RDP 2020-03: The Determinants of Mortgage Defaults in Australia – Evidence for the Double-trigger Hypothesis Appendix C: Robustness Checks – Multinomial Logit Models
July 2020
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The first-stage multinomial logit model shares many similarities with the competing risks, proportional hazards model, including producing similar results. The categories for dependent variable are entries to 90+ day arrears and full repayment, relative to the base category of remaining current on payments. It is estimated using quarterly observations for the same sample of loans and includes the same explanatory variables, plus seasoning (specified with a cubic term) as an explanatory variable.
The second-stage multinomial logit model differs more substantively to the baseline model. The dependent variable is each loan's status 12 months after entering arrears; the categories are foreclosure, curing and repayment, relative to the base category of remaining in arrears. Nonetheless, results are also similar to the proportional hazards model.
Dependent variable: | Entered 90+ day arrears | Full repayment | Entered foreclosure | Cured | Full repayment |
---|---|---|---|---|---|
Model stage: | One | One | Two | Two | Two |
Indexed scheduled LVR (base = (50,60]) | |||||
(0,30] | 0.943 (−1.18) |
0.885*** (−8.60) |
0.929 (−0.49) |
1.189* (−2.41) |
1.194* (−2.02) |
(30,40] | 0.813*** (−3.99) |
0.830*** (−16.28) |
0.826 (−1.15) |
1.181* (−2.39) |
1.099 (−1.13) |
(40,50] | 0.860*** (−4.02) |
0.870*** (−13.94) |
0.803 (−1.39) |
1.074 (−1.18) |
1.075 (−1.06) |
(60,70] | 0.904*** (−3.39) |
0.945*** (−7.43) |
0.786 (−1.92) |
1.067 (−1.04) |
1.023 (−0.36) |
(70,80] | 1.110*** (−3.67) |
0.950*** (−6.05) |
1.006 (−0.07) |
0.905 (−1.83) |
0.855** (−2.61) |
(80,90] | 1.253*** (−7.20) |
0.761*** (−25.35) |
1.529*** (−4.30) |
0.914 (−1.49) |
0.808** (−2.73) |
(90,100] | 1.407*** (−8.13) |
0.512*** (−32.39) |
1.980*** (−5.24) |
0.912 (−1.07) |
0.633*** (−4.16) |
(100,110] | 1.794*** (−9.95) |
0.377*** (−20.90) |
1.939*** (−4.40) |
0.667** (−3.29) |
0.399*** (−6.32) |
(110,120] | 1.976*** (−9.14) |
0.396*** (−9.33) |
3.956*** (−5.47) |
0.954 (−0.23) |
0.763 (−1.02) |
(120,150] | 2.117*** (−4.76) |
0.591** (−3.12) |
3.260*** (−4.52) |
0.754 (−1.32) |
0.602 (−1.62) |
(150,200] | 2.696*** (−3.89) |
0.654** (−2.63) |
5.708*** (−5.26) |
0.558* (−2.04) |
1.077 (−0.17) |
200+ | 3.310*** (−7.70) |
0.637* (−2.37) |
6.135*** (−7.59) |
0.338** (−2.65) |
2.052** (−2.83) |
Original LVR (base = (0,60]) | |||||
(60,80] | 1.013 (−0.37) |
1.035*** (−4.94) |
0.867 (−1.26) |
0.938 (−1.35) |
1.035 (−0.63) |
80+ | 1.339*** (−12.04) |
1.219*** (−22.40) |
1.073 (−1.04) |
0.946 (−1.37) |
1.076 (−1.44) |
Turnover ratio | 1.014 (−0.97) |
1.042*** (−8.01) |
0.897*** (−3.59) |
1.028* (−2.05) |
1.090*** (−4.52) |
Unemployment rate | 1.078** (−2.95) |
1.060 (−1.58) |
1.083 (−0.98) |
0.963 (−1.24) |
0.921* (−2.02) |
Unemployment rate^2 | 0.998* (−2.16) |
0.996 (−1.57) |
0.998 (−0.37) |
1.003 (−1.89) |
1.003 (−1.39) |
Serviceability ratio (base = (10,20]) | |||||
(0,10] | 0.606*** (−14.19) |
1.018** (−2.61) |
1.385** (−2.81) |
1.175* (−2.36) |
1.076 (−0.83) |
(20,30] | 1.413*** (−13.35) |
1.003 (−0.46) |
0.869 (−1.52) |
1.001 (−0.02) |
1.058 (−1.17) |
(30,40] | 1.789*** (−18.06) |
0.975** (−2.88) |
0.857 (−1.27) |
1.025 (−0.39) |
1.124 (−1.70) |
40+ | 1.922*** (−15.91) |
0.928*** (−5.51) |
0.994 (−0.04) |
0.980 (−0.23) |
0.988 (−0.12) |
Lagged change in interest rates (bps; base = (−2,2]) | |||||
<−25 | 0.781*** (−7.91) |
0.807*** (−23.77) |
n/a | n/a | n/a |
(−25,−2] | 0.934* (−1.99) |
0.873*** (−17.30) |
n/a | n/a | n/a |
(2,25] | 1.027 (−1.11) |
0.893*** (−17.23) |
n/a | n/a | n/a |
25+ | 1.185*** (−4.69) |
0.990 (−0.98) |
n/a | n/a | n/a |
Repayment buffer (months; base = (1,6]) | |||||
<1 | 2.315*** (−34.96) |
0.975*** (−4.44) |
n/a | n/a | n/a |
6+ | 0.335*** (−31.31) |
0.869*** (−19.69) |
n/a | n/a | n/a |
Income <$180,000 | 0.931* (−2.57) |
0.990 (−1.43) |
0.799 (−1.90) |
1.036 (−0.58) |
0.889 (−1.63) |
Loan type (base = P&I) | |||||
IO | 0.798*** (−9.98) |
1.039*** (−7.06) |
1.265* (−2.43) |
1.142** (−3.06) |
1.022 (−0.44) |
Switched to IO | 2.885*** (−13.88) |
1.195*** (−5.72) |
n/a | n/a | n/a |
Switched to P&I – IO period expired | 2.008** (−14.33) |
1.387*** (−17.32) |
1.096 (−0.78) |
0.996 (−0.05) |
1.131 (−1.58) |
Switched to P&I – voluntary | 0.298*** (−6.01) |
0.881*** (−4.11) |
n/a | n/a | n/a |
Investor | 0.676*** (−16.51) |
0.918*** (−10.32) |
1.277** (−3.02) |
0.994 (−0.14) |
1.110* (−2.31) |
Self-employed | 1.181*** (−6.77) |
0.862*** (−25.77) |
1.183* (−2.04) |
1.060 (−1.57) |
1.232*** (−4.93) |
Multiple debtors | 0.730*** (−16.28) |
1.081*** (−14.73) |
0.876* (−2.24) |
1.084* (−2.53) |
1.231*** (−5.13) |
SEIFA | 0.998*** (−8.17) |
1.000 (−0.78) |
1.000 (−0.48) |
1.002*** (−5.47) |
1.002*** (−4.34) |
Mining share of employment | 1.018*** (−3.46) |
0.984*** (−6.74) |
0.996 (−0.87) |
0.990 (−1.87) |
0.982** (−2.75) |
Previous discharge | 2.198*** (−19.64) |
1.280*** (−16.83) |
0.791 (−1.41) |
0.591*** (−5.71) |
0.727** (−2.89) |
Restructuring arrangements | n/a | n/a | 0.497*** (−5.81) |
1.464*** (−7.40) |
1.144* (−2.39) |
Low documentation | 2.040*** (−13.95) |
1.099*** (−4.96) |
0.731* (−1.98) |
0.574*** (−7.98) |
0.659*** (−4.67) |
Fixed rate | 0.625*** (−19.95) |
0.562*** (−87.48) |
0.862 (−1.31) |
0.971 (−0.57) |
0.807*** (−3.49) |
Loan purpose (base = purchase) | |||||
Construction | 1.083 (−1.47) |
1.019 (−0.98) |
1.053 (−0.44) |
0.795** (−3.29) |
0.718*** (−3.94) |
Further advance | 1.491*** (−3.77) |
1.235*** (−9.39) |
0.733 (−1.26) |
0.873 (−1.01) |
0.938 (−0.41) |
Refinance | 1.635*** (−24.12) |
1.175*** (−32.20) |
0.972 (−0.39) |
0.997 (−0.10) |
1.055 (−1.39) |
Broker-originated | 1.009 (−0.47) |
0.985* (−2.48) |
1.266*** (−3.62) |
1.100** (−2.90) |
0.812*** (−4.99) |
Region (base = capital city) | |||||
Major city | 1.026 (−0.51) |
1.003 (−0.14) |
1.338 (−1.61) |
0.984 (−0.20) |
0.944 (−0.60) |
Regional centre | 1.079 (−1.72) |
0.894*** (−6.82) |
1.681*** (−5.77) |
1.105* (−2.24) |
1.008 (−0.13) |
Remote | 1.344*** (−6.66) |
0.831*** (−12.37) |
1.731*** (−6.03) |
1.127* (−2.37) |
0.792*** (−3.42) |
Seasoning | 1.112*** (−19.53) |
1.067*** (−46.86) |
n/a | n/a | n/a |
Seasoning^2 | 0.998*** (−14.01) |
0.999*** (−32.20) |
n/a | n/a | n/a |
Seasoning^3 | 1.000*** (−11.83) |
1.000*** (−23.45) |
n/a | n/a | n/a |
State fixed effects | Yes | Yes | Yes | Yes | Yes |
Origination year fixed effects | No | No | Yes | Yes | Yes |
Time fixed effects | Yes | Yes | Yes | Yes | Yes |
Deal and issuer type | Yes | Yes | Yes | Yes | Yes |
No of observations | 12,370,838 | 12,370,838 | 32,816 | 32,816 | 32,816 |
No of events | 18,035 | 442,496 | 1,870 | 15,290 | 7,720 |
Pseudo R2 | 0.041 | 0.041 | 0.057 | 0.057 | 0.057 |
Notes: ***, ** and * denote statistical significance at the 0.1, 1 and 5 per cent levels, respectively; standard errors are in parentheses Sources: ABS; Author's calculations; CoreLogic data; RBA; Securitisation System |