Allowing for Interaction Terms
In this subsection we consider a logit regression with the delinquency rate as the dependent variable. As independent variables we use those from the baseline case presented in Table 3, plus the 10 interaction and quadratic terms that can be constructed from the four most important independent variables: the FICO score, the CLTV ratio, the mortgage rate, and subsequent house price appreciation.
Allowing for the above interaction terms, we take into account the effect of risklayering—such as, for example, the effect of a combination of a borrower's low FICO score and a high CLTV ratio—on the probability of delinquency. In the above example, it is a priori not clear what the sign on the FICOCLTV interaction variable is. A negative sign means that a low FICO and a high CLTV reinforce each other and give rise to a predicted delinquency probability that is higher than when the interaction is ignored.
A positive sign could be explained by lenders who originate a low FICO and high CLTV loan only if they have positive private information on the loan or borrower quality. It turns out that the coefficient on the FICOCLTV interaction term is positive and significant at the 1% level for delinquency 12 months after origination.
More certain is the sign we expect on the HPACLTV variable. Low house price appreciation is expected to especially give rise to a higher delinquency probability for a high CLTV ratio, because the borrower is closer to a situation with negative equity in the house (combined value of the mortgage loan larger than the market value of the house). Consistent with this intuition, we find a negative and significant (at the 1 percent level) coefficient on this interaction term for delinquency 12 months after origination.
Using this alternative regression specification, we plot in Figure 9 (left panel) the adjusted delinquency rates, as we did in Figure 2 (left panel) for the baseline case specification. Comparing Figure 2 (left panel) and Figure 9 (left panel) we see that adding the interaction and quadratic terms hardly changes the adjusted delinquency rates. Therefore, our result of a continual increase in the adjusted delinquency rate is robust to explicitly taking into account the effect of risklayering and other interaction effects.
Figure 9: Adjusted Delinquency Rate, Alternative Specifications.
The figure shows the adjusted delinquency rate under two alternative specifications; it should be compared to the adjusted delinquency rates presented in Figure 2, the baseline case. In the left panel, the adjusted delinquency rates are obtained using the variables of the baseline case plus 10 additional quadratic and interaction terms that can be constructed from the four most important independent variables—the FICO score, the CLTV, the mortgage rate, and house price appreciation. In the right panel, we estimated the baseline case regression using the data from 2001 to 2005 only.
Adjusted Delinquency Rate (%), with Interaction Terms
Adjusted Delinquency Rate (%), End of 2005
141210864 2 0
Adjusted Delinquency Rate (%), with Interaction Terms
141210864 2 0
14121086420
Weighted Av. Actual
2005
2004
2003
2002
2001
Adjusted Delinquency Rate (%), End of 2005
14121086420
Weighted Av. Actual
2005
2004
2003
2002
2001
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