# RDP 2020-03: The Determinants of Mortgage Defaults in Australia – Evidence for the Double-trigger Hypothesis Appendix C: Robustness Checks – Multinomial Logit Models

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.

Table C1: Multinomial Logits – Odds Ratios
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)
(−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