1.7 Results
1.7.3 The Case of Asymmetric Default Costs
In our benchmark model economy we assume that default costs are symmetric, in the sense that every household, independently of the idiosyncratic earnings shock realization and the level of indebtedness, will be equally penalised. Both high and low income households will suffer the consequences of default, and will be
temporarily excluded from credit market. To prove the strength of asymmetric default costs assumption, we modify our benchmark model in the following way.
Our model employs twelve idiosyncratic earnings states. We assume that households facing a high income state, while choosing to default, will face a higher punishment relative to those households in low states. This punishment takes the form of an earnings loss or alternatively a wage garnishment. This loss intends to capture the pecuniary costs of default.
In our framework, we further assume that this pecuniary cost is dependent on the level of income. The direct costs of default in our modified framework, similarly to Arellano (2008), takes the following form:
χ(y) =
(
wy if wy≤wγ
wγ if wy > wγ (1.16)
where γ is an exogenous parameter capturing the rate of labour income gar- nishment as in Chatterjee et al.(2007). The rationale behind the theory of pecu- niary costs is the notion of a bad credit rating, which will bear a loss of reputation in the credit market. We assume, as inChatterjee et al.(2008) that this pecuniary cost stems from the loss of one’s reputation in the credit market.
Nevertheless, this cost will not be applicable if your labour income realization is below a certain threshold.
Figure 1.7: Vo for Employed and Unemployed with γ = 0.75 : The left panel of this
figure presentsVoforunemployed households under two different realizations of labour earnings
shocks. The right panel of the figure presents Vo foremployed households under two different
realizations of labour earnings shocks. The realization is denoted asyLow,yHigh and is located
on the north-west part of both graphs.
This assumption is in line with the Federal Wage Garnishment Law and the
Consumer Credit Protection Act III. Title III of CCPAlimits the amounts of an individual earnings that may be garnished and further protects an employee from being fired.
It is administrated by the U.S Department of Labour’s Wage and Hour Divi- sion and applies in all fifty states. More importantly, if the disposable earnings of the individual are less than 217.5$ per week, there can be no garnishment. Based on this law we do not allow wage garnishment to take place, as presented in the previous equation when your realized labour earnings are belowwγ. In this manner, the default penalty becomes larger for households facing high earnings shock.
Figure 1.8: Net Savings for Employed and Unemployed withγ= 0.75: The left panel of this figure presents net savings for unemployed households under two different realizations of labour earnings shocks. The right panel of the figure presents 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 graphs.
Claiming that this mechanism has significant impact in the results of our model, we are expecting to see major changes in value, policy functions and equilibrium outcomes compared to our benchmark economy. We should state that all results presented in this section are based on a calibration of parameter
γ = 0.75. This implies that 25%25 of labour earnings will be garnished if you are at a high income state.
Indeed, as we observe in figure 1.7 and in contradiction to the results of our benchmark model, households with higher labour income default less compared
25Title III of the CCPA sets the maximum amount that could be garnished in any working
week or pay period. This is independent to the number of garnishments orders that might be received by an employer. For ordinary garnishments orders including bankruptcy, any state or federal tax normally this rate would not exceed 25% of the employee’s disposable earnings. There exist a few limitations or exceptions for cases of child support, alimony, non-tax debt owed to federal agencies, defaulted federal student loans, but 25% is in most cases the upper bound.
to those with lower. In the left panel of figure 1.7 is evident that employed households facing a high income shock default when their net worth to income ratio is below −0.7 while those facing a low income shock default when their net worth is below −0.55.
The results are similar for unemployed households, in the sense that house- holds with higher earnings realization default more. Nevertheless, unemployed households as observed in the left panel of figure1.7 default only when are highly indebted, or more precisely when their net-worth to income ratio is below −1.0 and very close to the model’s borrowing limit.
This result remains unchanged compared to our benchmark model, since these households as previously discussed are willing to sacrifice a part of their consump- tion to repay their debts and consequently maintain their access to credit market. This is due to their fear that a bad state will continue to be realized in the future and without access to borrowing, consumption might turn below subsidence level and very close to zero. In other words, “survival” is a key element in the decision making of these households.
For a better illustration of our results we present figure1.8 where is clear that employed households under a high income realization and positive net worth do not choose to borrow. This is different compared to the results of our benchmark model in figure 1.4. This is because default option is not any more so attractive, particularly for high income households.
With symmetric default costs, these households were enjoying the benefits of defaults, without facing an extra cost. In this manner, they would prefer to bor- row more and default, when they were given the option, while their high labour earnings would remain unaffected. With asymmetric default costs and when in- corporating wage garnishment, labour earnings would be affected after default, since a part of them will be garnished and essentially lost from the household’s budget set.
Figure 1.9: Consumption Levels for Employed and Unemployed withγ= 0.75: The left panel of this figure presents optimal consumption for unemployed households under two different realizations of labour earnings shocks. The right panel of the figure presents optimal consumption foremployed 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.
Precautionary savings motives for high earnings households strengthen, since borrowing and defaulting do not appear to be an optimal strategy to maximize consumption utility. For consumption smoothing purposes precautionary savings are less risky and guarantee that no earnings loss will be realized.
In a way, the introduction of this asymmetry dampens the strategic default motives and make default option appealing more in a bad state realization, when a household will have very little to lose and no option to borrow more, due to the model’s constraint.
Turning to optimal consumption behaviour we realize that in presence of asym- metric default costs, consumption of high income employed households is on av- erage less compared to the benchmark case of symmetric default costs. The right panel of figure1.9shows that consumption is smoother and on average lower com- pared to the right panel of figure1.5. The same holds for unemployed households.
Figure 1.10: Default Regions for Employed/Unemployed andyLow andyHigh earn-
ings with γ = 0.75 : The left panel of this figure presents default regions for an unem-
ployed/employed state when a low labour earnings shock is realised yLow. The right panel of
the figure presents default regions for an unemployed/employed state when a high labour earn- ings shock is realizesyHigh. To specify the default regions we compare value of repaymentVR
to value of defaultVD as depicted in the north-west part of all graphs.
However, we should mention that optimal consumption behaviour of low- income or unemployed households resembles closely the results of our benchmark model. This however is not the case for high-income employed households, exactly due to the extra costs being apparent when choosing to default.
Essentially high income households prefer to live in a state of lower consump- tion, while expanding their savings buffer. The asymmetric default cost is inter- nalized and the post default state features such high costs that becomes unde- sirable. In this respect, high income households strictly prefer to achieve perma- nently a lower consumption bundle, rather than enjoy a higher borrowing-boosted consumption temporarily and finally face a permanent earnings loss.
To conclude this section, we present the default regions in figure1.10. Firstly it is apparent that our benchmark model’s defaults result reverts as is depicted
from the Vo in figure 1.7. Defaults occur more in the low idiosyncratic state, and as in Arellano (2008) default incentives are stronger the lower the income realization. This serves as a proof that the assumption of asymmetric default cost is very strong and can alter the results.
However, this assumption does not appear to hold in data, especially when studying consumer bankruptcies with unsecured debt. We should further com- ment that this result in our model is only feasible for very high values of wage garnishment. For this reason we have chosen to calibrate this parameter to the highest possible value that could have an empirical support.
Nonetheless, Chapter 7 bankruptcy which is closely resembled in this chap- ter does not induce a wage garnishment. This can only be met in Chapter 13 bankruptcy code. Chapter 13 Bankruptcy code provides debtors an opportunity to save their assets (i.e. houses) from foreclosure, by allowing to enter a new payment plan. During this payment plan a portion of your income is garnished as a contribution towards your repayment instalments.