Figure 1.3: Vo for Employed and Unemployed: The left panel of this figure presentsVo
for unemployed under two different realizations of labour earnings shocks. The right panel of the figure presentsVo foremployed under two different realizations of labour earnings shocks.
The realization is denoted asyLow,yHighand is located on the north-west part of both graphs.
In figure 1.3 we observe the behaviour of value of the option for both employed and unemployed households. We present the value of the option for two dif- ferent realizations of labour earnings shock. Note that unemployed households (see Krueger et al. (2016)) carry the idiosyncratic state even if does not affect their current labour earnings directly, since they do not participate in the labour market. This occurs due to our definition of unemployment benefits, which are defined as a fraction of potential labour earnings of a household.
The value of the option, Vo , embodies the optimal choice between value of repayment and value of default for households with negative net worth23, along
with the regular value function for households with positive net worth. Recall that households with positive net worth are not allowed to default in this model. A striking result is that households with higher labour earnings realization both in the employed and unemployed state default more compared to low labour earnings households. In figure1.3the straight horizontal line of value of the option indicates the choice of the default option.
At a first inspection, this result appears to be counter-intuitive. We pose the following question: Why would households with lower labour earnings choose to default less? Firstly, we should recall that in this model default is strategic. In this sense, we disregard cases where households can’t pay and we only consider cases that households won’t pay, as a consequence of their optimal choice.
Analysing the right-hand-side part of figure1.3, we can indeed see that house- holds with low earnings, find default optimal only when their net-worth is very negative. The cost of default bears an exclusion from credit market, hence an exclusion from borrowing for a period of around seven years24. This is in line
with Chapter 7 bankruptcy law in the United States. A Chapter 7 bankruptcy remains on a household’s credit report for at least seven years from the date of filing the Chapter 7 petition. This implies that during this period households will have very restricted or no access to credit.
It is clear that in this model borrowing serves as a means to achieve consump- tion smoothing. In particular, households with very low earnings find crucial for their survival to have some access to credit that enables them to achieve even a low consumption level. In support of this argument is the left panel of figure 1.3. The graph indicates that unemployed households default less compared to employed households, or more precisely default only when featuring lower levels of net worth compared to employed households.
To further comprehend this result, we should recall that the only source of in- come for a household in an unemployed state is unemployment benefits. However,
23Note that net worth is expressed in every graph as a ratio of net worth to mean income. 24We calibrate parameterθin our model to 0.85 which captures an average exclusion period
this income might not be sufficient for a household to support even the essential lowest level of consumption while also repaying his debt.
One could argue that in such an event household should find it optimal to de- fault and enjoy the partial debt relief arising from the exercise of this option. In this manner these households could possibly achieve higher consumption. How- ever, as we observe in the left panel of figure1.4households in this state choose to borrow more and move to a higher level of negative net worth without defaulting. This behaviour confirms that unemployed households are willing to live in a state of limited consumption while maintaining their access to credit.
Figure 1.4: Net Savings for Employed and Unemployed: The left panel of this figure displays net savings forunemployedhouseholds under two different realizations of labour earnings shocks. The right panel of the figure displays net savings for employed households under two different realizations of labour earnings shocks. The realization is denoted as yLow,
yHigh and is located on the north-west part of both figures.
In that sense, access to credit appears to be more valuable for households in a bad state. Since the probability to remain unemployed is slightly above five times the probability to remain employed, unemployed households perceive their
current status as more “permanent”. Thus, they are not willing to take the risk of defaulting and loose their access to credit market. They are more concerned about the continuation of a bad state realization, under which they will not achieve even the lowest level of consumption if being excluded from credit. Hence, they adopt the strategy of accumulating more debt bearing its extra cost until a good state is realized in the future. These households only default when reaching the borrowing limit or more precisely when they lie very close to it. Essentially they are willing to borrow as long as someone is willing to lend them, mainly aiming to subsidise their consumption.
The finding of low default rates amongst the more financially distressed house- holds, can shed light on why lenders rarely renegotiate loan modifications with very high risk borrowers. This is because most of them continue to pay. (see Adelino et al. (2013)). Furthermore, these results provide theoretical support to new empirical evidence introduced by Gerardi et al. (2015). They find that the vast majority of borrowers with very low ability to pay avoid default and prefer to decrease their consumption to subsistence levels.
At the opposite end, households that are employed and face a higher labour income shock as observed in the right panel of figure 1.3 default for almost any non-positive value of net worth . Interestingly, even if it is not apparent in figure 1.3since we do not plot the highest income shock, they would be willing to default, if they were given the option, even for slightly positive values of net-worth.
This indicates that indirect cost of defaults for higher labour income employed households is not as large compared to the low income or unemployed households. This is because these households have enough earnings to support their consump- tion, even when being excluded from credit market.
We further argue that high labour income households will continue to borrow even for positive values of net worth to increase their consumption. This can be seen in the right panel of figure 1.4. Households with positive net worth and good realization of earnings shock, choose to borrow up to a net worth to income ratio of 1. However, and since in our framework positive net-worth households are not allowed to default, thus are forced to repay, they do not achieve perfect consumption smoothing. Clearly default option could serve as a means to smooth your consumption.
Consumption policy functions for employed and unemployed states are graph- ically illustrated in figure 1.5. Consumption exhibits spikes and higher volatility for positive values of net worth. Recall that, default is not an option for agents that hold positive net worth. Therefore, these borrowing households that would optimally decide to default and are not allowed, would be forced to reduce their consumption in order to repay. This would hinder their consumption smoothing, since the default option and not only borrowing/saving functions as a consump- tion insurance mechanism.
In the right panel of figure 1.5 it is evident that consumption is constantly larger for higher income employed households compared to lower income employed households up to a certain point of net worth. Above a level of net worth to income ratio around 1.5, consumption for both low and high labour income employed households is almost equivalent.
This can be explained by the fact that beyond a certain level of wealth the marginal propensity to consume from labour earnings is less than the marginal propensity to save. In support of this argument is figure 1.4. It is apparent that net savings is an increasing function of net worth independently of any labour earnings realization. Furthermore, households being in a higher income state tend to save more.
Finally, when a household is in an unemployed state while having positive net worth saves less compared to an employed household with equal net worth, since it finds necessary to subsidise his consumption.
Figure 1.5: Consumption Levels for Employed and Unemployed: The left panel of this figure presents optimal consumption forunemployedhouseholds under two different realizations of labour earnings shocks. The right panel of the figure presents optimal consumption for employed households under two different realizations of labour earnings shocks. The realization is denoted asyLow,yHighand is located on the north-west part of both graphs.