Borrowing and default

Before turning to the welfare comparisons it is instructive to look at how defaults happen in the model.

8

Increasing the number of discrete points to a level where the approximation becomes reasonable is not computationally feasible.

−2.5 −2 −1.5 −1 −0.5 0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Assets q(a, ι , β ;K,Z)

Unemployed, βL; Average capital, Recession Figure 3.3: Price schedules for defaultable bonds

Borrowing Figure 3.3 depicts an example of the bond price schedule posted by lenders.

In line with Theorem 6 in Chatterjee et al. (2007), at low levels of debt no consumer is expected to default, therefore the borrowing rate is constant in this region. This is actually the case for a fairly large interval of debts, but once the default probability becomes positive

it decreases bond prices rather steeply in every possible state (a, ι, β;K, Z).

Figure 3.4 depicts the same information, but instead of focusing on the price of each bond, it shows the (negative of the) total amount that borrowers receive upon entering the loan contracts. It is interesting to note that the maximum of the borrowing amount schedule is reached shortly after bond prices start to decrease. It will never be optimal to pick a

contract that is to the left of the minimum of the q(a)a schedule depicted on Figure 3.4,

−2.5 −2 −1.5 −1 −0.5 0 −1.8 −1.6 −1.4 −1.2 −1 −0.8 −0.6 −0.4 −0.2 0 Assets q(a, ι , β ;K,Z) ⋅ a

Unemployed, βL; Average capital, Recession

Figure 3.4: Amount received (q(a)a), when issuing adefaultable bonds

promising a small repayment. In general the limit depends on both the aggregate and individual state variables (including the borrower’s type), but the fluctuations in the credit limit due to aggregate shocks are practically small, less than 5 percent of quarterly wages.

Defaults While the model features a number of shocks to households’ income, Table 3.3

shows that in the simulations, the main reason for defaulting is unemployment: 97 percent of the bankruptcy filings are made by unemployed. Consequently, most of the defaults happen in recessions, when the probability of not finding work increases from 33.3 percent to 60. The mean of the transitory income shock conditional on defaulting coincides almost perfectly with the unconditional mean of the distribution it was drawn from indicating that temporary shocks to income do not push households into default. Permanent income shocks

Mean

Assets before default (normalized) -1.64

Permanent income shock before default 0.96

Transitory income shock before default 0.99

Share of defaulters unemployed 0.97

Share of defaults in recession 0.77

Average unemployment duration before default (quarters) 5.1

Table 3.3: Defaults in the simulations

are only slightly more correlated with defaults, on average defaulters suffer a 4 percent decrease in their permanent incomes in the period when they default. Assets relative to permanent income average -1.64, very close to the borrowing limit of impatient households in most aggregate states.

Based on these observations it is instructive to look at how households cope with long unemployment spells in the model with and without default. Figure 3.5 displays the time series of an impatient household that starts period 1 with zero assets and is employed. The household is assumed to become unemployed in the next period and remain unemployed for the following 5 periods. The income shocks are set to their mean values of 1. The solid (blue) line shows the evolution of the consumption and end-of-period asset series in the model with default and borrowing while the dashed (red) line shows the same series in the model without default and hence no borrowing. While employed in the first period, the household increases its asset holdings, though the increase is much bigger in the model without borrowing. Correspondingly, consumption is higher in the model with default. As the unemployment spell begins, both households decrease their consumption by similar amounts, with the household in the default model accumulating debt. At the beginning

of period 4 the household in the model without default runs out of savings and is down to consuming her income (unemployment benefit). While nearing its borrowing limit, the household in the default model is still able to supplement the unemployment benefit with additional funds through going further into debt. By period 5, the fourth period in unem- ployment, both households behave as essentially hand-to-mouth consumers consuming their current income (unemployment benefit), with the notable difference that for the household with outstanding debt, this still means incurring further debt just to pay the interest due on the accumulated credit. In period 6 the indebted household defaults and sees its asset

position return to 0, while incurring the pecuniary cost (γY) of bankruptcy.

All in all, the household with access to credit was able to enjoy significantly higher consumption for 4 out of the six periods in the simulation. Given that a 5 period long unemployment spell is rather rare, even in a recession its probability is just under 8 per-

cent (∼0.65), most households who start to go down this same route are likely to escape

somewhere along the way, without resorting to bankruptcy protection.