Table A1 Stochastic frontier–empirical...

Table A1

Stochastic frontier–empirical results

Variables	2017	2016	2015	2014	2013	2012
(a) Time period: 2012–2017
Net loans	−0.0006*	−0.0010*	−0.0013*	−0.0014**	−0.0016***	−0.0015***
Net loans	(0.0000)	(0.0000)	(0.0010)	(0.0010)	(0.0010)	(0.0010)
(NetLoans)²	0.0000	0.0000	0.0000	0.0000*	0.0000***	0.0000***
(NetLoans)²	(0.0000)	(0.0000)	(0.0000)	(0.0000)	(0.0000)	(0.0000)
Bank overdrafts/Loans	−0.5359***	−0.4059**	−0.2863	−0.3447*	−0.4775***	−0.2593*
Bank overdrafts/Loans	(0.0790)	(0.1940)	(0.1880)	(0.2030)	(0.1750)	(0.1550)
(Bank overdrafts/Loans)²	0.4319***	−0.1314	−0.4449	−0.2331	0.1016	−0.155
(Bank overdrafts/Loans)²	(0.1320)	(0.5360)	(0.4370)	(0.4600)	(0.3430)	(0.2660)
Mortgage/Loans	0.6426***	0.7040***	0.7513***	0.7675***	0.7310***	0.5061***
Mortgage/Loans	(0.1090)	(0.1150)	(0.1350)	(0.1380)	(0.1250)	(0.1100)
(Mortgage/Loans)²	−0.7542***	−0.8593***	−0.9595***	−0.9575***	−0.9372***	−0.6864***
(Mortgage/Loans)²	(0.0950)	(0.1110)	(0.1200)	(0.1270)	(0.1230)	(0.1020)
Consumer loans/Loans	−0.3469***	−0.3961***	−0.6920***	−0.7756***	−0.6651***	−0.5279***
Consumer loans/Loans	(0.0740)	(0.1120)	(0.1180)	(0.1240)	(0.1200)	(0.1200)
(Consumer Loans/Loans)²	0.2831***	0.3522***	1.2055***	1.3353***	1.0093***	0.6719***
(Consumer Loans/Loans)²	(0.0720)	(0.1160)	(0.3400)	(0.3340)	(0.3150)	(0.2360)
Average rate of loans	1.2916***	0.9298***	1.3351***	1.4681***	1.6727***	1.5789***
Average rate of loans	(0.2240)	(0.2920)	(0.3500)	(0.3570)	(0.3110)	(0.3120)
Constant	0.0064	0.0218	0.0201	0.0058	0.0231	0.0293
Constant	(0.0320)	(0.0270)	(0.0400)	(0.0420)	(0.0370)	(0.0480)
μ_i(≥ 0) ∼ i.i.d.θ exp(−θυ)	−7.4408***	−6.9520***	−7.2886***	−7.5142***	−7.6617***	−8.3560***
μ_i(≥ 0) ∼ i.i.d.θ exp(−θυ)	(0.2860)	(0.3620)	(0.4420)	(0.3990)	(0.4380)	(1252.00)
ν ∼ i.i.d.N(0, σν²)	−7.2355***	−7.0486***	−6.8441***	−6.9429***	−7.0127***	−7.0283***
ν ∼ i.i.d.N(0, σν²)	(0.1700)	(0.2040)	(0.2160)	(0.2080)	(0.2070)	(0.3150)
N. Obs	338	338	338	338	338	338
Log likelihood	650.13	597.92	598.78	622.58	638.57	669.68
συ	0.02	0.03	0.03	0.02	0.02	0.02
σν	0.03	0.03	0.03	0.03	0.03	0.03
Lambda	0.90	10.50	0.80	0.75	0.72	0.51

Variables	2017	2016	2015	2014	2013	2012
(a) Time period: 2012–2017
Net loans	−0.0006*	−0.0010*	−0.0013*	−0.0014**	−0.0016***	−0.0015***
Net loans	(0.0000)	(0.0000)	(0.0010)	(0.0010)	(0.0010)	(0.0010)
(NetLoans)²	0.0000	0.0000	0.0000	0.0000*	0.0000***	0.0000***
(NetLoans)²	(0.0000)	(0.0000)	(0.0000)	(0.0000)	(0.0000)	(0.0000)
Bank overdrafts/Loans	−0.5359***	−0.4059**	−0.2863	−0.3447*	−0.4775***	−0.2593*
Bank overdrafts/Loans	(0.0790)	(0.1940)	(0.1880)	(0.2030)	(0.1750)	(0.1550)
(Bank overdrafts/Loans)²	0.4319***	−0.1314	−0.4449	−0.2331	0.1016	−0.155
(Bank overdrafts/Loans)²	(0.1320)	(0.5360)	(0.4370)	(0.4600)	(0.3430)	(0.2660)
Mortgage/Loans	0.6426***	0.7040***	0.7513***	0.7675***	0.7310***	0.5061***
Mortgage/Loans	(0.1090)	(0.1150)	(0.1350)	(0.1380)	(0.1250)	(0.1100)
(Mortgage/Loans)²	−0.7542***	−0.8593***	−0.9595***	−0.9575***	−0.9372***	−0.6864***
(Mortgage/Loans)²	(0.0950)	(0.1110)	(0.1200)	(0.1270)	(0.1230)	(0.1020)
Consumer loans/Loans	−0.3469***	−0.3961***	−0.6920***	−0.7756***	−0.6651***	−0.5279***
Consumer loans/Loans	(0.0740)	(0.1120)	(0.1180)	(0.1240)	(0.1200)	(0.1200)
(Consumer Loans/Loans)²	0.2831***	0.3522***	1.2055***	1.3353***	1.0093***	0.6719***
(Consumer Loans/Loans)²	(0.0720)	(0.1160)	(0.3400)	(0.3340)	(0.3150)	(0.2360)
Average rate of loans	1.2916***	0.9298***	1.3351***	1.4681***	1.6727***	1.5789***
Average rate of loans	(0.2240)	(0.2920)	(0.3500)	(0.3570)	(0.3110)	(0.3120)
Constant	0.0064	0.0218	0.0201	0.0058	0.0231	0.0293
Constant	(0.0320)	(0.0270)	(0.0400)	(0.0420)	(0.0370)	(0.0480)
μ_i(≥ 0) ∼ i.i.d.θ exp(−θυ)	−7.4408***	−6.9520***	−7.2886***	−7.5142***	−7.6617***	−8.3560***
μ_i(≥ 0) ∼ i.i.d.θ exp(−θυ)	(0.2860)	(0.3620)	(0.4420)	(0.3990)	(0.4380)	(1252.00)
ν ∼ i.i.d.N(0, σν²)	−7.2355***	−7.0486***	−6.8441***	−6.9429***	−7.0127***	−7.0283***
ν ∼ i.i.d.N(0, σν²)	(0.1700)	(0.2040)	(0.2160)	(0.2080)	(0.2070)	(0.3150)
N. Obs	338	338	338	338	338	338
Log likelihood	650.13	597.92	598.78	622.58	638.57	669.68
συ	0.02	0.03	0.03	0.02	0.02	0.02
σν	0.03	0.03	0.03	0.03	0.03	0.03
Lambda	0.90	10.50	0.80	0.75	0.72	0.51

Variables	2011	2010	2009	2008	2007	2006
(b) Time period: 2011–2006
Net loans	0.0000	0.0002	0.0001	0.0000	0.0001	−0.0003
Net loans	(0.0000)	(0.0000)	(0.0000)	(0.0000)	(0.0000)	(0.0000)
(NetLoans)²	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
(NetLoans)²	(0.0000)	(0.0000)	(0.0000)	(0.0000)	(0.0000)	(0.0000)
Bank overdrafts/Loans	0.0095	0.0811	−0.0338	0.0321	−0.0064	−0.0943*
Bank overdrafts/Loans	(0.0860)	(0.0790)	(0.0800)	(0.0650)	(0.1270)	(0.0530)
(Bank overdrafts/Loans)²	−0.0373	−0.0885	0.1341	0.0708	0.1334	0.2518***
(Bank overdrafts/Loans)²	(0.1320)	(0.1480)	(0.1530)	(0.1060)	(0.1620)	(0.0910)
Mortgage/Loans	0.1501***	0.1047**	0.0819*	0.0218	−0.0045	−0.0149
Mortgage/Loans	(0.0560)	(0.0460)	(0.0460)	(0.0350)	(0.0680)	(0.0400)
(Mortgage/Loans)²	−0.1504**	−0.0910*	−0.0763	0.0069	0.0255	0.0171
(Mortgage/Loans)²	(0.0590)	(0.0480)	(0.0470)	(0.0400)	(0.0830)	(0.0410)
Consumer loans/Loans	−0.0914	−0.0645	0.0239	0.3435***	0.3218	0.6801***
Consumer loans/Loans	(0.0900)	(0.0670)	(0.0580)	(0.1050)	(0.1960)	(0.1410)
(Consumer Loans/Loans)²	0.0166	0.1603	−0.042	−0.7058**	−0.8217	−3.5158***
(Consumer Loans/Loans)²	(0.1550)	(0.1280)	(0.0580)	(0.3230)	(1384.00)	(1023.00)
Average Rate of Loans	1.1630***	0.9038***	0.8746***	0.4910***	0.6835***	0.8727***
Average Rate of Loans	(0.3170)	(0.1940)	(0.2130)	(0.1810)	(0.2320)	(0.1450)
Constant	−0.0316**	−0.0400***	−0.0284**	−0.0404***	−0.0400**	−0.0280***
Constant	(0.0140)	(0.0100)	(0.0120)	(0.0110)	(0.0180)	(0.0090)
μ_i(≥ 0) ∼ i.i.d.θ exp(−θυ)	−7.1399***	−7.0435***	−7.2286***	−7.3922***	−7.3610***	−7.5031***
	(0.2090)	(0.2220)	(0.2190)	(0.1750)	(0.2960)	(0.1570)
ν ∼ i.i.d.N(0, σν²)	−7.8377***	−8.3115***	−8.3111***	−8.9864***	−9.2712***	−8.9724***
	(0.2110)	(0.3070)	(0.2500)	(0.2110)	(0.6930)	(0.2420)
N. Obs	338	338	338	338	338	338
Log likelihood	683.67	708.64	727.43	786.58	798.04	797.7
συ	0.03	0.03	0.03	0.02	0.03	0.02
σν	0.02	0.02	0.02	0.01	0.01	0.01
Lambda	14.17	18.85	17.18	22.19	25.99	20.85

Variables	2011	2010	2009	2008	2007	2006
(b) Time period: 2011–2006
Net loans	0.0000	0.0002	0.0001	0.0000	0.0001	−0.0003
Net loans	(0.0000)	(0.0000)	(0.0000)	(0.0000)	(0.0000)	(0.0000)
(NetLoans)²	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
(NetLoans)²	(0.0000)	(0.0000)	(0.0000)	(0.0000)	(0.0000)	(0.0000)
Bank overdrafts/Loans	0.0095	0.0811	−0.0338	0.0321	−0.0064	−0.0943*
Bank overdrafts/Loans	(0.0860)	(0.0790)	(0.0800)	(0.0650)	(0.1270)	(0.0530)
(Bank overdrafts/Loans)²	−0.0373	−0.0885	0.1341	0.0708	0.1334	0.2518***
(Bank overdrafts/Loans)²	(0.1320)	(0.1480)	(0.1530)	(0.1060)	(0.1620)	(0.0910)
Mortgage/Loans	0.1501***	0.1047**	0.0819*	0.0218	−0.0045	−0.0149
Mortgage/Loans	(0.0560)	(0.0460)	(0.0460)	(0.0350)	(0.0680)	(0.0400)
(Mortgage/Loans)²	−0.1504**	−0.0910*	−0.0763	0.0069	0.0255	0.0171
(Mortgage/Loans)²	(0.0590)	(0.0480)	(0.0470)	(0.0400)	(0.0830)	(0.0410)
Consumer loans/Loans	−0.0914	−0.0645	0.0239	0.3435***	0.3218	0.6801***
Consumer loans/Loans	(0.0900)	(0.0670)	(0.0580)	(0.1050)	(0.1960)	(0.1410)
(Consumer Loans/Loans)²	0.0166	0.1603	−0.042	−0.7058**	−0.8217	−3.5158***
(Consumer Loans/Loans)²	(0.1550)	(0.1280)	(0.0580)	(0.3230)	(1384.00)	(1023.00)
Average Rate of Loans	1.1630***	0.9038***	0.8746***	0.4910***	0.6835***	0.8727***
Average Rate of Loans	(0.3170)	(0.1940)	(0.2130)	(0.1810)	(0.2320)	(0.1450)
Constant	−0.0316**	−0.0400***	−0.0284**	−0.0404***	−0.0400**	−0.0280***
Constant	(0.0140)	(0.0100)	(0.0120)	(0.0110)	(0.0180)	(0.0090)
μ_i(≥ 0) ∼ i.i.d.θ exp(−θυ)	−7.1399***	−7.0435***	−7.2286***	−7.3922***	−7.3610***	−7.5031***
	(0.2090)	(0.2220)	(0.2190)	(0.1750)	(0.2960)	(0.1570)
ν ∼ i.i.d.N(0, σν²)	−7.8377***	−8.3115***	−8.3111***	−8.9864***	−9.2712***	−8.9724***
	(0.2110)	(0.3070)	(0.2500)	(0.2110)	(0.6930)	(0.2420)
N. Obs	338	338	338	338	338	338
Log likelihood	683.67	708.64	727.43	786.58	798.04	797.7
συ	0.03	0.03	0.03	0.02	0.03	0.02
σν	0.02	0.02	0.02	0.01	0.01	0.01
Lambda	14.17	18.85	17.18	22.19	25.99	20.85

Note(s): The tables report regressions using the Stochastic Frontier approach. The dependent variable is the net NPLs ratio. The independent variables are: gross loans_i is the value of the gross loan portfolio expressed in EUR millions for the i-th bank; $g r o s s l o a n s_{i}^{2}$ ⁠; $(\frac{b a n k o v e r d r a f t s_{i}}{l o a n s_{i}})$ ⁠; ${(\frac{b a n k o v e r d r a f t s_{i}}{l o a n s_{i}})}^{2}$ ⁠; $(\frac{m o r t g a g e l o a n s_{i}}{l o a n s_{i}})$ ⁠; ${(\frac{m o r t g a g e l o a n s_{i}}{l o a n s_{i}})}^{2}$ ⁠; $(\frac{c o n s u m e r l o a n s_{i}}{l o a n s_{i}})$ ⁠; ${(\frac{c o n s u m e r l o a n s_{i}}{l o a n s_{i}})}^{2}$ ⁠; Average Rate on Loans represented by the ratio between interest revenues over total gross loans; Sample period: 2006–2017; *, **, ***denote the 10%, 5% and 1% significance level, respectively

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