3 The Contribution of Debt Aversion to Lower University Participation Rates among
3.3 Theoretical Model – Defining Debt Aversion
In his work on loans and grants for university participation in Canada, Finnie (2005) defines debt aversion as “situations where individuals are unwilling to take out loans to finance their post-secondary schooling even though they know the schooling represents a good investment and it could be facilitated by the loans in question”. He identifies three distinct kinds of debt aversion. These are:
1. Value-based debt aversion (owing/borrowing money is wrong) 2. Risk-based debt aversion (e.g. concerns about ability to repay)
3. Sticker price debt aversion (expected total debt to be incurred seems “excessive”)
Value based risk-aversion is related to personal, religious, class-based or other culture-related values. Risk-aversion is unlikely to pose as much of an issue in the UK, given the present system of student loans repayment out of wages post-graduation and only when wages are above a certain threshold, with outstanding debt being cancelled after a certain number of years. Sticker price debt aversion is likely to become more of an issue in coming
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years, due to increases in the fee cap. This kind of debt aversion is also related to information as studies have shown that students and their families (especially those from lower incomes backgrounds) tend to overestimate the debt that is likely to be incurred (Burdman, 2005).
In this section, I present a simple mathematical model that extends the traditional model of university participation choice in human capital theory (for example as presented in Borjas, 2001) to include debt aversion, based on the idea that people will not make their choice by comparing expected income streams absolutely, but rather their interpretation (perception, evaluation) of these income streams, and that they derive different utility from positive and negative assets of the same absolute value. This model draws on insights presented in Tversky and Kahneman (1992) regarding prospect theory and the way that people treat losses and gains differently.
In human capital theory, education is seen as an investment that is made in order to generate returns at a future point in time, in much the same way that investments in physical capital generate profits for companies. The decision regarding whether or not to participate in university will depend on the costs involved (including opportunity costs) and the expected future returns. It is often represented by a simple graph, as per the below:
Figure 3-1: Lifetime Earnings of a Graduate / Non-Graduate
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This graph depicts two income streams. One is the income stream of a secondary school graduate who does not progress to university, but rather starts working straight after secondary school. He enjoys a positive income stream for the whole period displayed and sees this rise slightly year by year. The other income stream is that of a person who decides to undertake a university degree. This person’s earnings are negative for the first few years (however long it takes him to complete the degree) due to fees and other direct costs. He also forgoes the earnings he would have had from working. However, after graduation, his earnings are higher than the other person and also increase faster. The decision to participate or not is made by weighing up the direct and opportunity costs incurred while studying against the present value of the additional earnings enjoyed from the point of graduation until retirement.
Describing this in equations, let the earnings at a given point in time for the person who attends university be given by Euni where
(3.1)
and ( ) = − − (for example) (3.2)
and the earnings of the person who does not attend university be given by Enouni, where
= √ (for example) (3.3)
-d is the amount of debt the person incurs at each year of university for fees (the direct costs of university attendance). d may be different for each individual depending on their access to credit or if there are differential fees for different courses/ institutions. Living expenses (which they would have incurred either way) are represented by the opportunity cost of what they would have earned if working – in reality, the student will need to make up these costs through grants or bursaries, taking out a student loan or a bank loan, relying on their family, working part-time, using their own personal savings, or some combination of these. tG represents the point where the
0 ( ) G uni G d t t E W t t t
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person graduates. W(t) is the graduate’s wage path and P and Q represent individual ability, which affects how much the person earns.
Assuming for simplicity that there is no consumption, the net present value of the persons total lifetime earnings are defined as A (assets). The person who decides to study will have negative assets while they are at university and for a period after this until their debt is paid off, namely .
To allow for different perceptions of assets in periods where the person is in the red / in the black, I define
(3.4) and
(3.5) Integrating the earnings profile gives us an assets profile similar to the graph below:
Figure 3-2: Lifetime Earnings and Assets of a Graduate / Non-Graduate
Source: own representation
This can be represented by the following equations: 0 B t R t A
E B T B t A
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The net present value of the total lifetime earnings of the person who attends university is given by Auni where
(3.6)
or (3.6b)
and assuming, once again for simplicity, that debt is only incurred for the purposes of studying, the total lifetime assets of the person who does not attend university are given by Anouni where
= ∫ = ∫ √ (3.7)
where δ represents the persons discount rate, including interest rate and time preferences.
The contribution of this model is to illustrate the effect of the person’s
interpretation of assets gained under the two income streams on the
university participation decision. People will not base their decision solely on the comparison of Auni and Anouni, but rather on their interpretation of these amounts, i.e on U(Auni) and U(Anouni).
It is not necessary to fully define the utility function, however, the following assumptions are made concerning U(A):
a) U(0) = 0
b) U(A) is increasing in A
Debt aversion can be said to mean that the negative utility associated with a debt will be greater than the positive utility associated with an asset of the same absolute value as the debt. As such, it is defined as associating a greater absolute value of utility to negative amounts than to the equivalent positive amount i.e. (3.8) 0 0 ( ) ( ) G B B G B G B t t T T t t t t uni uni t t t t t A E d dt W t dt W t dt
0 0 ( ) G G G t T T t t uni uni t t t t A
E
d dt
W t dt ( ) ( ) U x U x x 75
or alternatively − (− ) = ( ) ℎ > 1 (3.9) Allowing the person to associate different utility to assets of the same absolute value depending if they are negative or positive, I define
( ) = − ( ) + ( ) (3.10)
where represents the person’s attitude towards debt and it is assumed that enters as a positive number.
The person should be indifferent between attending / not attending university if U(Auni) = U(Anouni),
i.e if + = + ( ) (3.11)
which simplifies to + = ( ) (3.12)
as the person does not incur any debt unless they attend university, solving
for K gives, = ( )
( ) (3.13)
This shows that the participation decision depends not only on the expected earnings differential for graduates / non-graduates, and the amount of debt incurred, but also on the way the individual perceives the positive utility of greater earnings as a graduate relative to the negative utility of being in debt. As debt increases (holding the earnings differential constant), the person must be more and more debt tolerant to remain indifferent between the two options. There will be a critical level of K such that a person will switch their decision from uni to nouni due to debt aversion, i.e where U(Auni) < U(Anouni) even though (Auni) > A(nouni).
Expanding the equations to include the full specification introduced at the start of the section, we can also see how family income influences almost every parameter. The equation below is a long form of the expected utility of participating in university:
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(3.14) Family income will especially affect how a student funds themselves while at university: someone who cannot rely on their parents for money is much more likely to work part-time during term time, which may have an adverse effect on their grades and future earnings, on the other hand, grants and bursaries are more readily available for students from poorer backgrounds. The level of student loans available also depends on family income. Studies have shown that young people from poorer backgrounds tend to leave university with more debt and have lower expected earnings on graduation (Callender et al, 2003). This relates to parameters d and P in the model7. Low family income may also affect a person’s access to credit,
possibly making it more expensive to borrow, and there is some evidence (see Delaney and Doyle, 2012) of a link between family background and time preferences, both of which would affect δ. It is the hypothesis of this chapter that family income affects K. It could also affect the time taken for the studies, tG, especially through part-time work. Thus every parameter is
influenced by family income. This shows how integral the effects of family income are to the university participation decision.
This simple model expresses the idea that someone’s decision whether or not to invest in further education will not depend on the actual total lifetime earnings expected for each pathway, but rather their perception of these flows. If people associate utility to positive and negative sums differently, this will impact on their assessment of the two options, as negative assets are only experienced by those who chose to study. Debt
7 More precisely – it relates to the gap between -d and their potential earnings stream if they had not studied, and to a potential employer’s perception of their ability P based on their grades.
0 0 0 ( ) ( ) ( ) ( ) ( ) ( ( ) ( ( ) )) ( ( ) ) ( ( ) ( ) )) ( ( ) ) B B G B G B G B G B G B G B
uni uni uni
R B t T uni uni t t t t T t t t t t t t t t t T t t t t t B G B t t t U A KU A U A KU E U E K U d dt U W t dt U W t dt K U d dt U P t t d dt U P t t d dt
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aversion may thereby act as a barrier to university participation by causing those who would otherwise have chosen the stream with higher lifetime earnings post-graduation to evaluate this less positively than the alternative stream due to the large negative utility experienced at the outset. The model also reveals how multifaceted the effect of family income on the participation decision is, as it impacts a range of factors associated with the decision.