. (JEL H28, I22, I28, J24)
a
Crawford School of Economics and Government, Australian National University, Canberra, Australia
b
Dhurakij Pundit University, Bangkok, Thailand
* Corresponding author. Tel.: +61 2 61254050; fax: +61 2 61250167. E-mail address:
[email protected]
2
Repayment Burdens with US College Loans The design of student loan schemes is critical to their success, with one of the most important aspects being the extent of loan repayment burdens faced by graduates. Repayment burdens relate to the financial difficulties associated with debtors meeting loan obligations and is the subject of this paper. In historical context we note that as long ago as 1993 President Bill Clinton 1 promoted changes to US student loans with a so-called “income based repayment” option, designed to take into account graduates’ capacity to repay student debt, saying: A student torn between pursuing a career in teaching or corporate law, for example, [should] be able to make a career choice based on what he or she wants to do, not how much he or she can earn to pay off the college debt. 2
In essence this was recognition of the fact that for many graduates at the time the burdens of student loan repayments were affecting career choices, away from public sector and community jobs and towards employment in which the earnings were sufficiently high to facilitate debt servicing (Chapman, 2006). In acknowledgement of the problem, several prominent law schools, including those from Georgetown and Duke Universities, and NYU, developed Law School Loan Repayment Assistance Programs (LRAP) in which law graduates are offered loan relief conditional on community or public sector employment. It is extraordinary to record that the number of law schools involved in LRAP has now grown to 100 3 , implying strongly that the significance of repayment burdens with respect to career choices has expanded significantly. Indeed, Field (2009) documents the fact that large numbers of law graduates do not consider public sector employment because of this problem. Clearly then, rather than being addressed successfully through changes to student loan policy, the problem for many law graduates has become more severe. Less attention has been given to what repayment burden issues might mean for the training of other groups, such as teachers, perhaps because the debts of members of this group are likely to be relatively low. However, repayment burdens are a function of both debts and incomes, and we note that in 2010 teacher annual starting salaries are both 1
Bill Clinton’s personal student loan experience involved him being part of the Yale College Deferred Payments Plan in the early 1970s, the first income contingent loan scheme (Palacios, 2004; Chapman, 2006). 2 President Bill Clinton Radio Address to the Nation (1 May 1993). 3 See Equal Justice Works (2010).
3 relatively low and differ between as much as $50,111 in New Jersey and $30,375 for South Dakota. 4 There is potential then that decisions concerning professional employment with respect to school teaching are also affected by loan repayment burdens. We offer a special contribution to these matters through the provision of new information on the incidence and extent of loan repayment burdens. This is addressed through considering empirically the implications of Stafford loans, the most commonly used student financing instrument for college students in the US. There are three contributions in what follows. First, in the literature there is a paucity of modeling designed to make explicit the relationship between repayment burdens and the life-time welfare of the borrower. We supplement existing utility-maximizing loan approaches by analyzing the conceptual interrelationships involving contributions to the extent and size of student loan repayment burdens, such as: expected incomes; the size of the loan; the rate of interest on the loan; the time required to repay in full; and the individual’s rate of time preference. The analysis is then extended to allow insights into the connection between career choices and repayment burdens. Second, for the first time we estimate the probability that students face concerned with future repayment difficulties. This highlights the potential benefits associated with a different approach to loan collection which takes into account capacity to repay loans, such as through income contingent collection. There are elements of the US student loan debate, and on-going changes to Stafford loan collection, which attempt to take into account the potential benefits of income contingency but these have not been institutionalized as yet in a way that accurately reflects this need, a point considered further below (Chapman and Shavit, 2010). Third, a major empirical contribution is the computation and presentation of repayment burden calculations well beyond what has typically been used in the literature, which has until now only reported ratios of repayments with respect to average graduate incomes (Ziderman, 2003), or hypothetically constructed illustrations of ratios for low income debtors (Baum and Schwartz, 2006; Schwartz and Finnie, 2002). Instead we use unconditional quantile regression to estimate repayment burdens across the entire range of debtor’s incomes by age, using actual rather than hypothetical data and with reference to the occupations of both lawyer and teachers. We find that a significant number of borrowers face very high repayment burdens at some stages during their working lives, with attendant consumption hardships and elevated default probabilities; this must impact upon educational and career choices. 4
See Di Carlo, Johnson and Cochran (2008). Their data has been adjusted for inflation in calculations of 2010 levels.
4 Our approach should be seen to be complementary to the analysis of Rothstein and Rouse (2007), which sets out to test directly the career choices/student debt nexus with reference to an unusual panel survey from a single higher education institution in the 2000s. A particularly useful contribution is the support found for the direct test of the proposition that students with higher levels of debt are more likely to undertake employment in jobs with relatively high starting salaries. The lack of similar studies highlights the value of the current exercise, since the evidence we are providing allows a generalization of the issues. The policy consequences are potentially profound. Prospective students expecting a combination of relatively high debts and low earnings might as a result decide to avoid college, or to choose jobs with higher projected earnings than are available in community or government sectors. Faced with these concerns governments might attempt to modify loan policies to take account of potential repayment burdens, such as with so-called income based repayment (IBR) arrangements for US college loans, which were extended in 2010. On this last issue a significant point with respect to the recent IBR reforms is that if repayment burdens are sufficiently important to call into question the basis of Stafford loans this constitutes a case for a future critical analysis of the right forms that income contingent collection might take. A critical secondary question is whether or not IBR is the correct direction for policy reform to take (see Chapman and Shavit, 2010).
I. Motivating Analysis of Repayment Burdens A. What Is a Loan Repayment Burden? Education economists and others have examined the concept and implications of student loan repayment burdens for more than a quarter of a century. 5 Defined simply in a comparative static context, a loan repayment burden is the proportion of a person’s income that needs to be allocated to service a debt per period, or, formally:
(1)
5
Repayment burden in period t =
Loan repayment in period t . Income in period t
See Woodhall (1987), Ziderman (1999), Schwartz and Finnie (2002), Salmi (2003) and Baum and Schwartz (2006).
5 There are several policy design issues usually raised with respect to repayment burdens. The first is motivated by the importance of difficulties faced by debtors in meeting their obligations, it obviously being the case that - in a world in which borrowing against expected future earnings is difficult 6 - the higher is a debtor’s repayment burden the less consumption and/or savings are possible at any given income. This is of importance in comparisons of different student loan policies: specifically, Stafford student loans are quite different to income contingent loans in this respect. This is due to the fact that the latter are explicitly designed to avoid high repayment burdens and this is achieved through per period debt servicing obligations being capped by legislation (Chapman and Lounkaew, 2010). 7 A second is that greater repayment burdens are associated with higher prospects that debtors will be forced to default on loan repayments because of low incomes. This issue is substantiated by the finding of Dynarski (1994) and Gross, Cekic, Hossler and Hillman (2009) that student loan defaulters in the US are much more likely to have low levels of income. Typically student loan schemes (such as Stafford loans) come with a government guarantee to cover the debts when a student defaults, 8 which means that taxpayers pay. An associated policy mechanism relates to the provision of interest rate subsidies on student loans, 9 which are presumably designed to diminish consumption hardship and default probabilities. Woodhall (1987) integrates these concerns by stressing that governments face an balancing act in the design of mortgage-type loan schemes. Specifically, ceteris paribus, the lower are interest rate subsidies the higher will be repayment burdens. The design complexities don’t end with this obvious trade-off because the lower are interest rate subsidies the greater is the prospect of default, with this adding to taxpayer contributions. Important research is provided by Shen and Ziderman (2009) which offers calculations of taxpayer interest rate subsidies for a large number of student loan schemes from many countries, and Schwartz and Finnie (2002) which presents repayment burdens for hypothetical debtors in the Canada Student Loans scheme. As well, Chapman, Lounkaew, Polsiri, Sarachitti and Sitthipongpanich (2010) illustrates taxpayer subsidies associated with
6
The issue of credit constraints is critical in understanding repayment burdens and is addressed in Rothstein and Rouse (2007) and Chapman (2006). 7 In the Australian income contingent college loan scheme, for example, the maximum percentage of taxable income of the debt that is repaid is 8 per cent per annum. 8 It is commonly understood that the commercial financing sector will not provide loans to students because of their lack of collateral in the event of default (Friedman, 1955; Barr, 2003; Chapman, 2006). 9 For recent analyses see Ziderman (2003) and Chapman and Lounkaew (2010).
6 the Thai Student Loan Fund. With this as policy background we now examine several empirical aspects of the debate. B. Repayment Burdens: How Much Is Too Much? Do we know what proportion of a debtor’s income repayment burdens should be limited to? A definition of what this means in practice is illusory, and different terms are used to imply similar debtor experiences. For example, Woodhall (1987) uses the term “manageable debt” and suggests that this depends “…partly on the level and pattern of graduates’ expected earnings, and partly on what students and society regard as a “reasonable” level of debt” (page 15). Second, Ziderman (1999) suggests that loan conditions need to be set so as “…to avoid imposing unduly harsh repayment burdens on borrowers…” (page 82). Third, Baum and Schwartz (2006) argues that the policy design issue is to avoid repayments which would “…impose too heavy a burden on young people leaving school.” (page 1). Clearly there is not an agreed definition for assessing what constitutes an excessive repayment burden, but there are nevertheless several different pointers for understanding what this might be in practice. The following provide useful indications of a range of views: (i)
“A rough yardstick, used in several countries, is that loan repayments should not exceed 8 to 10% of a graduate’s income, and that this should determine the maximum debt that students may incur” (Woodhall,1987, page 15); and
(ii)
Salmi (2003) notes that in Venezuala the government loan agency “…has established 15 per cent as the ceiling for monthly repayments.” (page 15), and goes on to suggest that “Experience shows that no repayment schedule can be sustainable when the monthly debt exceeds 18 per cent of income”.
The most comprehensive analysis is in Baum and Schwartz (2006), which refers to the socalled “8 percent rule”, a standard suggesting that “…students should not devote more than 8 per cent of their gross income to repayment of student loans.” (page 2). Their paper quotes an extensive literature in support, albeit recognizing the range of suggested boundaries. However, an obvious point is that if a person’s income is very high even a relatively high percentage of this income being used for loan repayment may not constitute a concern. Thus an important point is that if there is a consensus world-wide that it is undesirable for repayment burdens to be higher than, say, 8 – 18 per cent of a debtor’s income, because graduate earnings in the US are relatively high, Stafford repayment burdens could be
7 considered to be excessive at the highest point of the range, and in what follows we use a cutoff of 18 per cent. We stress that there remains no objective rule. C. Measuring Expected Incomes in Calculations of Repayment Burdens The denominator of equation (1), the per-period income received by student loan debtors, is critical to the exercise. An important point is that significant research so far has used very aggregate proxies of incomes, such as that received by graduates on average. Ziderman (2003), for example, in an analysis of the repayment burdens associated with the Thai Student Loan Fund, compared debt servicing obligations to the earnings of graduates using predictions from Thai earnings functions. From this Ziderman concludes that “The annual repayment burden in terms of annual income is very light, in the region of only 2-4 per cent annually” (page 83), and adds that “…the Thai student loan scheme is overly generous…which may be effortlessly repaid out of higher income received on courses of schooling.” (page 83). However, beyond average graduate earnings there are wide dispersions of income received by graduates, a fact highlighted by the relatively low explanatory power for these models. 10 Like many issues in economics, some of the most interesting empirical aspects concern the tail of the distributions. Chapman et al. (2010) analyse earnings distributions of Thai graduates and find that repayment burdens differ by extraordinarily high amounts; the range is between 1 per cent for the top 25 per cent of earners and 70 per cent for the bottom 10 per cent of earners. This is a significant point for what follows since we focus on the distributions of graduate earnings and what this means for our understanding of US repayment burdens. But before examining the data we model the conceptual bases of repayment burdens. II. Formal Analysis of Repayment Burdens A. A Two-Period Model Rothstein and Rouse (2007) and Field (2009) formulate utility maximizing frameworks concerning the impact of loan levels on career choices, but these models do not address directly the links between loan design, repayment burdens and career choices. To consider 10
For example, Chapman and Lounkaew (2010) found R2 of around 0.4 for Thai earning functions; a plethora of other earnings function studies typically explain no more than 20-30 per cent of the variance.
8 this and help motivate the empirical exercises we analyse repayment burdens using a twoperiod utility maximizing model; this highlights the importance of both interest rates and loan size in determining the welfare of borrowers. Following Lawrence (1995), the life-time welfare of a borrow is
(2)
W (c1, c2 , ) u c1 E U(c2 ) ,
where W (.) is the life-time welfare of a borrower; c1 and c2 are consumption in periods 1 and 2; and is the subjective rate of time preference. It is assumed that the utility function is concave, that is u (.) 0 and u (.) 0 , 11 and that the borrower enters tertiary education in period 1 financed by period 1 income, y1 , and a student loan of size l . We show below that the extent of repayment burdens will be influenced by interest rates, and in this context it is of policy relevance to note that it is common for student loan schemes to have built-in subsidies which take the form of less than full interest rates being charged for the whole period of the loan (Ziderman, 2003; Shen and Ziderman, 2009; Chapman and Lounkaew, 2010). 12 The interest rate subsidy s(r,T) can be formalized as follows:
(3)
s( r, T ) 1
T
t 1
e t Rt ( r, T )dt l
,
where l is the total loan disbursed; the government cost of borrowing is γ 0,1 ; r is the real rate of interest charged on the loan; T is the length of loan repayment; and Rt is the repayment required to service the loan at time t. With two periods and a fixed cost of borrowing to the government, interest rate subsidies can be expressed as a function only of the real interest rate charged. Thus, by simplifying equation (3), the amount of the loan recovered is:
To rule out corner solutions we impose the further restriction that u (0) . By adding administrative cost and defaults the total unrecoverable part of the loan we can compute what is called the hidden grant (Ziderman, 2003; Shen and Ziderman, 2009). Shen and Ziderman (2009) reports the hidden grant to range between -8 and 88 per cent for 44 loan schemes operated in 39 countries. 11 12
9
1 r l . 1
1 s ( r ) l 1
(4)
Let y1 be gross income in period 1 which is known to the borrower and y2 be the period 2 gross income with expected value and variance being given by E ( y 2 ) and 2 . Consumption in each period is constrained by disposable income: (5.1)
Period 1: c1 y1 l ;
(5.2)
Period 2: c2 y2 1 s(r) l .
Substituting (5.1) and (5.2) into (2) yields
(6)
W ( y1, y2 , , l, r) u1( y1 l ) E u2 ( y2 1 s(r) l ) . Equation (6) recasts the maximization problem in relation to income, the amount
borrowed to finance higher education, and the level of the interest rate subsidy. Applying a second order Taylor approximation around the mean of the expected utility function in the second period, 13 the life-time utility function can be approximated by:
(7)
1 W ( y1, E( y2 ), , l, r) u1 ( y1 l ) u2 ( E( y2 ) 1 s(r) l ) u2'' ( E( y2 ) 1 s(r) l ) 2 . 2
In summary, this section has modeled life-time welfare in the presence of student loans allows us to develop empirical predictions in a comparative static context.
B. Comparative Static Analysis of Repayment Burdens
Following equation (1), the repayment burden RBt is defined as the ratio between the repayments required and total income in period t: 13
The same technique has been employed by Padula and Pistaferri (2001), Hartog and Serrano (2003), and Migali (2006).
10
RBt
(8)
Rt ( r, T ) . yt
By normalizing total disposable income for each period by gross income in that period, equation (7) can be expressed as:
(9) W ( y1 , E ( y2 ), , l , r ) u1 (1
u1 (1
l 1 s( r ) l ) 1 u '' (1 1 s( r ) l ) 2 ) u2 (1 2 2 y1 E ( y2 ) E ( y2 ) 1 l ) u2 (1 RB ( r, E ( y2 ), l )) u2'' (1 RB( r, E ( y2 ), l )) 2 . 2 y1
Holding expected income in period 2 constant, a higher interest rate increases repayment burdens, and thus lower the life-time welfare of debtors. Taking the partial derivative of equation (9) with respect to the real interest rate charged on the loan, and dropping the third order derivative yields:
(10)
W(.) u (.) RB(r) 2 0. r RB r
The impact of a higher loan size on life-time welfare can be seen from equation (11). Partial derivative of the welfare with respect to the loan size shown in equation (11) reveals that the first term on the right hand side is positive and the total effect of the second term is negative, with the net effect depending on the relative gain through higher consumption in the first period and the utility cost from having less net income in the second period. A concave utility function implies that, for low income borrowers expecting to earn sufficiently high income in the second period, a higher loan size increases life-time welfare. For a borrower who expects period 2 income to be low, a higher loan size decreases life-time welfare because concavity the marginal disutility from lower net income in period 2 prevails over the welfare gain in period 1.
11
(11)
u1 (.) u2 (.) RB (.) 0 if l RB(.) l W (.) u1 (.) u2 (.) RB (.) u1 (.) u2 (.) RB(.) . 0 if l l RB (.) l l RB (.) l u1 (.) u2 (.) RB(.) 0 if l RB(.) l
An individual’s discount rate also plays an important part in determining the outcome. Two borrowers with the same income in period 1 with a similar period 2 income expectation, but with different subjective discount rates, value a higher loan size differently. A borrower who discounts the future more heavily may find increasing loan size to be welfare-improving, but those who place higher weight on future consumption will find the change to be welfaredecreasing. The model clarifies the relationship between repayment burdens and the life-time welfare of borrowers. Two important results emerge. First, holding constant loan size l, higher interest rates must increase repayment burden, and thus lower debtors’ welfare. Second, the effect of a higher loan size is ambiguous because while this increases first period welfare, it also lowers second period net income, with the net result depending on the relative effects on discounted utility in each period. C. Repayment Burdens and Career Choices Based on the insights from Rothstein and Rouse (2007), this section extends the model developed above by making explicit the relationship between expected repayment burdens and career choices in a world in which there are non-wage job attributes. We add to the model the value of amenities, denoted by a, which is the extra utility gained from working in a job that possesses attractive non-wage characteristics, such as a public service contribution. It is assumed that amenities are traded off with wages and can thus be scaled in dollars terms as forgone income, with the upper bound of the choice set being denoted by . This means that the job in period 2 which offers amenity level a2 will have a total salary of y 2 a 2 . To accommodate the role played by a trade-off between amenities and wages, Rothstein and Rouse (2007) assume that the post-university period can be broken down into two sub-
12 periods, with borrowers paying off the loan in the second period and thus able to use all income on consumption in a third period. The optimal rule for inter-temporal consumption dictates that borrowers adjust their consumption to the point at which expected marginal utility in the second period equals the expected discounted marginal utility of the third period. This can be stated as follows: (12)
E U 2 ( c2 , a2 ) E U 3 ( c3 , a3 ) .
Rothstein and Rouse (2007) show both formally and empirically that education debts matter for career choices if borrowers are credit-constrained, because credit constraints prevent borrowers from smoothing consumption between periods 2 and 3. The optimal consumption rule states that the expected marginal utility of consumption in period 2 after the debts have been repaid must equal the expected discounted marginal utility of consumption in period 3. Putting c2 y 2 1 s ( r ) a 2 1 s ( r ) and c3 y 3 a 3 into the Rothstein and Rouse optimality condition, the consumption rule can be written as follows:
(13)
E U 2 ( a2 1 s( r ) l ) E U 3 ( a3 ).
Normalizing each period by its income and using the definition of repayment burden discussed above, equation (13) can be written as:
(14)
E U 2 (1 RB ( r, y2 , l , a2 )) E U 3 (1) .
For the equality in equation (14) to hold, RB( r, y2 , l , a2 ) 0 . Since RB( r, y2 , l , a2 ) is increasing in a2, it follows that borrowers with high expected repayment burdens will choose a job with low amenity because of their need for higher income employment. The model predicts that, with credit constraints and a Stafford student loan, borrowers who expect to face high repayment burdens prefer low-amenity/higher wage private sector jobs. As will be illustrated empirically, the impact of repayment burdens on career choices is very significant for those with very high debts, such as lawyers, but can be important in other areas of study.
13 D. The Modeling Results and Empirical Analysis of Repayment Burdens This section developed a formal model to investigate the affect of repayment burdens on borrowers’ expected welfare. The model explains that repayment burdens diminish welfare through their reduction of net income available for consumption, meaning that higher repayment burdens make borrowers worse-off. Since repayment burdens are affected by both debt levels and expected incomes, the lower utility from this aspect of debt is expected for borrowers at lower levels of income distribution. A critical consequence of high repayment burdens is their affect on the career choices of credit constrained borrowers. The empirical prediction from the above is that debtors will be more likely to seek employment in which they can command higher incomes, at a cost to them of lower amenity. While this prediction cannot be tested directly, comparisons of repayment burdens between alternative career choices are indicative of borrowers’ likely choice sets. We can now demonstrate empirically the importance of these propositions for different cases – typical graduates and teachers, and both public sector and private sector lawyers – in aggregate and for different expected income distributions. III. Understanding Stafford Loans
A. Stafford Loan Rules There are two types of Stafford loans: subsidized and unsubsidized. 14
A subsidized
Stafford loan is available to students with assessed financial needs based on information concerning household family incomes. With subsidized loans the federal government pays the interest (as long as the student is enrolled at least half-time) with repayments beginning after a six-month repayment grace period following graduation. The second type of loan, unsubsidized Stafford, is available to all full-time students regardless of financial need, with the interest being capitalized during study and with a six-month repayment grace period after graduation. There are two principal repayment options for all Stafford loans. The first is a mortgagetype standard repayment plan under which the student is required to repay a constant nominal 14
Data from National Postsecondary Student Aid Study (2010) reveals that about 35 per cent of enrolled university students are the recipients of Stafford loans. About 60 per cent of this group receives unsubsidized Stafford.
14 amount per period. The other option is the graduated repayment plan, in which the repayment requirement increases step-wise every two years. For a debt of less than $30,000 both plans have a fixed repayment period of 10 years, but if the debt exceeds this amount the student qualifies for an extended repayment plan with a maximum period of 25 years. 15 Interest rates and the repayment conditions for Stafford Loans are shown in Table 1. TABLE 1−STAFFORD LOAN REPAYMENT CONDITIONS* Loan Subsidized Unsubsidized
Interest rate per annum
Grace period
Repayment
(per cent)
after graduation
period
Repayment plan
Enrolment
Repayment
(months)
(years)
Standard
0
5.6
6
10
Graduated
0
5.6
6
10
Standard
6.8
6.8
6
10
Graduated
6.8
6.8
6
10
*The interest rates are in nominal terms.
B. Stafford Debts: Levels and Repayments An essential aspect of the calculation of repayment burdens concerns the numerator of equation (1), the amount of money required to service the debt per period, and this will depend on the size of the loan, the interest rates imposed and the length of the repayment period. Our analysis assumes an average loan size in 2010 for a typical university graduate (called “All Graduates”) at to be approximately $20,000 per degree 16 and the same loan size is assumed for graduates working as teachers (called “Teachers”). Also, following Schrag (2007), the total debt of law graduates debt is assumed to be $100,000. Figure 1 illustrates repayment streams in real terms for the standard repayment plan for Unsubsidized Stafford loans with the debt levels assumed in this study. 17 While the
15
As well, Stafford loans charge a 1 per cent origination and a 1 per cent guarantee fee. There is also an upfront rebate of 1.5 per cent which means that the net disbursement is 99.5 per cent of the gross loan amount. The borrower must make the first 12 payments on time to retain the rebate. 16 This figure is based on the estimate provided by FinAid (2010). FinAid’s estimate is based on data from the National Postsecondary Student Aid Survey 2007-2008. From the data used in the study, Field (2009) estimates an average loan size to be $20,000. 17 Subsidized Stafford loan repayments of the same nominal level will be about 5 per cent per annum lower. Since the amount borrowed by law graduates exceeds the maximum limits of Subsidized Stafford, the repayment stream illustration combines both Unsubsidized and Subsidized Stafford.
15 repayment is fixed in nominal terms the real level of repayment declines as a result of CPI inflation which is assumed to be 3 per cent per annum. 18
Real $ per year 20,000 Debt=$20,000 (10‐year repayment)
18,000
Debt=$100,000 (10‐year repayment) 16,000 Debt=$100,000 (25‐year repayment) 14,000 12,000 10,000 8,000 6,000 4,000 2,000 0 1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 Year
FIGURE 1. INFLATION ADJUSTED REPAYMENT STREAMS IV. Methods
What follows describes the empirical methods employed in this study, which are used in an examination of two separate issues. The first is the probability that borrowers face difficult repayment burdens, defined as being equal to or in excess of 18 per cent. Second, we estimate the extent of repayment burdens for loan conditions defined above and for different assumptions lifetime earnings structures. Within this second category we examine ageincome profiles and distributions to measure the denominator of equation 1. A. Probability Distributions of Income In order to get a broad handle on the likely incidence of problematic repayment burdens the first part of the exercise involves the calculation of probabilities that a borrower will experience repayment burdens of at least 18 per cent in any given year. Several approaches are available to carry out this exercise, for example simple ratios, non-parametric density estimates and parametric density estimates. The parametric approach is chosen because it is a standard tool exercises of this nature (Cowell, 2000). 18
We employ the Singh-Maddala
This is approximately the 15 year average of the US inflation rate (Bureau of Labor Statistics, 2010).
16 distribution to approximate the income distribution of the borrowers’ cohort given that this calibration distribution outperforms lognormal and gamma distributions in approximating skewed income distributions (Singh and Maddala, 1976; McDonald and Ransom, 1979; McDonald, 1984). The function takes the form:
(15)
1 F ( x) 1 1 x b
b
. a
where a≥0, b≥0, q>1/a are parameters for random variable x, in this case income. The shape of the distribution is determined by parameters a and q, while parameter b scales the distribution. By denoting z=1+(x/b)a, the distribution function can be written as F(x)=1-z-q; the corresponding probability density function is then:
(16)
b z
f ( x ) aq
( q 1)
( x )( a 1) . b
B. Income Functions and Age-Income Profiles For calculations of expected repayment burdens we need to estimates of expected graduate income paths, and for this we use variants of the standard earnings function of the following form: (17)
l nI ij =β0j +β1jexperienceij +β 2jexperienceij2 +ε ij ,
where i 1, 2, 3,..., n represent individuals; j = all graduates, teachers, public and private sector lawyers; I i is the sum of annual earnings, social security payments and unemployment insurance payouts of individual i, differentiated by sex; potential experience is defined as: (18) Experience = age - time to complete a degree/dropout – age at which schooling begins The unconditional quantile regression (UQR) technique is employed to estimate earnings functions, with this technique being chosen to address the shortcomings associated with the
17 use of OLS, in two senses. The first is that OLS estimates the mean value conditional on the distribution of the dependent variable, with a concern arising if the conditional distribution of dependent variable is skewed, asymmetric, and/or does not have a unique mode. Using OLS estimates may not give robust results, this problem being common in the context of wage determination given the asymmetry in wage distributions. 19 A second attractive feature of (and the most important reason for us to use) unconditional quantile regression is that it provides a disaggregated picture of income distributions. This advantage is crucial to our analysis of student loans since repayment burdens must be highest for those in the lowest parts of the income distribution (Chapman and Lounkaew, 2010; Chapman et al., 2010), a feature which cannot be captured by the use of standard OLS. Thus we estimate age-income profiles for the 25th, 50th (median) and 75th quantiles of income distributions by age, with separate estimations being carried out for males and females. 20 Our unconditional quantile regression method follows Firpo, Fortin, and Lemieux (2009), a technique which relies on a transformation known as re-centered influence function (RIF). The RIF for the quantile of interest q is
(19)
RIF ( I ; q ) q
D( I q ) f I q
,
where f I . is the marginal density function of I where D is an indicator function. In practice RIF ( I ; q ) is not observed, hence its sample counterpart is used instead:
(20)
RIF ( I ; qˆ ) qˆ
D ( I qˆ ) fˆI q
,
where qˆ is the sample quantile and fˆI q is the kernel density estimator, with this transformed variable being used in place of the original dependent variable. One crucial distinguishing feature of the UQR is that it provides us with a way to recover the marginal impact of the regressors on the unconditional quantile of I; in the context of this study it is the
19
Many recent studies have used disaggregated approaches to analyse wage distribution and wage determination (Buchinsky, 1994; Machado and Mata, 2001). Firpo, Fortin, and Lemieux (2009) uses unconditional quantile methods in a detailed exploration of wage distributions. 20 These profiles have been adjusted using OLS standard errors (see Wooldridge, 2006).
18 marginal impact of additional years of potential experience on income of each income quantile. Usual inference procedures of the OLS are also applicable to the UQR estimates. V. Data and Results
Statistical description of the data now follows with estimates of income distribution and the probabilities that a borrower experiences repayment hardships are reported in the second subsection. We then illustrate the levels of average and median repayment burdens for borrowers followed by disaggregated analyses of repayment burdens. The penultimate section examines the repayment burden of the extreme case of lawyers whose debts reach the life-time limit of Stafford loans.
A. The CPS Data Data used to estimate graduate and teacher age-earning profiles are from the Current Population Survey March Supplement 2009. However, a single CPS does not contain sufficient observations for law graduates and we therefore pool law graduates’ data from four March data sets: 2005, 2007, 2008, and 2009. 21 The income information in the early year data sets have been adjusted by wage inflation of 3 per cent per annum 22 to obtain their 2010 values. The CPS data contain information concerning sex, income, age, education, and employment status. Since we are interested in the calculation of repayment burdens of borrowers generally the age-income relationships are considered irrespective of employment. Two groups of individuals have been omitted, the self-employed and individuals who are studying; the former because it is difficult to determine their incomes with any precision, and the latter because members of this group are not required to repay student loans (if they are studying at least half-time). Descriptive statistics of the data are reported in Appendix A.
21
We exclude the 2006 data due to some data interpretation problems. When the 2006 data are pooled with the data in 2007 to 2009 some of the age-income profiles do not exhibit a regular empirical pattern of downward concavity, the cause of which is unclear; using the 2005 data, the age-income profiles behave as they are expected to. 22 This is roughly the average of wage inflation in the period 1995-2009.
19 B. Calculating the Probability of Repayment Hardships What are the probabilities that borrowers are likely to experience hardships as a result of high repayment burdens? This is addressed by combining the calculations of loan repayments reported in Section III (as illustrated in Figure 1) with approximations of income distributions using the Singh-Maddala approach. Essentially we are presenting probabilities that young graduates will experience loan servicing difficultie defined as having repayment burdens equal to or in excess of 18 per cent. Males PDF 0.00003
0.000025
0.00002
0.000015
0.00001
0.000005
0 0
18,400
37,000
55,250
74,000
92,750
111,500
130,250
149,000
Annual income ($2010)
Females PDF 0.00003
0.000025
0.00002
0.000015
0.00001
0.000005
0 0
18,400
37,000
55,250
74,000
92,750
111,500
130,250
149,000
Annual income ($2010)
FIGURE 2. PROBABILITY DISTRIBUTIONS OF MALE AND FEMALE GRADUATE INCOMES (AGED 22-25)
20 For the denominator of Equation 1 we analyse income distribution data separately for males and females, and with respect to all graduates, teachers and all lawyers. 23 We assume that borrowers use the standard 10-year repayment plan, and borrowers are assumed to begin a four year degree at age 18 and graduate in the minimum time. For illustrative purposes a subset of the data is presented in Figure 2, the probability distributions of income for all male and female graduates aged 22 to age 25. TABLE 2−PROBABILITIES OF EXPERIENCING HIGH REPAYMENT BURDENS Income Borrower
Years of Repayment After Graduation
Cutoff Debt
(PA)
($)
($)
1-2
3-4
5-6
7-8
9-10
Male:
All graduates
20,000
≤15,400
0.43
0.23
0.13
0.09
0.08
Teachers
20,000
≤15,400
0.64
0.27
0.09
0.08
0.04
100,000
≤108,250
0.81
0.69
0.66
0.57
0.44
100,000
≤46,333
0.30
0.25
14.6
0.07*
0.00*
All graduates
20,000
≤15,400
0.49
0.27
0.19
0.29
0.18
Teacher
20,000
≤15,400
0.47
0.29
0.18
0.17
0.15
All lawyers
100,000
≤108,250
0.82
0.75
0.70
0.69
0.62
100,000
≤46,333
0.45
0.30
0.26
0.16
0.20
All lawyers (Standard) All lawyers (Extended) Female:
(Standard) All lawyers (Extended) * We only calculate the proportion for the first 10 years of the extended repayment plan.
As noted, and based on the literature reported in Section I, we use an 18 per cent repayment burden as the cut-off to calculate the proportion of borrowers classified as experiencing repayment hardships. To clarify our approach, the repayment requirement for a 23
There are insufficient data points for lawyers aged 22 to 31 to allow a disaggregation between those working in the public and private sectors. We are able to achieve this breakdown in analyses following of repayment burdens.
21 debt size of $20,000 is about $230 per month or $2,762 per annum and for this debt there will be a repayment burden of at least 18 per cent when a borrower’s annual income is less than $15,400. The probabilities of experiencing high repayment burdens are shown in Table 2. Under our debt assumptions and repayment hardship definition the most important results are as follows: (i)
The proportion of graduates whose incomes are at or below the cutoff is about 4349 per cent in the first two years after graduation, but decline subsequently to around 8-18 per cent in the last two years of repayment;
(ii)
About 47-64 per cent of teachers are expected to experience repayment hardships in their first two years after graduation, a figure which falls to about 4-15 per cent by the last two years of repayment;
(iii)
Due to the assumption of very high debts, and even given their relatively high incomes, the probability that law graduates using the standard repayment plan experience repayment hardships is about 80-82 per cent in the first two years after graduation, (about 40 percentage points more than for all graduates with average debt);
(iv)
Even for the last two years of repayment, the proportion is still around 44-62 per cent for lawyers for standard repayments, which is about 4 to 5 times higher than is the case for a typical graduate; and
(v)
The extended repayment arrangement (borrowers with debts exceeding $30,000 are able to extend their repayment to a maximum period of 25 years) reduces the proportion of law graduates estimated to experience repayment difficulties to 3035 in the first two years after graduation and by the last two years of repayment, the proportion falls to zero for males and to about 20 per cent for females.
C. Repayment Burdens: The Use of Aggregate Analysis The results reported above show an important aspect of the incidence of repayment burdens, the probability that graduates on average are likely to experience difficulties in meeting loan obligations. While this aspect of the exercise is very instructive, it does not show the level of repayment burdens experienced. There are two quite distinct approaches in an illustration of repayment burden levels, aggregated and disaggregated. As argued above much of the literature has focused on very broad calculations of repayment burdens, and this is where we begin.
22 Males Annual income ($2010) 400,000 All Graduates
Teachers
Public Sector Lawyers
Private Sector Lawyers
350,000 300,000 250,000 200,000 150,000 100,000 50,000 0 22
24
26
28
30
32
34
36
38
40
42
44
46
48
50
52
54
42
44
46
48
50
52
54
Age
Females Annual income ($2010) 400,000 All Graduates
Teachers
Public Sector Lawyers
Private Sector Lawyers
350,000 300,000 250,000 200,000 150,000 100,000 50,000 0 22
24
26
28
30
32
34
36
38
40
Age
FIGURE 3. MALE AND FEMALE OLS AGE-INCOME PROFILES This section considers average, and median, repayment burdens associated with the standard repayment plan 24 with respect to four groups of borrowers: all graduates, teachers, and law graduates working in the private and public sectors. Based on the income functions discussed in the previous section, we construct expected lifetime profiles separately for male and female for all graduates, graduates working as teachers, and law graduates. In addition, since career choices of law graduates are central to the policy issue it is instructive to compare the income paths of private and public sectors lawyers. Figure 3 reports age-income profiles for graduates derived from OLS estimates of the earning functions. 24
Less than 6 per cent of borrowers choose to use graduated repayment (Choy and Carroll, 2006).
23 Investigations reveal that repayment burdens do not differ importantly between the Unsubsidized and Subsidized Stafford loans. As a result discussion in the ensuing section focuses only on the repayment burdens associated with Unsubsidized Stafford loans. Average repayment burdens for average (OLS) and median income groups are shown in Table 3. TABLE 3−AVERAGE AND MEDIAN REPAYMENT BURDENS* Borrowers
*
Debt
Male
Female
level
Average
Median
Average
Median
All graduates
$20,000
0.07
0.04
0.09
0.05
Teachers
$20,000
0.11
0.06
0.12
0.06
Private sector lawyers (Standard)
$100,000
0.11
0.10
0.12
0.11
Public sector lawyers (Standard)
$100,000
0.22
0.16
0.29
0.21
Private sector lawyers (Extended)
$100,000
0.06
0.05
0.06
0.06
Public sector lawyers (Extended)
$100,000
0.11
0.09
0.15
0.11
We only report the repayment burdens for the first 10 years of the extended repayment plan.
The major findings are as follows: (i)
Graduates’ average and median repayment burdens are around 7-9 and 4-5 per cent, which should be considered to be low and unproblematic;
(ii)
Average and median teachers’ repayment burdens are around 11-12 and 6 per cent;
(iii)
Private sector lawyers under the standard plan have repayment burdens of the order of 10-12 per cent for males and females;
(iv)
However, the average and median repayment burdens under the standard repayment plan for public sector are as high as 16 to 22 per cent for males, and 20-30 per cent for females; and
(v)
The repayment burdens are reduced by half when the lawyers are placed under the extended repayment plan.
Overall the results do not reveal that repayment burdens are a serious problem, even when the debt is high, with the exception of public sector lawyers under the extended repayment plan. This, however, is not the case when patterns of repayment burdens and income asymmetry are taken into account. One of our most important contributions is to take these two elements into account and the following subsections illustrate empirically how both age
24 and income distributions critically affect our understanding of the importance of repayment burdens for quite different groups of graduates.
D. The Real Situation of Repayment Burdens: Disaggregate Analysis A major contribution of our exercise is to illustrate the great importance of disaggregated analyses of the data. Indeed, we contend that it is not possible to understand the breadth of the US loan repayment burden issue outside this context. Since standard repayment imposes the same repayment throughout the repayment period, the associated repayment burden is usually higher at the beginning of the period and declines as incomes rise. Critically, and in addition, individual repayment burdens depend on where borrowers lie in the income distribution. This is the reason that we now use unconditional quantile regressions of the ageincome profiles. 25 In section IIC we illustrated formally the effect of repayment burdens on occupational choice, relationships driven by the trade-offs inherent between salary and non-salary components of remuneration. While we are unable to test this directly, it is relatively straightforward to calculate differences in repayment burdens both between jobs, as done above in aggregate, and within job categories. Unconditional quantile regressions are well suited to this task because they allow comparisons of repayment burdens for distributions of incomes at given ages for different job classifications. There are however, several limitations of the approach, one being the requirement for simplicity to limit the number of quantiles. We have chosen to use a very simple disaggregation into three income quantiles only: the 25th (low), the 50th (medium) and the 75th (high). This has the implication of under-representing repayment burdens for those with very low incomes (less than the 25th quantile) and over-representing the repayment burdens for those with very high inomces (greater than the 75th quantile). There are two steps to the process. First, we estimate unconditional quantile regressions for males and females with respect to: all graduates; teachers; private sector lawyers and public sector lawyers. To provide an illustration of the results Figure 4 shows age-earnings profiles by quantiles for all graduates. 26
25
The unconditional quantile estimates of the earning functions are shown in the Appendix B. Illustrations of the age-income profiles for the remaining groups of borrowers are available from the authors. 26 The other quantile regressions results are available from the authors.
25 Males Annual income ($2009) 300,000
Q25
Q50 (Median)
Q75
250,000
200,000
150,000
100,000
50,000
0 22
24
26
28
30
32
34
36
38 Age
40
42
44
46
48
50
52
54
Females Annual income ($2009) 300,000
Q25
Q50 (Median)
Q75
250,000
200,000
150,000
100,000
50,000
0 22
24
26
28
30
32
34
36
38 Age
40
42
44
46
48
50
52
54
FIGURE 4. MALE AND FEMALE GRADUATES’ UNCONDITIONAL QUANTILE AGEINCOME PROFILES The main points from the quantile regressions are: (i)
For both males and females graduate incomes at the 25th quantile are about 60 per cent of the median income, and incomes at the 75th quantile are about 40 per cent higher than median incomes;
(ii) Teachers with income at the 25th quantile earn about 75 per cent of median teacher income, and incomes for teachers at the 75th quantile are about 20 per cent higher than teachers’ median incomes;
26 (iii) The median income of male teachers is about 40 per cent lower than the median income of all male graduates, and female teacher median incomes are 20 per cent lower than the median income of all female graduates; (iv) The median incomes of both male and female law graduates working in the private sector are both about 70 per cent higher than the median incomes of law graduates working in the public sector; (v) Law graduates working in the private sector at the 25th quantile receive incomes which are 60 per cent lower than the median incomes for this group. Incomes at the 75th quantile are about 60 per cent higher than median income for this group of law graduates; and (vi) Law graduates working in the public sector at the 25th income quantile receive about 70 per cent of the median income of this group. Incomes at the 75th quantile are about 40 per cent times higher than their median income. The second step in the process involves the calculation of repayment burdens for all age and sex income quantiles computed for each job, using the loan obligations presented in Section IIIB and employed to illustrate the aggregate burdens shown in Section VC. There are several ways to present these results, and a graphical example shows what the repayment burdens look like for all job groups at the 25th income quantile (Q25). We have chosen this part of the distribution since it is at Q25 that the burdens are at their highest. From Figure 5 it can be seen that repayment burdens decline with age, which is a result of a combination of higher incomes with age and falling per period loan servicing obligations in real terms. The most significant points apparent from the Figure are: (i)
For young low income graduates, irrespective of job, repayment burdens are around or above our cut-off of difficulty of 18 per cent (at the lowest they are 1314 per cent for female graduates in aggregate and teachers, and 16-20 per cent for comparable males);
(ii)
The repayment burdens for low income public sector lawyers using the standard repayment plan are extremely high, at around 60 and 77 per cent for males and females; and
(iii)
Repayment burdens for low income private sector lawyers using the standard repayment plan are much lower than is the case for the public sector, but are still very high at over 40 and 30 per cent for males and females.
27 Males Repayment burdens 1.0 All Graduates
Teachers
Private Sector Lawyers
Public Sector Lawyers
0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 1
2
3
4
5
Year
6
7
8
9
10
9
10
Females Repayment burdens 1.0 All Graduates
Teachers
Private Sector Lawyers
Public Sector Lawyers
0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 1
2
3
4
5
Year
6
7
8
FIGURE 5. REPAYMENT BURDENS FOR LOW INCOME BORROWERS (25th QUANTILE) Highly disaggregated results are shown in Table 4 which has columns for the maximum burden per year as well as the annual average experienced in the assumed loan servicing period.
28 TABLE 4−REPAYMENT BURDENS BY INCOME QUANTILEa Borrowers
Income quantile
Male Maximum
Female b
Average
c
Maximumb
Averagec
25th
0.16*
0.09
0.13
0.08
50th
0.07
0.04
0.07
0.05
75th
0.04
0.03
0.05
0.03
25
0.20**
0.11
0.16*
0.11
50th
0.09
0.06
0.07
0.06
75th
0.07
0.05
0.06
0.04
Private sector
25th
0.43**
0.21**
0.32**
0.19**
lawyers
50th
0.16*
0.10
0.16*
0.11
All graduates
Teachers
th
th
(Standard)
75
0.11
0.07
0.11
0.07
Public sector
25th
0.60**
0.31**
0.77**
0.39**
lawyers
50th
0.24**
0.16**
0.34.**
0.21**
(Standard)
75th
0.15
0.11
0.21**
0.14
Private sector
25th
0.25**
0.12
0.19**
0.12
lawyers
50th
0.10
0.06
0.09
0.07
(Extended)
75th
0.07
0.04
0.07
0.04
Public sector
25th
0.38**
0.19**
0.46**
0.23**
lawyers
50th
0.16*
0.10
0.21**
0.13
0.10
0.07
0.13
0.08
(Extended)
th
75
a
Debt level is $20,000 for typical graduates and teachers; $100,000 for lawyers.
b
Refers to the highest repayment burdens in any one year after graduation.
c
We only report the average repayment burdens for the first 10 years of the extended repayment plan.
* Repayment burden exceeds 15 per cent. ** Repayment burden exceeds 18 per cent.
There are several additional important points from the data of Table 4: (i)
For graduates and teachers at the median and 75th quantiles, repayment burdens do not pose serious problems since at their maximum they are only 7 per cent;
(ii) Lawyers with median income under the standard repayment plan still face burdens of 19 to 35 per cent, which exceeds the 18 per cent difficulty benchmark; (iii) For lawyers using the extended repayment plan the maximum repayment burdens fall by about 45 per cent. Yet for lawyers in Q25 the burdens remain very high, from
29 25 to 38 per cent for males in the private and public sectors, and 19 to 46 per cent for females in the private and public sectors. E. Illustrating the Extreme Repayment Burden Case: Public Sector Lawyers This final empirical section considers the extreme situation in which the amounts borrowed have reached the Stafford life-time limit of $138,500, a real situation for lawyers graduating from a high cost private university (Schrag, 2007). The repayment burdens are reported in Table 5 for different types of lawyers under both the standard and extended repayment plans. TABLE 5. REPAYMENT BURDENS OF LOW INCOME LAWYERS WITH MAXIMUM DEBT* Borrowers
Repayment
Male
Female
plan
Maximuma
Averageb
Maximuma
Averageb
Private sector lawyers
Standard
0.49**
0.25**
0.38**
0.23**
Public sector lawyers
Standard
0.76**
0.38**
0.93**
0.47**
Private sector lawyers
Extended
0.29**
0.15
0.23**
0.14
Public sector lawyers
Extended
0.46**
0.23**
0.56**
0.28**
We only report average repayment burdens for the first 10 years of the extended repayment plan. * Repayment burden exceeds 15 per cent. ** Repayment burden exceeds 18 per cent.
It is quite clear from Table 5 that the repayment burdens faced by high-debt lawyers on the standard repayment plan and with low incomes greatly exceed the 18 per cent benchmark, and they are as high as 76-93 per cent the case of public sector lawyers, and 38 to 49 per cent for those in the private sector. Repayment burdens for lawyers in the extended repayment plan fall by about 40 per cent, but are still as high as 46-56 per cent for those in the public sector, and even as high as 23-30 per cent for those in the private sector. The lowest calculation or burdens for low income lawyers is the average annual obligation of 14-15 per cent for those in the private sector, and even this relatively benign calculation is very close to our benchmark of difficulty of 18 per cent.
30 F. Discussion of the Findings The previous two sections have illustrated the importance of income paths and income distributions in determining repayment burdens. Analysis based on average (or median) income show modest burdens only, but they do not capture the hardships faced by graduates with low incomes. The more interesting quantile regression analysis shows very marked differences to the aggregated situation, and in some cases the repayment burdens are extremely high indeed. It follows that some groups of graduates face repayment burdens which are so harsh that they must be deterred from pursuing less well-paid jobs, such as teaching, and the story is extremely obvious with respect to public sector lawyers. VI. Conclusion
There are profound problems associated with US student loans policy which can be traced in large measure to the expected difficulties faced by many students in repaying their debts. While so-called “repayment burdens” are examined in the student financing literature we have extended the analyses through a formal modeling approach in the context of career choices. As well, we have analyzed very broad ranges of expected lifetime earnings distributions by job and this has provide new insights into the meaning and importance of repayment burdens. There are several important findings from these broadly-based empirical applications. The most important and obvious of these in concept are that anticipated repayment burdens are a function of loan size, interest rates, expected incomes and students’ time preferences. In empirical terms it can be shown that a significant proportion of student debtors can expect to face repayment difficulties in a situation in which many assess with accuracy the probability that they will experience labor market situations that place them in the lowest parts of the graduate earnings distributions. We show also that there are critical differences in the impact of repayment burdens associated with career choices: in particular, public sector lawyers are likely to be in situations in which anticipated repayment burdens are such as to make this type of employment quite difficult in material terms and, thus for many, undesirable. It follows that occupational choices will be influenced, perhaps critically, by the design of student loans. The conceptual modeling and the empirical results suggest that typical student loan schemes which require set repayments on the basis of time, such as Stafford loans, are
31 inevitably compromised because of their lack of capacity to take into account the future financial situation of student debtors. Income contingent loan schemes, now in operation in many OECD countries, avoid these problems because repayment burdens have maximum repayment levels set as parameters. It is not a surprise that there have been attempts to move the US student loan systems towards income contingent collection, but it is still an important question as to whether the current compromises in this direction are sufficient to address what is required (Chapman and Shavit, 2010). Our modeling has several limitations. One is that, apart from with respect to lawyers, we have not as yet explored repayment burdens for Stafford loan users with extremely high debt levels, and there is little doubt that the problems raised in our analysis are significantly understated for a small group of potential students. Two, while our use of unconditional income quantiles is a major improvement over the use of either average graduate earnings or hypothetical income scenarios, so far we have focused on cross-sectional data only. An improved way to proceed would be the use of panel earnings information which allows a relaxation of the implicit restriction inherent from cross section data that individuals remain in the distributions imposed by point-in-time methods.
32 APPENDIX A DESCRIPTIVE STATISTICS Variable
Male
Female
Mean
S.D.
Mean
S.D.
73,249
64,562
44,575
39,543
40.5
10.2
39.7
10.4
University graduate (Age 22-60)
Total annual income ($) Age
8,009
N
8,986
Teacher (Age 22-60)
Total annual income ($) Age
42,691
19,707
33,823
21,229
38.6
10.3
39.8
10.7
378
N
1,332
Law graduate (Age 25-54)
Total annual income ($) Age N
165,153
132,518
124,771
112,984
40.6
7.9
38.1
7.8
755
494
33 APPENDIX B TABLE B1−INCOME FUNCTIONS FOR ALL GRADUATES Male Variable Constant Experience 2
Experience R2
Female
OLS
Q25
Q50
Q75
OLS
Q25
Q50
Q75
9.6931**
9.5036**
10.2779**
10.8545**
9.4754**
9.5852**
10.1695**
10.5199
(0.0501)
(0.0404)
(0.0219)
(0.0176)
(0.0554)
(0.0469)
(0.0203)
(0.0166)
0.1260**
0.1188**
0.0827**
0.0586**
0.0800**
0.0560**
0.0461**
0.0462
(0.0060)
(0.0045)
(0.0028)
(0.0027)
(0.0069)
(0.0057 )
(0.0026)
(0.0025)
-0.0028**
-0.0026**
-0.0017**
-0.0012*
-0.0017**
-0.0012**
-0.0010**
-0.0009
(0.0002)
(0.0001)
(0.0001)
(0.0001)
(0.0002)
(0.0001)
(0.0001)
(0.0001)
0.0624
0.1023
0.1003
0.0589
0.0207
0.0158
0.0421
0.0397
N
*Significant at 10 per cent level of confidence **Significant at 5 per cent level of confidence
8,009
8,986
34 TABLE B2−INCOME FUNCTIONS FOR TEACHERS Male Variable Constant Experience Experience2 2
R
Female
OLS
Q25
Q50
Q75
OLS
Q25
Q50
Q75
9.4810**
9.5020**
10.2867**
10.6173**
9.2372**
9.5200**
10.2973**
10.5670**
(0.1604)
(0.1325)
(0.0562)
(0.0462)
(0.1374)
(0.1606)
(0.0436)
(0.0332)
0.1198**
0.1084**
0.0444**
0.0235**
0.0882**
0.03991**
0.0176**
0.0104**
(0.0199)
(0.0156)
(0.0077)
(0.0074)
(0.0172)
(0.0196)
(0.0055)
(0.0047)
-0.0027**
-0.0024**
-0.0009**
-0.0003
-0.0019**
-0.0007
-0.0003**
-0.00003
(0.0005)
(0.0004)
(0.0002)
(0.0002)
(0.0004)
(0.0005)
( 0.0001)
(0.0001)
0.0977
0.1470
0.1036
0.0869
0.0246
0.0072
0.0197
0.0359
N
*Significant at 10 per cent level of confidence **Significant at 5 per cent level of confidence
378
1,332
35 TABLE B3−INCOME FUNCTIONS FOR PRIVATE LAWYERS Male Variable Constant Experience Experience2 2
R
Female
OLS
Q25
Q50
Q75
OLS
Q25
Q50
Q75
10.9981**
10.2872**
11.2403**
11.5833**
10.9778**
10.4344**
11.1319**
11.5004**
(0.1204)
(0.1780)
(0.1253)
(0.1286)
(0.1583)
(0.1913)
(0.1527)
(0.1335)
0.1067**
0.1409**
0.0633**
0.0829**
0.0612**
0.0759**
0.0396
0.067**
(0.0175)
(0.0242)
(0.0188)
(0.0217)
(0.0254)
(0.0284)
(0.0247)
(0.0251)
-0.0026**
-0.0036**
-0.0012*
-0.0020**
-0.003
-0.0017*
-0.0004
-0.0014
(0.0006)
(0.0007)
(0.0006)
(0.0007)
(0.0009)
(0.0009)
(0.0008)
(0.0009)
0.1114
0.0964
0.0714
0.0383
0.0468
0.0475
0.0468
0.0392
N
*Significant at 10 per cent level of confidence **Significant at 5 per cent level of confidence
549
345
36
TABLE B4−INCOME FUNCTIONS FOR PUBLIC SECTOR LAWYERS Male Variable Constant Experience Experience2 R2
Female
OLS
Q25
Q50
Q75
OLS
Q25
Q50
Q75
10.5226**
10.0043**
10.8945**
11.3628**
10.0732**
9.7264**
10.5163**
10.990**
(0.1495)
(0.1634)
(0.1217)
(0.0987)
(0.3100)
(0.2343)
(0.1654)
(0.1290)
0.1003**
0.1350**
0.0691**
0.0396**
0.1237**
0.1365**
0.0770**
0.06502**
(0.0211)
(0.0218)
(0.0191)
(0.0177)
(0.0454)
(0.0314)
(0.0261)
(0.0273)
-0.0024**
-0.0032**
-0.0016**
-0.0007
-0.0026*
-0.0030**
-0.0013
-0.0010
(0.0006)
(0.0007)
(0.0006)
(0.0006)
(0.0014)
(0.0009)
(0.0008)
(0.0010)
0.1830
0.2088
0.0928
0.0687
0.1260
0.2507
0.1892
0.1242
N
*Significant at 10 per cent level of confidence. **Significant at 5 per cent level of confidence
189
134
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