Some Notes and Observations Concerning the
Functioning of Consumer Credit Markets
David Andolfatto
University of Waterloo
dandolfa@watarts.uwaterloo.ca
May 1999
Abstract
This paper summarizes some basic information that may serve as a guide
toward modelling the way consumer credit markets function.
1 The Household Balance Sheet
A balance sheet summarizes the structure of an agent’s assets and liabilities. Constructing the balance sheet of a household is, in principle, straightforward. In practice,
however, measurement problems make it difficult to form a complete balance sheet
position. A major practical problem stems from the fact that major asset groups,
such as human capital and entitlements to social programs, are not traded so that
no market prices are available to value these assets objectively.1 I will ignore this
measurement problem for now and simply state what the household balance sheet
should look like in principle.
Assets are sometimes divided into two broad categories: real and financial. Real
assets are instances of physical capital, which can be used to generate a service flow
of goods and services (output). A real asset is recorded as such on the household
balance sheet if the household both owns and operates the asset.2 Human capital
is likely the most valuable real asset owned by most households. Other important
real assets of the household sector include housing capital, automobiles, and a variety
of consumer durables. Financial assets are instances of time/state-contingent claims
Galenson (1981) gives an interesting account of the market for human capital created by the
institution of indentured servitude in colonial America.
2
I am not sure whether this is conventional. If a household owns a real asset that it does not
operate, then I think of the household as owning equity (a financial asset) in a business that employs
capital and labour to produce output.
1
1
against the output (or assets) of other individuals or agencies. Important financial
assets found on household balance sheets include stocks, bonds, and entitlements to
output provided by the government sector.3 These claims enter as liabilities on the
balance sheet of individuals or agencies that issue them. Liabilities of the household sector predominantly take the form of debt instruments such as mortgages, car
loans, and consumer loans (e.g., credit line and credit card debt). Another important
liability for households is their tax liability. The difference between the value of a
household’s assets and liabilities is termed net worth or wealth.
For some purposes, it is important to specify which items on the household balance
sheet are considered to be inalienable, by which I mean assets or liabilities that are
either legally or technologically inseparable from the individual. Human capital and
entitlements to various government services are examples of inalienable assets; the
household tax liability is an example of an inalienable liability. Such information
would be relevant for understanding certain aspects of the market for consumer credit.
For example, a young person’s loan application cannot be collateralized with his or
her social security entitlement, which may possibly result in a binding borrowing
constraint. Since inalienable assets cannot be marketed, there is a temptation to
exclude them from the balance sheet statement. In general, however, the existence
of such assets may affect debtor behavior and therefore the terms under which credit
is granted.
For reasons that are still not fully understood, the balance sheet positions of
households seem to vary tremendously. One puzzle has do with why net worth differs
so greatly across individuals, even when controlled for factors such as age. Another
puzzle has do with why individuals appear to expose themselves to so much idiosyncratic (i.e., diversifiable) risk. A mortgage financing the purchase of a house, for
example, leaves the homeowner exposed to fluctuations in local property values. An
individual could instead purchase a mutual fund consisting of a diversified portfolio
of housing capital and rent the required shelter services from the mutual fund. In
fact, all idiosyncratic risk could be eliminated if households were willing to hold their
net worth in the form of a share in a mutual fund that aggregated all physical capital
(including human capital). Presumably, a number of technological and legal restrictions limit the extent to which such diversification can be achieved through private
and/or social contracts. This problem seems to be particularly acute with respect to
the diversification of human capital. Whatever the reasons, one consequence of this
failure is that unexpected or uninsured economic developments (e.g., technological
change or shifts in the structure of tastes) can leave some households with very low
net worth, thereby leaving them insolvent.
3
Typically, such entitlements are legally non-negotiable.
2
2
Insolvency and Default
Technically, a person is said to be insolvent if they have negative net worth. Of
course, the measure of net worth depends on what is included in the balance sheet
and how items in the balance sheet are valued (with valuation being especially difficult
for nonmarketed assets). More commonly, insolvency refers to a financial situation
where the household is unable to pay debts as they fall due. Such a situation may
occur even when net worth is strictly positive. For example, courts may not allow
creditors to liquidate a household’s assets beyond what is deemed necessary to sustain
a minimally acceptable standard of living.4
An insolvent household must ‘default’ on at least a part of their debt. Most household debt is the form of secured loans, which limit the scope for default. Secured loans
are instances of private debt that are backed or collateralized with existing physical
(but nonhuman) or financial assets. Examples of secured loans include mortgages,
home equity lines of credit, and automobile loans. These loans typically grant the
creditor property rights in the debtor’s assets should the debtor at any time deviate
from the agreed upon repayment schedule. In the case of secured debt, the gain from
defaulting for the debtor is obviously limited, as use of the collateralized asset is lost.
Similarly, for the creditor, the loss from default is limited primarily to the transaction
costs associated with foreclosure or repossession.
Default is more likely to occur with unsecured household debt. Unsecured loans
are instances of private debt that are not explicitly collateralized by any specific asset.
Usually, repayment is expected to be made out of the income generated by human
capital services that are sold at some time in the future by the debtor in the labour
market (e.g., student loans). As such, the value of an unsecured loan is in a sense
collateralized with a claim against the debtor’s human capital. The value of such
claims depends on the willingness and ability of the debtor to honour such promises,
as well as the willingness and ability of the existing legal institution to enforce such
claims.
When economic circumstances change for a household that renders it insolvent,
creditor and debtor often resort to debt-renegotiation, resulting in only a partial
default of unsecured debt.5 With unsecured debt, there is also the problem that
some individuals may wish to default even though they are not technically insolvent.
However, there are a number of mechanisms that limit the willingness and/or ability
of a debtor to default on an unsecured loan. To begin, the demand for information
on personal credit history typically gives rise to credit bureaus that collect and pool
4
Courts will typically limit, for example, the amount of wage income that can be garnished by
a creditor. In addition, personal bankruptcy laws typically allow for exemptions in what property
creditors can seize.
5
Households in financial distress are often advised to meet with their creditors and put forth a
‘consumer proposal’, which outlines a modified debt-repayment plan.
3
such information from creditors and make it available back to creditors (for a fee).
With access to such information, the credit market may be able to punish defaulters
by making it more difficult (or impossible) for these individuals to obtain unsecured
loans in the future. Secondly, creditors may take actions that make default unpleasant
for the debtor. In particular, creditors may sell an outstanding loan (at a discount)
to a collection agency that specializes in harassing debtors to pay up. Thirdly, a
creditor may take the debtor to court in order to garnish a part of the debtor’s
wages. As human capital is inalienable, the efficacy of this approach depends in part
on the willingness and ability of the debtor to substitute time away from market
work into other activities that generate an excludable consumption flow, such as
home production or leisure. Finally, if the debtor has clear title to some physical or
financial assets (e.g., a bank account), the creditor may be awarded claims to these
assets by a court.
3
Debt Collection Activities
When a debtor either chooses or is forced to default on some outstanding unsecured
debt, creditors will often attempt to seize various assets through legal action (presumably, this will only happen in cases where the value of available assets exceeds
the expected recovery cost). Even if the debtor owns no physical capital or financial
assets, but is employed, the creditor can in effect ‘seize’ a portion of the debtor’s
human capital through wage garnishment (of course, the debtor is free to reallocate
human capital to other uses beyond the grasp of creditors).
Exactly how the process of debt collection functions depends to a large extent on
the existing legal environment. In the absence of rules governing the debt collection
procedure, two basic problems are thought to exist with respect to the way the
process functions. The first problem deals with the way creditors (are alleged to)
behave toward each other when there are competing claims on a limited number of
assets. The second problem deals with the way creditors (are alleged to) behave
toward debtors.
The first problem may occur in the case where a debtor becomes insolvent but
owns significant assets (that are not already pledged as collateral). If there is a large
number of creditors that are positioned such that communication and negotiation
amongst themselves is difficult, then the debtor’s assets effectively become a ‘common
property’ subject to the familiar ‘tragedy of the commons’. Relative to a ‘first-best’
situation, resources will be needlessly consumed along two dimensions: (i) as creditors
fight among themselves to assert property rights; and (ii) as assets are dismantled
in parts that are worth less than when they are whole. From the perspective of
creditors, a collectivized debt-collection procedure that liquidates and divides assets
in an efficient and ‘fair’ manner may be preferable to what may prevail under a purely
4
noncooperative solution; this is the primary rationale for corporate bankruptcy law,
and the logic also applies to personal bankruptcy law.
The second problem might be termed the ‘knee-capping’ problem.6 Evidently,
creditors can sometimes try ‘really hard’ to get their money back. It is not uncommon
for creditors to sell (at a discount) an unpaid loan to another agency that specializes in
debt collection activities. Some of these debt collection agencies have been described
as ‘unscrupulous’ in their behaviour, for example, by ‘tricking’ a person into paying
a debt by pretending to have started a court action.7 It is difficult to know how
much of a problem such behaviour poses in practice; legally, it is a criminal offense
(in Canada) for a collection agency to harass, intimidate, or threaten a debtor in any
way.
But aside from the possible ‘psychic’ knee-capping associated with verbal harassment, creditors may end up physically knee-capping (not literally, of course) a debtor
by gaining title over assets that are used to generate a ‘subsistence’ living standard.
A creditor may, for example, come after your tools, pots and pans, clothes, pets,
and granny’s electric wheelchair.8 Furthermore, a creditor may be able to garnish
wages and bank accounts to a point that leaves the debtor with income at or below
‘subsistence’ levels. Again, it is difficult to know how much of a problem this potential behaviour poses. In practice, creditors must take debtors to court and win
judgements from (presumably) sensible and compassionate judges. As well, the legal
system usually provides guidelines (independent of personal bankruptcy laws) that
restrict creditors in extracting resources from debtors that would leave the latter
living at ‘unacceptably’ low living standards.9
For an individual, becoming insolvent and being faced with the prospect of subsistence living cannot be a pleasant experience. However, one view is that most
individuals have some idea of the risks that they are taking when incurring high
6
Breaking the knee-caps of a debtor in default is supposed to have been the punishment favoured
by loan sharks and mobsters.
7
This information is based on what I have read at the following website:
www.lsuc.on.ca/public/other_collectionagencies_en.shtml
8
Although it is difficult to imagine how a court might award such assets to a creditor, note that
New Brunswick’s bankruptcy law explicitly mentions that ‘necessary medical and health aids’ and
‘pets belonging to the debtor’ are items of property to be exempt from seizure. See the following
website: www.personalbankruptcy.com/rules.htm
9
In Saskatchewan, for example, when creditors garnish wages, the debtor is permitted
to keep $500 per month for living expenses plus $100 per month for each dependent. In
addition, creditors cannot garnish money that is forthcoming from social assistance programs.
(Neither of these restrictions apply if the creditor is Revenue Canada).
See,
www.sfn.saskatoon.sk.ca/education/pleaseask/Debts.html
In the United States, Federal law requires that a minimum of 75% of wages or 30 times the Federal
minimum hourly wage per week, whichever is higher, be exempt from garnishment. Some states
(Texas, Pennsylvania, Alaska, South Dakota and Florida) prohibit wage garnishment entirely; see
Fay, Hurst and White (1998, pg.16).
5
levels of debt to finance either consumption or risky investments (e.g., one’s own human capital); responsible people should expect to pay back their creditors to their
full ability even when things do not quite turn out the way one would have hoped
and even when doing so may involve significant personal sacrifices. On the other
hand, some segments of society may take the view that incidents of insolvency occur
through ‘no fault’ of the debtor and should therefore be forgiven; this is the second
‘rationale’ for personal bankruptcy law, i.e., to give individuals ‘a new lease on life’
(there does not appear to be an equivalent rationale for corporate bankruptcy law).
There are two types of arguments that I have heard been made here; one that relies
on some instance of ‘market failure’ and one that relies on what might be termed ‘the
uniformed-agent hypothesis’.
The market-failure argument relies on the observation that many types of insurance are not available in private markets.10 Consider a young person who secures a
loan in order to finance an education with a risky return, but with positive net present
value. Private insurance markets may not be available to insure against this type of
risk. Consequently, some individuals will experience bad outcomes, even though their
investment choices were sound. An institution that allowed for debt forgiveness in
such circumstances could be viewed as a public alternative to a missing insurance
market. The uniformed-agent hypothesis typically has strong paternalistic overtones
to it. Basically, the argument is that some adults are children; that children sometimes get into trouble, and that children should be taught a lesson, but at the same
time forgiven and given a second chance. It has been argued, for example, that with
the rise of the consumer credit industry and its aggressive advertising and sales techniques, households tended to accumulate ‘too much’ debt, leaving them vulnerable to
‘unexpected’ events such as illness, layoff, or pregnancy.11 For further evidence that
bankruptcy legislation is to some extent guided by the uniformed-agent hypothesis,
note that bankrupts are usually required to undertake counselling sessions with a
trustee.
4
Personal Bankruptcy Law
Bankruptcy laws appear to differ quite substantially across state/provincial governments and are occasionally subject to change across time within a given jurisdiction.
Nevertheless, these laws appear at the same time to share a number of similar characteristics, which I now describe.
Of course, there are those who would assert that the reason that such markets are absent can be
traced to various legal restrictions that prevent well-functioning insurance markets from operating.
11
This argument has been made by the 1973 Commision on the Bankruptcy Laws of the United
States; see Gropp, Scholz and White (1997, pg. 218).
10
6
4.1 Outline of Procedure and Some History
In order to file for personal bankruptcy, an individual or household must be deemed
‘insolvent’. I am not sure how insolvency is defined operationally. As far as I can tell,
it is up to a judge to determine whether an individual has an income level (i.e., not
necessarily asset level) that is insufficient to pay for living expenses and the carrying
cost of personal debt.12 If this requirement is met, then an individual may file for
bankruptcy (at a cost of about $1500 plus $100 per counselling session).13
Once bankruptcy status is attained, all actions against the bankrupt must legally
cease (except for the actions undertaken by secured creditors). All subsequent interaction between creditors and debtor is mediated through a court-appointed trustee.
Where significant assets are involved, a notice is placed in newspapers informing
creditors of a meeting date where discussions concerning disbursement presumably
take place. If there are minimal assets, creditors are simply informed by mail. Any
legal filing of a bankruptcy is a public document; from this documentation, a Credit
Bureau is notified and the bankruptcy is recorded.14
A key aspect of bankruptcy law is in what property is stipulated to be exempt
from seizure. These exemption levels can vary widely across provinces and states.
In Canada, it is not uncommon for a bankrupt to retain property (home equity,
cars, tools, etc.) valued in excess of $30,000. A bankruptcy normally lasts for about
nine months (but may last longer). During this time, the trustee is responsible
primarily for disbursing the debtor’s assets (those available beyond exemption levels)
to creditors, possibly garnishing some fraction of the bankrupt’s wages on behalf of
the creditors, and counselling the bankrupt. After the required period of bankruptcy,
most of the bankrupt’s debts are discharged.15
I am not familiar with how bankruptcy law has evolved in Canada. In the United
States, bankruptcy exemption levels prior to 1978 were specified by state and tended
to be very low. The Bankruptcy Reform Act of 1978 specified a uniform exemption level of $7500 for equity in homesteads and $4000 for non-homestead property.
However, the Act allowed states to opt out of the Federally specified exemptions and
adopt their own exemptions, with most states apparently doing so by 1983 (however,
12
If one is not deemed to be insolvent, then the debtor may be instructed to renegotiate a debt
repayment schedule with creditors.
13
How is a bankrupt expected to pay for such costs? By borrowing, of course! One Vancouver
law firm advertises an easy payment plan that allows the debtor to spread the cost of bankruptcy
over time; see www.sands-trustee.com/question.htm
14
Legally, the bankruptcy can remain on an individual’s credit record for up to 6 or 7 years
(depending on the province).
15
In Canada, student loans can only be discharged if the bankruptcy occurs ten years after graduation. Alimony and maintenance payments are not affected by bankruptcy. Likewise, debts such
as fines, money owing for stolen property, and so on, are not discharged following bankruptcy.
7
bankruptcy remains a matter of Federal law).16 Federal exemption levels were doubled in 1994 and a recent report of the National Bankruptcy Review Commission
(1997) has apparently proposed further significant increases (Fay, Hurst, and White,
1998).
4.2 The Secular Rise in Personal Bankruptcy Rates
It is well known that personal bankruptcy rates have been rising steadily in the United
States since the early 1980s. Fay, Hurst and White (1998) report that filing rates
have risen from 0.3% of households in 1984 to 1.3% in 1997, with losses to lenders
amounting to about $32 billion. Personal bankruptcy rates have risen sharply in
Canada as well. In 1966, there were fewer than 2000 bankruptcies. In 1987, this
number increased to 24,000 and in 1997 there were 85,000 personal bankruptcies.
The number of households in Canada is in the neighbourhood of 14 million, so the
rate of bankruptcy appears to be in the same order of magnitude as in the United
States.
A number of hypotheses have been put forth in an attempt to explain the secular
rise in personal bankruptcy rates. These include: (a) recent increases in exemption
levels; (b) changes in banking regulation leading to more aggressive lending activities;
(c) increased dispersion in earned incomes and wealth; (d) reduced levels of stigma
associated with filing; (e) increased divorce rates; (f) increased government lending to
students and small businesses (based on need rather than ability to repay); and (g)
increased rates of self-employment. It appears that much work remains to be done in
trying to understand the role played by each of these factors and how they may be
related to each other.
4.3 Economic Characteristics of Bankrupts
Anderson and Schwartz (1998) provide a demographic and economic profile of Canadians seeking personal bankruptcy protection in 1997; this data is compared with
that of a similar study conducted by Brighton and Connidis (1984) for Canada in
1977. Some interesting patterns are evident in the data.
Both sets of authors observe that consumer bankrupts are drawn quite heavily
from the lower socio-economic categories, with a small, but significant proportion
drawn from professional, managerial, and skilled worker groups. Also, while bankrupts tend to be relatively ‘income-poor’, they are not the poorest segment of the
population.17 The median asset and liability levels of potential bankrupts across the
16
Some states allow debtors to choose between the state and Federal bankruptcy exemptions.
The very existence of debt indicates that at least some creditors viewed the future income
prospects of the debtor rather favourably.
17
8
two samples is not very different. In 1977, the median asset level was (in current
dollars) $1000 and the median liability level was $28,000; in 1997, the median asset
level was $3000 and the median liability level was $26,000.
While there is little difference in the size of the median liability across the two
samples, interesting patterns emerge with respect to the structure of the liabilities.
In particular, the proportion of debts that were owed to the government and credit
card companies rose considerably, while the proportion of debts owed directly to
retailers or to private individuals fell (the proportion of bank loans remained roughly
constant). In the more recent sample, almost 70% of potential bankrupts had at least
one credit card debt; but 30% did not have any outstanding credit card debt. The
most common liability were debts owed to the government, either for student loans,
business loans, unpaid taxes, or some other purpose. The median government debt
was $6000 among those who had such debts, while the median credit card debt was
just over $3500.
What was the purpose for which debt was incurred? In the more recent sample,
the vast majority of bankrupts did not have mortgages. Nor did the majority have
either car loans or student loans; in each case, roughly 75% had no such liabilities.
Almost half of all bankrupts, however, had debts to Revenue Canada. The median
student loan, for those that had one, was about $10,000. Debts to Revenue Canada,
while much more prevalent, were also much smaller, with a median value of $2500.
4.4 The Secular Rise in Personal Bankruptcy Rates: An Explanation
I believe that we can go a long way toward understanding the growth in personal
bankruptcies since the late 1970s by examining the borrowing behavior of young
persons (students), self-employed individuals, and the lending practices of the government.18 Some people may prefer to focus on the lending practices of the private
sector, but I find such explanations difficult to swallow (although, I am willing to be
persuaded otherwise). Private creditors can reasonably be expected to be fairly prudent about who they lend money to. Thus, if bankruptcy laws change in a manner
that is ‘favourable’ to debtors, or if there is an increased incidence of divorce and
single-parent families, I think that it is reasonable to suppose that the private sector
restricts its supply of credit in a manner that keeps the probability of defaul low.
Government sector agencies, on the other hand, may be less concerned with default
probabilities, preferring to focus on ‘need’ rather than ‘ability to repay’.
Here are some facts, taken from Anderson and Schwartz (1998), which I think
18
For the purposes of this discussion, I will assume that there has been no significant change in
personal bankruptcy laws over this time period. If bankruptcy laws have been relaxed, then my
argument will only be strengthened.
9
make the hypothesis above an attractive one to pursue. First, since 1977, the number
of self-employed individuals has almost doubled to something like 3 million people.
Over this time, several government programs aimed at helping Canadians start their
own business emerged. These programs likely gained political support based on empirical evidence showing the high rates of job creation associated with small business
enterprises (evidently, the high rates of job destruction associated with such enterprises must have been downplayed). In their sample of potential bankrupts, Anderson
and Schwartz (1998) reveal that more than 80% of the self-employed owed money to
various levels of government, compared to 66% who were not self-employed. The
median level of liabilities for the self-employed was $51,000, compared to $21,000 for
those who were not and government debt was roughly twice as big for the former
group. Another big difference is in the debt owed to Revenue Canada; the median
debt level for the self-employed was $7000, compared to $1500 for those who were
not self-employed.
Another form of ‘self-employment’ that has increased significantly over the last
two decades is post-secondary education (one could interpret a student as employed
in a sector that produces human capital). Apparently, students today are much
more likely to borrow in order to finance their human capital investments. And, of
course, the government has been there to help finance this activity. Even over the
short period from 1989 to 1994, the volume of federal and provincial student loans
almost tripled from $768 million to $2132 million. Over the past decade, on the order
of $20 billion has been lent to hundreds of thousands of post-secondary students.
Roughly one-third of Anderson and Schwartz’s sample of potential bankrupts was
under 30 years old. While 65% of the young and 70% of the old had outstanding
credit card debts, the balances of the young were quite modest, with a median of
$2000, compared to a median of $4300 for those over 30 years of age. Where the
young face considerably higher (unsecured) debt is in student loans. More than 45%
of the young had a student loan, compared to 16% of the old; the median student
loan amount for both groups was $10,000.
So, in summary, here is the pattern I see emerging. First, the government introduces (or relaxes) a set of personal bankruptcy laws that provide initial relief for
debtors (especially ‘rich’ debtors, as I will explain below). These laws allow ‘insolvent’ debtors to default with virtual impunity on unsecured debt (students had to
wait a full two years subsequent to graduation, before their student debt could be
discharged in a bankruptcy). Credit granting agencies in the private sector responded
to these rule changes by altering their lending practices in a manner that reflected
the increased likelihood of default on unsecured credit. At the same time that credit
market conditions tightened for those seeking unsecured loans, unemployment began to rise and skill-augmenting technological developments led to an increase in the
demand for human capital accumulation. Responding to political pressure pointing
out the failure of the private sector to finance worthwhile investments and create
10
jobs, governments were compelled to supply the perceived shortfall in credit; this primarily took the form of small-business loans (as well as loans in the form of unpaid
taxes) and student loans. The combination of easier government credit, less-stringent
screening, and favourable bankruptcy laws, all contributed to higher rates of personal
bankruptcy.19
There is unquestionably an element of truth to the story told above. Whether
these forces were quantitatively important is another matter and this should be investigated. Also note that there is nothing ‘normative’ about what I have just said. In
particular, it may very well be that the government acted in an entirely appropriate
manner (according to some social welfare function) and that higher rates of personal
bankruptcy are on the whole associated with higher levels of individual welfare. Such
a question can only be answered within the context of a fully specified general equilibrium model that makes explicit reference to individual preferences; this too should
be the subject of future research.
4.5 The Political Economy of Personal Bankruptcy Law
What are the political forces behind the implementation of personal bankruptcy law?
In other words, which segments of society are harmed and which are helped by the
sudden implementation of a particular set of rules governing debt repayment? Answers to this question appear to be wanting in the literature.
One possibility is that all segments of society are made better off with the implementation of a well-designed bankruptcy law. Such an argument would likely hinge
on the premise of incomplete insurance markets or the inability of individuals to coordinate their debt-collection activities privately. In principle, the government might
be able to design a mechanism that results in an overall efficiency gain, making its
political implementation a straightforward matter.
Another possibility is that bankruptcy law (and, in particular, asset exemption
levels) result in overall efficiency losses, but that certain groups benefit at the expense of others and are able to pressure the government into enacting the requisite
legislation.
19
Note that recently, there have been significant changes in the market for student debt. In
particular, I believe that student loans are now administered by one or two major private banks in
Canada. My understanding is that the government promised to back all student debt that it passed
on to these corporations and that further student debt was the responsibility of the bank. At the
same time (or shortly thereafter), the personal bankruptcy law was amended such that student debt
could no longer be discharged in a personal bankruptcy, unless the bankruptcy occurred at least
10 years after graduation. Since the gain from declaring personal bankruptcy on the basis of high
student debt is now significantly reduced, one would expect significantly lower bankruptcy filings in
this category. Of course, whether students have been made better or worse off as a result of these
changes remains to be seen.
11
One idea that might be challenged is that bankruptcy legislation by itself helps
people who have persistently low incomes (the income-poor).20 Low income individuals are unlikely to be accumulating large debts, at least, from private sector sources.
It is conceivable that bankruptcy legislation may make it even more difficult for this
segment of society to acquire unsecured loans. Of course, bankruptcy legislation together with a set of particular lending practices from the public sector may make
low income individuals better off. As described earlier, the government may wish to
provide credit to individuals based on ‘need’ rather than ‘ability to repay’. Such a policy, together with a bankruptcy option, effectively translates into a transfer program
for low income individuals.21 To the extent that this is true, the political support
for bankruptcy law can be expected to come from the same source that argues for
redistributive policies in general.22
One group of individuals that may stand to benefit from a ‘surprise’ implementation of bankruptcy legislation is the current cohort of ‘net debtors’; i.e., individuals
who have managed to issue private debt in excess of the value of their physical capital
holdings (as argued earlier, such net debt is in effect collateralized by human capital). In the short run, net debtors can gain at the expense of net creditors. However,
there is a question of the ‘long-run’ costs of such a program. Presumably, the supply
of credit will adjust in a manner that reflects the greater ease of default, thereby
harming all future credit market participants.23
Another dimension that may be important for understanding the design of bankruptcy law may be in how household balance sheets are structured in terms of their
asset and liability components across various segments of the population. Most economic analysis that I am familiar with abstracts from balance sheet structure, preferring to focus simply on the net asset position. But from this perspective, it is difficult
to understand why bankruptcy law often specifies huge exemptions for certain classes
of assets. One can immediately see, however, how these types of exemptions can make
‘rich’ debtors much better off. Consider, for example, the following balance sheets,
which feature two households with equal net worth but different asset/liability struc20
Of course, bankruptcy may provide insurance for those individuals making transitions from
high-income to low-income states.
21
Thus, for example, the government may wish to either distribute student ‘grants’, as they have
done in the past, or extend easy credit with the option of default. Another example would be for
the government to distribute ‘welfare’ to individuals, or to make easy credit for self-employment
available, together with the option of default.
22
Cite Metzler and Stiglitz.
23
Andolfatto and Redekop (1998) demonstrate how a redistributive program may gain the political
support for implementation even though the majority of individuals are in the long-run made worse
off.
12
tures:
Household 1
Household 2
Assets
Liabilities
Assets Liabilities
House $100 000 Mortgage $80 000
$0
$0
Credit Card $10 000
Old Student Loans $10 000
Net Worth: $0
Net Worth: $0
In the absence of bankruptcy laws, the equity in the first household’s equity in housing
capital is effectively (although perhaps not in writing) serving as collateral for credit
card loans and student debt. Imagine now that a bankruptcy law is passed that allows
for a $20 000 exemption for homestead property. Household 1 is now in a position
to default on its unsecured debt (i.e., creditors will be legally restricted from seizing
home equity as compensation).
,
,
,
,
,
4.6 How Important is Bankruptcy Phenomena?
Gropp, Scholz and White (1997) report that for the United States in the year 1983,
there were 313,000 personal bankruptcy filings with an estimated loss to creditors
equalling about $12.5 billion. While numbers like these sound large, from a macroeconomic perspective, they are not. In particular, 300,000 households represents
‘only’ on the order of one-half to one percent of all households. I am not sure what
the total volume of personal credit is per year, but I would not be surprised to find
it on the order of trillions of dollars.
One should also keep in mind that bankruptcy is just a specific instance of debt
default. While it is an extreme form of default, it is also in all likelihood relatively an
infrequent form. My guess (I have no data to back this up) is that the volume of debt
that is lost to creditors through debt-renegotiation (with partial default) probably
outweighs the amount of debt lost through outright bankruptcy (perhaps this only
holds true for corporate bankruptcy?). As well, I suspect that a good deal of debt
is simply abandoned by creditors because the costs of recovering it are simply too
high.24 These types of defaults have been going on since time immemorial, well before
bankruptcy laws came into existence. There is the possibility that with the advent
of bankruptcy laws, individuals used this mechanism as a substitute for other, more
conventional ways of defaulting. One possibility is that the aggregate amount of
default (relative to the volume of transactions) has remained unchanged, with only
the composition of defaults having changed over time.
Of course, from a microeconomic perspective, the circumstances surrounding personal bankruptcy can have very important implications for individual well-being.
24
I have plenty of anecdotes on this matter acquired from friends and my own experiences in the
construction sector.
13
However, while rising rates of personal bankruptcy naturally draw the concern of
policymakers, one has to be careful in interpreting bankruptcy rates as measures of
financial distress or economic well-being. Presumably, bankruptcy laws are in place
to relieve financial distress; i.e., in the absence of bankruptcy protection, the financial distress associated with (say) job loss would still be present even though it would
not be reflected in the bankruptcy statistics. Also, to the extent that rising bankruptcy rates reflect the increased popularity of an alternative form of transfer payment
(e.g., easy government credit for schooling substituting for a decline in grant money),
personal bankruptcy rates may bear absolutely no relation to changes in individual
well-being.
5 Model Economies with Debt Constraints
5.1
Model 1
Consider an individual who lives for two periods, which will be referred to as the
present and the future. There is no uncertainty, so there is no need to define preferences over state-contingent goods. Preferences are simply defined over deterministic
sequences of consumption {c1 , c2 }, where cj is consumption at date j = 1, 2. Let these
preferences be represented by the utility function:
V
= ln(c1 ) +
δ ln(c2 )
where δ ≥ is a subjective discount factor.
Assume that each person has one unit of indivisible time which they may allocate
either to the market sector or to the home sector. Let n ∈ {0, 1} denote time allo0
j
cated to the market sector in period j . For simplicity, assume that market-produced
goods and home-produced goods are perfect substitutes in consumption; consequently,
cj represents a ‘composite’ consumption bundle comprised of both market and home
goods and services.
Opportunities in the market {w1 , w2 } and in the home {v1 , v2} are taken as pa-
rameters, where w can be interpreted as either labour productivity or the real wage,
and v can be interpreted as the productivity of leisure (i.e., the productivity of time
spent in the home sector). Assume that goods and services produced in the home
sector are nontransferable. In the absence of any other source of income and opportunities for intertemporal trade, consumption in each period would be given by
j
j
cj = wj nj + vj (1 − nj ).
There is a competitive market for risk-free private debt, which yields a (gross)
real rate of interest equal to R; assume that R is exogenous. Individuals are endowed
with no initial financial assets or liabilities. For simplicity, we impose the following
14
pattern on intertemporal opportunities: {w1, w2} = {0, w} and {v1, v2} = {0, v}. The
idea here is that young people expect that their human capital (in both the market
and the home) will be more valuable (productive) in the future. If possible, the young
will want to borrow against these higher future earning capabilities in order to finance
consumption expenditures in the present period.
Let b denote the amount of debt issued by a young person (measured in units of
consumption). Assume for now, as is standard, that debt contracts can be costlessly
enforced. In particular, what this means is that when an individual is negotiating
for a loan in the present period, he can collateralize the loan by committing to work
in the future. In this case, the individual maximizes the utility function above by
choosing {c1, c2, n, b}, subject to the following constraints:
c1
c2
= nb;
≤
wn − nRb + v(1 − n).
The structure of this problem is such that we can anticipate n = 0 will never
be optimal, since this would mean that the person would be unable to secure a loan
to finance consumption in the present period (notice that the person really wants
to borrow, as his own time produces nothing of value in the present period). With
n = 1, one can solve for the individual’s desired net debt position:
bd =
1
1+δ
w R
.
(1)
The term (w/R) represents the present value of the individual’s marketable output.
Evidently, it is optimal for the person to borrow an amount equal to some fraction
(1 + δ)−1 of this wealth; in this manner, the person is able to smooth consumption
across time.
Assume now that the economy is populated by a continuum of individuals who
differ only in their future labour productivity; let Φ(w) denote the fraction of individuals with productivity no better than w, where Φ > 0. In this case, the desired net
debt position (current account deficit) for this small open economy can be calculated
as:
w Bd (R) =
5.2
1
1 +
δ
R d w.
Φ(
)
(2)
Model 2
Let us now assume that an individual cannot commit (perhaps because of legal restrictions) to future labour supply. The legal environment is such that, should the
person decide to work and generate wage income, default is not possible because the
creditor can garnish wages. However, the debtor can default by refusing to work;
15
this can be done by reallocating time to the home sector where the individual can
produce an excludable consumption flow.
Consider the individual’s choice problem having contracted for debt b and now
entering the future period. How will the person behave? If the individual honours
the terms of the debt contract at this stage, he will receive a utility payoff equal to
ln(w − Rb); defaulting, on the other hand, will yield utility payoff ln(v ). Consequently,
the optimal default strategy is given by:
n=
if w − Rb ≥ v
,
if w − Rb < v
1
0
where n = 0 corresponds to a default. What this says is that if the person in question
can generate something in the home sector that is of greater value than what can be
produced in the market sector net of loan repayment, then the person can be expected
to default on the loan agreement. Creditors, understanding these incentives, would
naturally wish to adjust their lending practices relative to what was described in
Model 1. In the simple case where creditors can observe each person’s w, then an
upper bound on the amount of debt they will be willing to extend is given by:
bM
ax
= m
w − v R
,0 .
(3)
If w − v ≥ 0, then this is the maximum that any creditor could ever hope to legally
recover (in the future) from a prospective debtor; R−1 (w − v) represents the present-
value of this amount.
As individuals differ in terms of their future labour market opportunities according
to the (continuous) distribution function Φ, we can identify a critical wage w∗ that
satisfies bd = bM ,
1 w∗ w ∗ − v =
;
(4)
which implies:
1+δ
1+δ R
R
which can be solved for w∗ = δ v. Individuals who are endowed with future labour
market productivity w∗ will have a loan demand that is just equal to the maximum
any credit agency is willing to lend them. It follows that any individual with w < w∗
will be credit-constrained (relative to a situation where they could commit not to
default), while any individual with w > w∗ will be able to borrow freely at the going
interest rate. Credit-constrained individuals in this economy are those people whose
future market prospects are anticipated to be poor relative to other uses for their
time.
Notice that as the value of ‘outside opportunities’ v increases, creditors become
more discriminating with respect to ‘quality’ of potential debtors; w∗ increases. Creditors also raise their standards when potential debtors are perceived to be more ‘impatient’; i.e., w∗ increases as the discount factor δ falls. In general, one would expect
16
that lending standards might depend on the interest rate as well, but in this specification of the model, they do not. Notice that as the interest rate rises, the maximum
amount that creditors will be willing to lend bM falls (for any given w). That is, given
an ability to repay w, a higher interest rate implies a higher loan repayment for any
given loan size; consequently, it is optimal to scale back the size of the loan. As it
turns out, loan demand bd falls in exactly the same proportion as bM when interest
rates rise, leaving w∗ unchanged. For more general preference specifications, loan
demand may be either more or less interest-rate elastic. If loan demand was not very
sensitive to the interest rate, then one would expect lending standards to rise; the
opposite would hold true if loan demand was sensitive to interest rate changes.
The number of credit-constrained individuals in this economy is given by Φ(w∗);
for each person of type w, the amount of debt they can issue is given by bM (w) =
max {R−1(w − v), 0} . Individuals with w < v will not be able to borrow at all; their
mass is given by Φ(v ). Consequently, the current account deficit (desired net debt
position) for this economy is given by:
B̂
Clearly,
5.3
d
1 w∗
−
1
−
1
= (0)Φ(v) + R
(w − v )dΦ(w) +
R
1+δ
v
w∗
wdΦ(w).
B̂d < Bd .
Model 3 (Incomplete)
was that creditors were able to identify each individual’s future labour productivity w. The idea behind this assumption is that debtors
have a good idea of what their future earnings capabilities are going to be like, and
that they can credibly convey this information to creditors. Suppose, however, that
creditors cannot identify w ex ante ; in this case, potential debtors will be indistinguishable from the perspective of creditors (although, we will continue to assume that
Φ is common knowledge).
How will creditors respond to such a situation? In general, one might expect
creditors to devise a loan schedule that conditions loan size and the interest rate on
a signal sent by the debtor. Such a loan schedule might be feasible if individuals
could commit not to default (i.e., if they could commit to their future labour supply).
However, in the present case, it seems apparent that creditors cannot gain by conditioning a contract on any signal, since individual debtors can costlessly provide a
signal that generates the largest loan, and then subsequently default. Consequently,
the only equilibrium possible, if one exists, will be a pooling equilibrium where each
debtor is offered the same loan size and interest rate.
There are a number of different ways in which one might model the functioning of
the credit market when information is incomplete. We know that, in any equilibrium,
One assumption made in Model 2
17
each individual will have to be offered the same loan size b. Assume that individual
creditors view the going loan size b as a parameter; given b, creditors choose a repayment amount x in order to maximize profit:
Π(b) = max max
{[1 − Φ(v + x)] x − Rb} , 0
x
.
The optimal repayment amount x∗ (if positive) satisfies:
[1
− Φ(v + x∗)] = x∗Φ(v + x∗).
Increasing the repayment amount by one small unit will return [1 − Φ] in additional
revenues (this is the fraction of the population that will actually repay the loan).
However, increasing the loan repayment level will also increase the probability of
default by Φ , so that x∗ Φ in revenue will be lost. The restriction above balances
these two margins.
The repayment amount x∗ will be offered only if creditors find it profitable to do
so; i.e., if and only if Π(b) ≥ 0. If we assume free-entry into the banking sector, then
it is reasonable to suppose that ‘market forces’ drive the equilibrium loan amount to
a level that satisfies Π(b∗ ) = 0; i.e.,
b∗ = R−1 [1 − Φ(v + x∗ )] x∗.
The implicit rate of return that is charged on this risky debt can be calculated as
R̂ = x∗/b∗ ; or
R̂ =
R
.
1 Φ∗
−
In this model, the ‘equilibrium’ (I am not sure of the solution concept imposed here)
features some individuals ‘defaulting’ on their loans.
6
Redistribution Policy and Debt Constraints
In this section, I consider the effects of a government policy designed to equate aftertax incomes. Let y = wdΦ(w) denote the second-period real per capita output
generated in the economies modelled above. Assuming that w can be observed, the
tax policy τ (w) = y − w will guarantee equal incomes (not
including interest income)
and balance the government budget constraint; i.e., τ (w)dΦ(w) = 0. Let us now
explore the consequences of such a program under various assumptions concerning
the legal environment.
6.1
Transferable Tax Assets
Here, we employ the assumptions of Model 1; in particular, there are no legal restrictions over what can or cannot be contracted upon. In the present context, this means
18
that a person can effectively sell his human capital (or use it as collateral). Equivalently, a person can commit to honour the terms of private debt contracts regarding
future labour supply.
When a government implements a redistribution policy, it effectively alters the
distribution of financial assets in the economy. In particular, those individuals who
are eligible to receive a future net transfer have in effect been endowed with a financial
asset that promises a ‘dividend’ payment equal to the amount of the transfer. Similarly, those individuals who are obliged to contribute future taxes have in effect been
endowed with a financial asset that promises a negative ‘dividend’ payment equal to
the amount of the tax (in other words, they have been endowed with a liability).
What effect this shift in financial assets has on the credit market depends on what
rights individuals have in buying or selling these ‘tax assets’.
In the spirit of Model 1 above, assume that property rights in tax assets are fully
negotiable. Given the homotheticity of individual preferences, it should come as no
surprise that the redistribution policy τ (w ) = y − w has absolutely no effect on the
aggregate net debt position of the economy (and would have not effect on the interest
rate, in a closed-economy version of this model). In particular, note that if a person
expects an after-tax income equal to y, then from (1), his desired loan amount is
given by:
bd =
1
1+δ
y ,
R
which corresponds to the (per capita) net debt position B d in (2).
Under this legal environment, the redistribution policy here manages to equalize
consumption across individuals in each time period.
6.2
Nontransferable Tax Assets
In reality, entitlements to transfer income (or obligations for tax contributions) are
typically not legally negotiable property. Such a legal restriction has an interesting
asymmetric effect on individuals, depending on whether they are net contributors or
net recipients of transfer income.
When entitlements to future transfer income are transferable, as in the previous
subsection, then individuals are able to increase current consumption by selling off
these entitlements (or, equivalently, by issuing private debt that is collateralized with
the government asset). When obligations to future taxes are transferable, individuals
may likewise sell off their tax liabilities; by doing so, however, consumption would
have to be reduced, since these liabilities would sell for a negative price. Thus,
selling off tax liabilities constitutes an act of saving, while selling off an entitlement
to transfer income constitutes an act of borrowing. Consequently, for individuals who
wish to be net borrowers (as in our model), prohibiting the sale of such assets and
19
liabilities will affect only those who have entitlements to future transfer income, i.e.,
those for which τ (w) < 0. For those who have future tax obligations, selling off their
tax liability does little good, as this is an act of saving and, by assumption, they
wish to borrow more, not less. Consequently, for those individuals with τ (w) > 0,
prohibiting the sale of tax liabilities is not a binding constraint.
Following Model 1, we know that n = 1 must be a part of any equilibrium; let
us impose this fact now. For individuals with τ (w) > 0, the maximum that they
could conceivably borrow is the present value of their after-tax income, y/R.
yAs
1
d
their optimal net debt position is some fraction of this amount, b = 1+δ R ,
these individuals are not ‘debt constrained’. However, for individuals expecting net
transfers τ (w) < 0, the maximum that can be borrowed is given by the present
value of future income that creditors can legally garnish, which is given by w/R. For
individuals that expect low future earnings, the inability to commit future transfer
income to pay off creditors means that they may find themselves ‘debt constrained’.
In fact, all individuals with future earnings w < w0 will be debt constrained, where
w0 satisfies:
1
1+δ
y = w0 ,
R
R
1
so that w0 = 1+δ
y < y.
The economy-wide net debt position for this economy is given by:
B =
d
0
w0
0
wdΦ(w) + [1 −
1
Φ(w0)]
1+δ
y R ,
which is clearly less than the desired net debt position derived in the earlier subsection.
Consequently, we see how a government redistribution policy, together with a policy
that makes entitlements to transfer income inalienable to the individual, can together
result in a situation where some individuals find themselves debt-constrained (relative
to the case where transfer entitlements are marketable).
6.3 Inalienable Human Capital and Transferable Tax Assets
When the tax policy τ (w ) = y − w is combined with a law that allows creditors to
garnish government transfers, all individuals (in our model) end up with the same
consumption allocation; i.e., the analysis reduces to that of a single ‘representative’
individual with future income given by y.
Now, if the government was to make human capital inalienable, thereby making individual time allocation legally nonenforceable, then the analysis in Model 2
suggests that the representative individual faces the following borrowing constraint:
bM = max
y − v R
20
,
0
,
(5)
=
y
R
> bM , then the representative individual
will be debt-constrained. In this case, one scenario that presents itself as a possibility is where a uniform debt-constraint is imposed across individuals in place of the
distribution of debt-constraints (some which do not bind) characterized in Model 2
above.
which is analogous to (3). If bd
1
1+
δ
6.4 Inalienable Human Capital and Nontransferable Tax Assets
We now combine Model 2 with the assumption that entitlements to transfer income
are inalienable.. Recall that when human capital is inalienable, the commitment to
supply labour in the future (n = 1) must be ‘self-enforcing’, since by assumption, the
legal system will not enforce such a stipulation.
Define bM (x) ≡ max xR−v , 0 . For individuals who expect to pay taxes (i.e.,
w > y), it turns out that bM (y ) is the relevant debt constraint (which is equivalent to
equation (5)). For individuals that are expected to receive nontransferable transfers,
the relevant debt constraint is given by bM w . This latter debt constraint is identical
to the one faced by individuals in Model 2 in the absence of redistribution policy;
i.e., see equation (3). A critical feature that generates this latter result is to be found
in our assumption that the transfer payment τ w is made conditional only on the
person’s productivity w and not on the person’s earnings wn. Thus, in the second
period, the person is faced with the following payoffs:
w − τ w − Rb if n
−τ w v if n .
Since the transfer occurs whether the person works or not, for these preferences it
turns out that the critical debt level that makes a person just indifferent between
defaulting or not, is independent of the transfer payment. Thus, in this example, the
redistribution policy has no effect on how hard debt constraints bind for ‘low income’
individuals w < y. (With transferable entitlements, the debt constraint would be
relaxed). On the other hand, ‘high income’ individuals are subject to a tighter debt
constraint, since bM y < bM w for w > y.
(
)
(
ln(
(
ln(
( )
7
(
(
)
)+
)
)
)
= 1
= 0
)
Legal Restrictions on Debt Collection Activities
In the models above, it was assumed that if a person worked and generated wage
income, that the full amount of this income was subject to garnishment by creditors.
In reality, court judgments take into account the economic hardship likely to befall
a delinquent debtor when forced to repay debt via wage garnishment. In particular, there seems to exist (either legally or as a convention in the mind of judges) a
21
minimum material standard of living m such that any w < m is considered to be
legally beyond the reach of creditors. Let us consider the effects of such a policy in
the context of Model 2.
In Model 2, the absolute upper limit on the amount of credit that would be
extended to a person with future market prospects w is given by w/R (i.e., the
present value of his market income). If courts impose a law that effectively makes
any w < m inalienable to the individual, then the maximum credit that will be
extended (assuming that the person will work) is given by max {(w − m)/R, 0} . In
other words, a debtor can now only effectively ‘secure’ a personal loan by using as
‘collateral’ the present value of any income generated beyond m. If the minimum
consumption standard is not relevant (for example, if w is very large or m is very
small), then the appropriate borrowing constraint is given by max {(w − v)/R, 0} ,
as developed in Model 2. For creditors, the appropriate debt constraint to impose is
given by:
bM
w − m w − v , 0 , max
(6)
R ,0
w − max{m, v} , 0 .
= max
R
Essentially, the introduction of m adds another source of excludable consumption
= min max
R
flow for the debtor; whether this flow is economically relevant depends on whether it
exceeds the excludable consumption flow that can be generated in the home sector.
If m > v, then we see that this will serve, if anything, to tighten existing debt
constraints.
7.1 Personal Bankruptcy Law
How does the existence of personal bankruptcy law affect debt constraints in the
credit market? Again, let us ask this question within the context of Model 2.
The main advantage of bankruptcy law for a debtor is that it allows one to separate
the decision to default from the labour supply decision (recall that in the models
above, a person could escape wage garnishment and default only by reallocating time
to the home sector). With personal bankruptcy law, an individual may be able to
default on accumulated unsecured debts without having to divert time away from the
labour market.
In reality, however, one cannot simply declare bankruptcy and renege on all unsecured debt. In order to obtain the legal status of bankrupt, one must first be deemed
eligible for bankruptcy by a judge. In essence, the eligibility requirement is that a
person’s income, net of the carrying cost of debt, is insufficient to maintain some minimum material standard of living. In the present context, we can model the eligibility
requirement as w − Rb < m.
22
Assume that m ≥ v. Clearly, a creditor would be unwilling to extend a loan beyond
the level bM , where w − RbM = m. Thus, with the implementation of bankruptcy
law, the individual would face a debt constraint bM = max {(w − m)/R, 0} , which
is equivalent to (6). In other words, incorporating the bankruptcy code in a credit
market model adds nothing beyond what was discussed in the earlier subsection.25
I think that what the model is trying to tell us here about bankruptcy law is
that its existence cannot be explained in terms of its role in protecting low income
individuals saddled with high debt levels when creditors can fully anticipate the effect
of bankruptcy law on debtor behaviour. The model developed here can be interpreted
as a scenario where bankruptcy law has been in place for a period of time, allowing
the supply of credit to adjust to the parameters of the legal environment. In this
case, we see that bankruptcy law, if anything, can only harm debtors, since the law
leads to tighter borrowing restrictions.
In order to understand why bankruptcy laws exist, I think that it may be necessary to talk about unanticipated changes in the economic environment that lead
to increased political power for debtor groups. With more effective lobbying, these
debtor groups can gain (at the expense of creditors) with a ‘surprise’ implementation of bankruptcy law. The analysis above, however, suggests that future cohorts of
debtors will be harmed as creditors restrict the supply of consumer loans.26
8
Insurance Markets and Credit Markets
Let us briefly explore how insurance and credit markets interact and are affected
by government policy. To this end, let us dispense with Φ and model individual
heterogeneity more simply. In particular, assume that there are only two possible
employment productivities {w, 0}; the latter occurs with probablity 1 − θ. Conse-
quently, θ represents the probability of ‘unemployment’ or, invoking some law of
large of numbers, the fraction of individuals with lousy employment prospects. Assume that w > v > 0, so that people with good market prospects generally prefer to
work, while people with bad market prospects prefer to spend their time in the home
sector.
25
There is a minor difference in that filing for personal bankruptcy requires a real resource cost.
Adding this cost into the analysis would serve to relax the debt constraint, since creditors would
understand that default (through this mechanism) is now more costly for the debtor (assuming that
debtors did not have the protection of the law as modelled in the previous subsection).
26
Of course, future debtors could presumably exert their influence to have bankruptcy laws removed. Alternatively, they may continue to lobby for increased exemption levels.
23
8.1 Closed Economy and Full Insurance
All individuals are ex ante identical. Consequently, there will be no intertemporal
trade in a closed economy and, given the way we have modelled preferences and
endowments, the equilibrium interest rate R∗ will equal infinity. Nevertheless, because
people are risk-averse and are subject to idiosyncratic risk, they will wish (and be
able) to insure themselves. With no impediments to trade, any number of institutions
would be able to implement a ‘full-insurance’ outcome as an equilibrium. By ‘fullinsurance’ I mean an outcome that equates the marginal utility of broadly-defined
consumption across states of the world.
Let (ce , cu ) denote the market consumption that accrues to employed and unemployed people, respectively. Full insurance implies that broadly defined consumption
is equated across states of employment and unemployment; i.e.,
ce
= cu + v.
Notice that in this model, a full-insurance consumption allocation is incentive compatible ; i.e., the insurance agency need not be able to observe individual outcomes
{w, 0} as people have no incentive to lie. The allocation {ce , cu } must satisfy the
resource constraint:
(1 − θ)ce + θcu = (1 − θ)w.
These two equations can be solved for:
ce
= (1 − θ)w + θv;
cu
= (1 − θ)(w − v ).
Notice that ce > cu . In other words, employed people get more market consumption
in order to compensate for the fact that they have to work (and thereby sacrifice
home production).
There are any number of ways to implement the full-insurance allocation above.
For example, imagine that competitive insurance agencies offer individuals the following contract. Let r ∈ {w, 0} denote the individual’s report to the insurance company.
Then, if an individual reports r = 0 (unemployment), the insurance company is
legally obliged to pay the person xu = (1 − θ)(w − v) units of consumption. If an
individual reports r = w (employment), the insurance company is legally entitled to
xe = θ(w − v) units of consumption (i.e., the employed individual is legally obliged
to pay the insurance company this amount). Such a contract yields the insurance
company zero profit and will be accepted by individuals. Alternatively, imagine that
the government implements a tax/transfer scheme (τ,z), where a tax τ = xe is applied to working people and a subsidy (unemployment insurance) z = xu is provided
to unemployed people. Such a government program is balance budgeting and makes
people better off (relative to autarky).
24
8.2 Open Economy
People in the economy above would like to borrow; suppose that there exists a market
for risk-free debt with exogenous interest rate R. Given that individuals have insured
themselves in the manner described above, they are in a position to issue risk-free
debt and hence are able to borrow funds at rate R. Notice, however, the ability to
borrow funds means that, in essence, individuals are able to ‘collateralize’ their debt
by promising (or selling off) claims to their insurance income (policy).
From the perspective of a creditor, each insured individual can be viewed as
an asset with a prospective ‘dividend’ stream equal to {w − xe, xu} in employed
and unemployed states, respectively. Since w − xe > xu , the creditor can know
with certainty that every individual in this economy will have income of at least xu .
Consequently, a creditor would be willing to extend a loan at interest rate R up to
the maximum level xu /R.
8.3
Implications
Notice that a well-functioning insurance market facilitates the operation of a wellfunctioning credit market (i.e., individuals gain access to low interest rate loans).
Apparently, the converse does not hold true; i.e., in this model, a well-functioning
insurance market can exist even in the absence of a market for debt.
Secondly, notice that the imposition of restrictions on debt collection activities
(such as personal bankruptcy laws) would have no effect on the ability of individuals
to insure themselves here. In other words, bankruptcy law does not provide insurance
for the individuals in this model; all it serves to do is to restrict the supply of credit.
Finally, suppose that the insurance program was operated by the government
with a tax/transfer program (τ , z) = (xe , xu ). Here, z represents government supplied unemployment insurance income. In Canada, such income cannot be garnished
by private creditors (Revenue Canada, however, has the legal right to garnish such
income). Consequently, to the extent that unemployment insurance is run by the
government and makes entitlements to the program inalienable, individuals may find
themselves debt-constrained since they cannot commit to paying creditors in the event
of a bad market shock.
25
R
1. Anderson, Leigh, and Saul Schwartz (1998). “An Empirical Study of Canadians
Seeking Personal Bankruptcy Protection,” Office of Consumer Affairs, Canada.
http://strategis.ic.gc.ca/SSG/ca00891e.html
2. Andolfatto, David and James Redekop (1998). “Redistribution Policy in a
Model with Heterogeneous Time-Preference,” Manuscript: University of Waterloo. http://arts.uwaterloo.ca/~dandolfa/research.html
3. Brighton, J.W. and J.A. Connidis (1984). “Consumer Bankrupts in Canada,”
Ottawa. Consumer and Corporate Affairs Canada.
4. Fay, Scott, Erik Hurst, and Michelle J. White (1998). ‘The Bankruptcy Decision: Does Stigma Matter?” Manuscript: University of Michigan.
5. Galenson, David W. (1981). “The Market Evaluation of Human Capital: The
Case of Indentured Servitude,” Journal of Political Economy, 89(3): 446—467.
6. Gropp, Reint, John Karl Scholz, and Michelle J. White (1997). “Personal
Bankruptcy and Credit Market Supply and Demand,” Quarterly Journal of
Economics, CXII, pp. 217-252.
7. Meltzer and Stigler.
26