## Results

Table 3 shows the results of the logit regression described in Section 3.1 with the delinquency (panel A) or foreclosure (panel B) dummy variables 12 months after origination as the dependent variables. The explanatory variables are listed in the first column. Focusing on the marginal effect of the regression coefficients, defined in Equation 2, we see that the mortgage rate is the most important factor explaining cross-sectional differences in loan performance. The positive sign means that a higher mortgage rate

11 We also studied specifications that included loan purpose, reported in Table 1, and housing outlook, defined as the house price accumulation in the year prior to the loan origination. These variables were not significant and did not materially change the regression coefficients on the other variables.

Table 2: Variable Definitions

This table presents definitions of the variables used in the regression analysis. The first two variables are used as dependent variables. The other variables are used as independent variables. We report the expected sign for the independent variables in parentheses and sometimes provide a brief motivation.

Variable (Expected Sign)

Explanation

Delinquency Dummy Foreclosure Dummy FICO Score (-)

Combined Loan-to-Value Ratio (+) Debt-to-income Ratio (+) Missing Debt-to-income Dummy (+) Cash-Out Dummy (-)

Investor Dummy (+) Documentation Dummy (-)

Prepayment Penalty Dummy (+)

Mortgage Rate (+)

House Price Appreciation (-) Product Type Dummies (+)

Origination Amount (?)

Payments on the loan are 60 or more days late, the loan is in foreclosure, or the loan is real estate owned.

The loan is in foreclosure or is real estate owned.

Fair, Isaac and Company (FICO) credit score at origination.

Combined values of all liens divided by the value of the house at origination. A higher combined loan-to-value ratio makes default more attractive.

Back-end debt-to-income ratio, defined by the total monthly debt payments divided by the gross monthly income, at origination. A higher debt-to-income ratio makes it harder to make the monthly mortgage payment.

Equals one if the back-end debt-to-income ratio is missing and zero if provided. We expect the lack of debt-to-income information to be a negative signal on borrower quality.

Equals one if the mortgage loan is a cash-out refinancing loan. Pennington-Cross and Chomsisengphet (2007) show that the most common reasons to initiate a cash-out refinancing are to consolidate debt and to improve property.

Equals one if the borrower is an investor and does not owner-occupy the property.

Equals one if full documentation on the loan is provided and zero otherwise. We expect full documentation to be a positive signal on borrower quality.

Equals one if there is a prepayment penalty and zero otherwise. We expect that a prepayment penalty makes refinancing less attractive.

Initial interest rate as of the first payment date. A higher interest rate makes it harder to make the monthly mortgage payment.

Margin for an adjustable-rate or hybrid mortgage over an index interest rate, applicable after the first interest rate reset. A higher margin makes it harder to make the monthly mortgage payment.

MSA-level house price appreciation from the time of loan origination, reported by the Office of Federal Housing Enterprise Oversight (OFHEO). Higher housing equity leads to better opportunities to refinance the mortgage loan.

We consider four product types: FRMs, Hybrids, ARMs, and Balloons. We include a dummy variable for the latter three types, which therefore have the interpretation of the probability of delinquency or foreclosure relative to FRM. Because we expect the FRM to be chosen by more risk-averse and prudent borrowers, we expect positive signs for all three product type dummies.

Size of the mortgage loan. We have no clear prior on the effect of the origination amount on the probability of foreclosure and delinquency, holding constant the loan-to-value and debt-to-income ratio.

increases the probability of delinquency (panel A) and foreclosure (panel B). Based on the point estimate in panel A, a one standard deviation increase in the mortgage rate increases the probability of delinquency by 1.9 percentage points 12 months after origination.

The second most important marginal effect is associated with the FICO score. A higher FICO score decreases the probability of delinquency (panel A) and foreclosure (panel B), as one would expect. In general all the variables have the expected signs (as discussed in Table 2) and all variables are statistically significant at the 1% level. We also experimented with several interaction and quadratic terms, which yielded very similar results, both qualitatively and quantitatively (see also Section 6.1).

In panel C of Table 3 we report the "Deviation," defined as the difference between the average value of a variable in 2001/2006 and the average value over the whole sample, expressed in standard deviations (see Equation 3). In particular, the average mortgage rate was high in 2001 and the average house price appreciation was low in 2006, both compared with the average values over the whole sample period.

In panels A and B, "Contribution" measures to what extent a variable can explain why the delinquency and foreclosure rates in 2001 or in 2006 differed from the average over the entire period. We see that the high mortgage rate for vintage 2001 loans was quantitatively the most important factor explaining high observed delinquency and foreclosure rates for that year. Additionally, the low average FICO score for 2001 loans and the low house price appreciation in the months following origination help explain the poor performance of 2001. One could say that in 2001 we had "the perfect storm."

For vintage 2006 loans, low subsequent house price appreciation, in particular, contributed to their weak performance, and accounted for a 1.1 percentage point increase in delinquency rate and a 0.6 percentage point increase in foreclosure rate, 12 months after origination. The mean values in 2006 for the other variables were not sufficiently different from the sample mean to contribute much to a different delinquency or foreclosure rate in 2006. It is worth noting that the increase in the average CLTV ratio and the decrease in the fraction of loans with full documentation over time does not contribute a lot to the high delinquency and foreclosure rates in 2006.

We also computed the contributions of all explanatory factors for the other vintage years (the results are not reported). For loans originated in 2003 and 2004, the high subsequent house price appreciation between 2003 and 2005 contributed to a lower actual delinquency rate. For example, the explained change in the delinquency rate 12 months after origination was -0.3 percentage points and -0.6 percentage points for 2003 and 2004, respectively. The house price appreciation variable had the largest (absolute)

Table 3: Determinants of Delinquency and Foreclosure

The table shows the output of the the logit regression defined in Equation 1, where the event is that a loan is delinquent (panel A) or in foreclosure (panel B), 12 months after origination. The first column reports the explanatory variables (constant not reported). In panels A and B we report the marginal effect of a variable, defined in Equation 2, and the contribution of a variable to explain a different probability of delinquency or foreclosure in 2001/2006, defined in Equation 4. Panel C reports the deviation of the 2001/2006 value of a variable from the average over 2001—2006, defined in Equation 3. We have the first-order approximation contribution ¡=s marginal X deviation. All coefficients are statistically significant at the 1% level.

Panel A: Delinquency Rate Panel B: Foreclosure Rate Panel C: Deviations

Explanatory Marginal Contribution Contribution Marginal Contribution Contribution Deviation Deviation

Variable Effect (%) 2001 (%) 2006 (%) Effect (%) 2001 (%) 2006 (%) 2001 2006

Explanatory Marginal Contribution Contribution Marginal Contribution Contribution Deviation Deviation

Variable Effect (%) 2001 (%) 2006 (%) Effect (%) 2001 (%) 2006 (%) 2001 2006

Fico Score |
-1.75 |
1.03 |
-0.26 |
-0.45 |
0.24 |
-0.06 |
-0.37 |
0.11 |

Combined Loan-to-Value Ratio |
1.60 |
-0.26 |
0.16 |
0.58 |
-0.09 |
0.06 |
-0.20 |
0.12 |

Debt-to-income Ratio |
0.73 |
-0.07 |
0.10 |
0.19 |
-0.02 |
0.03 |
-0.11 |
0.15 |

Missing Debt-to-income Ratio |
0.57 |
0.04 |
-0.06 |
0.11 |
0.01 |
-0.01 |
0.08 |
-0.12 |

Cash-Out Dummy |
-0.32 |
-0.04 |
0.02 |
-0.12 |
-0.01 |
0.01 |
0.11 |
-0.07 |

Investor Dummy |
0.37 |
-0.04 |
0.01 |
0.18 |
-0.02 |
0.00 |
-0.12 |
0.03 |

Documentation Dummy |
-0.68 |
-0.22 |
0.15 |
-0.25 |
-0.08 |
0.06 |
0.30 |
-0.20 |

Prepayment Penalty Dummy |
0.10 |
0.01 |
0.00 |
0.05 |
0.01 |
-0.00 |
0.12 |
-0.01 |

Mortgage Rate |
1.90 |
2.22 |
0.10 |
0.94 |
1.11 |
0.05 |
1.14 |
0.07 |

Margin |
0.68 |
-0.07 |
-0.01 |
0.23 |
-0.02 |
-0.00 |
-0.11 |
-0.02 |

House Price Appreciation |
-1.01 |
0.62 |
1.10 |
-0.44 |
0.31 |
0.56 |
-0.48 |
-0.80 |

Hybrid Dummy |
0.07 |
-0.01 |
-0.02 |
0.08 |
-0.01 |
-0.02 |
-0.12 |
-0.23 |

ARM Dummy |
0.04 |
-0.01 |
0.01 |
0.00 |
0.00 |
-0.00 |
-0.23 |
0.20 |

Balloon Dummy |
0.21 |
0.01 |
0.11 |
0.09 |
0.01 |
0.05 |
0.06 |
0.52 |

Origination Amount |
0.77 |
-0.26 |
0.20 |
0.32 |
-0.10 |
0.08 |
-0.39 |
0.27 |

contribution among all variables considered for those years. Therefore, we can say that high house price appreciation between 2003 and 2005 masked the true riskiness of subprime mortgages.12

The product type has a relatively small effect on the performance of a loan, beyond what is explained by other characteristics (see Table 3). In Figure 4 we showed that FRMs experience a much lower delinquency rate than ARMs, which must be driven by borrowers with better characteristics selecting into FRMs.13

To examine to what extent the logit regression model is capable of explaining the large observed delinquency and foreclosure rates in 2006, we compare the adjusted delinquency and foreclosure rates for different ages and different vintages in Figure 2. The adjusted rate at a given age equals the prediction error (the actual rate minus the predicted rate) plus the weighted average rate over the 2001-2006 period, with weights equal to the number of loans originated in each year. The predicted delinquency and foreclosure rates are determined using Equation 6. We add up the weighted-average actual rates to facilitate the comparison with the actual rates plotted in Figure 1. Interestingly, both the adjusted delinquency and foreclosure rates have been increasing over the past six years. In other words, loan quality deteriorated monotonically between 2001 and 2006. This picture is in sharp contrast with that obtained from actual rates, depicted in Figure 1, where 2003 was the year with the lowest delinquency and foreclosure rates, and 2001 was the year with the second-highest rates.

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