Interfaces de usuario

1.3.1

Mortgage Defaults

The starting point to discuss households’ defaulting possibilities is to consider the put option component of the mortgage (Bajari, Chu, and Park, 2008). Consider a frictionless economy, absent any de- faulting costs, borrowers would default when the present value of their asset (the house) is lower than the outstanding value of their debt (the mortgage). This is the implicit assumption behind many

1.3. The Model Economy 15

of the models that consider endogenous default possibilities and it is sometimes referred to in the literature as the “ruthless defaulting condition”. However, the literature on mortgage defaults points both at the presence of additional costs of defaulting and to motives that might abstract from pure economic reasons. Guiso, Sapienza, and Zingales (2013)show that not only pecuniary motives, but also con- siderations related to fairness and morality play a role in determining defaulting decision. Furthermore, they argue that being exposed to strategic defaulters increases the chances of behaving similarly. The presence of further components affecting the decisional problem of homeowners justifies the idea of the so-called negative equity con- dition, which tells that homeowners will default when the level of their equity (housing) is strictly negative and sometimes the differ- ence between the current value of their housing and the value of the mortgage they have to pay back is quite large. It does not surprise then, that a large body of literature tried to estimate how negative the “negative equity” actually is. Indeed,Foote, Gerardi, and Willen (2008)show that in the recession of 1990-1991 in Massachusetts only 6.4% of homeowners decided to default even if they were in a neg- ative equity position. Independently from the particular level of the threshold below which borrowers prefer to default, defaulting is con- sidered strategic when reaching a particular level of negative equity the homeowners would still be able to repay his or her loan but rather prefers to default. According to our approach, all defaults, being them coming from primers or sub-primers, are strategic, the difference being that we design a financial contract that allows sub- primers to exercise the put option as long as their housing value falls below the mortgage repayment, while primers exercise the option at a lower threshold.8

In our approach we do not aim at describing with extreme realism this decision. However, by allowing sub-prime borrowers to default 8_{In our approach we do not consider an important aspect highlighted in the} literature which affects homeowners decisions to default, that of liquidity con- straints, derived from idiosyncratic shocks to homeowners’ income –Foote, Ger- ardi, and Willen (2008)call the joint combination of a negative equity and liquidity shocks the double trigger hypothesis. However, we do allow for the possibility of an idiosyncratic shock to the value of housing investment, which somehow ren- ders the idea of an income shock.

on the basis of a utility-based approach we explicitly refer to the idea of strategic default. Furthermore, following the findings of those studies, we introduce an exogenous component that we callstigma, which is added to the defaulting condition. By taking on a positive value for primers, this component ensures that their rate of default in steady state is lower than that of sub-primers. Thestigmacomponent is a catchall variable, a short cut that we take in order to consider all the motives which attenuate home-owners willingness to default. Introducing strategic default option in a DSGE framework allows us to have a clear separation between two distinct classes of borrowers with the advantage of rendering some key aspects of the mortgage market, such as the different LTV ratios, different risk premia and default rates.

1.3.2

An overview of the model

The model economy is composed by three categories of households (savers, prime and sub-prime borrowers), by banks and firms, which are owned by savers and by unions.

There is a continuum of households over the [0,1] interval, and each household is composed by a large number of members. Households groups share the same utility function which comprises, a part from consumption, an aggregate non-durable good – housing – and labor services. We follow FL assuming that housing investment, for each single household member, is subject to an idiosyncratic shockωι_t af- fecting its final value, and allowing borrowers to default, though one first important novelty of our approach is to explicitly model primers and sub-primers separately. The idiosyncratic shock is private infor- mation of the investor and it is assumed to be independently and identically distributed (i.i.d.) across members of the same household and across time. In particular, ωt follows a log normal distribution

with p.d.f equal toft(ωt)and cumulative distribution function equal

toFt(ωt)9. Furthermore, its expected value is Et(ωt) = 1at all time

for each households in each group. This means that there is no aggre- gate risk in housing investment at the household level. This reason,

9_{We follow BGG by imposing a restriction on the hazard rate h(ω) =} F.(ω)

1−F(ω).

1.3. The Model Economy 17

coupled with the fact that savers do not borrow and therefore never default, suffices to ignore the effect of the shock on savers.

All households members in the prime and sub-prime group are ex- ante identical. When members are required to pay back their loan they can decide to default strategically. We assume that there is per- fect insurance among household members so that consumption of non-durable goods and housing services are ex post equal across all members of the household. Hence, borrower household members are also ex post identical.

The riskiness of housing investment changes over time through a change in the standard deviationσω,tof the shocks’ distribution. The

idiosyncratic shock is private information of the household member and to observe it the lender must pay an auditing cost that is a fixed proportionµof the realized housing stock value. This constitutes an agency problem that introduces a first financial friction in the model since borrowers are endogenously constrained in the amount they can borrow from banks. The presence of an agency problem between borrowers and lenders allows us to endogenize the constraint and to introduce a risk premium in a way similar to the problem developed by BGG. As explained by FL, the shock can be thought as a shock to the investment itself or as a shock to the price of houses, given by geographical differences. Considering the nature of the shock, which displays an unchanged mean productivity of housing invest- ment, we can also think about it as an increase in uncertainty that endogenously triggers a higher number of defaults in the housing sector (Pataracchia et al., 2013). Finally, as noted byDemyanyk and Hemert (2011), the quality of loans considerably deteriorated during the 6 years before the financial crisis, therefore we can also interpret the shock to the standard deviation as a way to reproduce this dete- rioration of loans in the sub-prime sector.

Banks collect deposits from savers and lend to impatient house- holds. Lending assumes the form of a one period contract, where a state-contingent contractual interest raterk_t is paid each period by non defaulting borrowers to ensure that the banks get a safe return (rl

t), therefore the risk is entirely borne by borrowers. If a household’s

the agent, after having paid the monitoring cost. Banks are subject to an optimal leverage ratio, which can be thought as arising from regulatory requirements as for example the Basel framework on cap- ital adequacy. In deviating from that optimal level, the bank incurs into a cost, that endogenously pushes the bank to get back to the op- timal level of leverage. The deviation of the bank from the optimal level reduces banks’s margins and exacerbates its capital position, entailing a reduction of the loan rate, which moves sluggishly given monopolistic competition in the bank market.