Table 3 Stochastic frontier–empirical...

Table 3

Stochastic frontier–empirical results

Variables	2017	2016	2015	2014	2013	2012
(a) Time period: 2012–2017
Gross Loans	−0.0011**	−0.0012	−0.0013	−0.0012	−0.0015**	−0.0010**
Gross Loans	(0.0000)	(0.0010)	(0.0010)	(0.0010)	(0.0010)	(0.0010)
(GrossLoans)²	0.0000	0.0000	0.0000	0.0000	0.0000**	0.0000*
(GrossLoans)²	(0.0000)	(0.0000)	(0.0000)	(0.0000)	(0.0000)	(0.0000)
Bank overdrafts/Loans	−0.9635***	−0.8004***	−0.5468*	−0.5354*	−0.6598***	−0.2392
Bank overdrafts/Loans	(0.1340)	(0.2550)	(0.2810)	(0.3080)	(0.2360)	(0.1840)
(Bank overdrafts/Loans)²	0.8001***	0.0614	−0.472	−0.2918	0.1153	−0.3804
(Bank overdrafts/Loans)²	(0.2220)	(0.6440)	(0.6520)	(0.7370)	(0.4890)	(0.3550)
Mortgage/Loans	0.9979***	1.0789***	1.1276***	1.0260***	0.9156***	0.5819***
Mortgage/Loans	(0.1770)	(0.2060)	(0.200)	(0.1860)	(0.1630)	(0.1240)
(Mortgage/Loans)²	−1.1609***	−1.3025***	−1.3952***	−1.2697***	−1.1780***	−0.7857***
(Mortgage/Loans)²	(0.1560)	(0.1890)	(0.1790)	(0.1730)	(0.1550)	(0.1190)
Consumer Loans/Loans	−0.5023***	−0.5482***	−0.9283***	−0.9820***	−0.7598***	−0.5211***
Consumer Loans/Loans	(0.1100)	(0.1900)	(0.1980)	(0.1810)	(0.1550)	(0.1400)
(Consumer Loans/Loans)²	0.3799***	0.4759**	1.7244***	1.7511***	1.1080***	0.6017**
(Consumer Loans/Loans)²	(0.1080)	(0.200)	(0.5260)	(0.4600)	(0.4140)	(0.3030)
Average Rate of Loans	1.8792***	1.2215***	1.8821***	2.2005***	2.4343***	2.1457***
Average Rate of Loans	(0.3780)	(0.4640)	(0.5050)	(0.4890)	(0.4030)	(0.3720)
Constant	0.046	0.0693	0.0344	0.0179	0.0411	0.026
Constant	(0.0510)	(0.0530)	(0.0540)	(0.0520)	(0.0480)	(0.0400)
μ_i(≥ 0) ∼ i.i.d.θ exp(−θυ)	−6.8434***	−6.4832***	−6.6101***	−6.6651***	−7.1313***	−7.5086***
μ_i(≥ 0) ∼ i.i.d.θ exp(−θυ)	(0.4820)	(0.4680)	(0.3870)	(0.3020)	(0.3720)	(0.4850)
ν ∼ i.i.d.N(0, σν²)	−6.1312***	−6.0397***	−6.1331***	−6.3634***	−6.5338***	−6.7351***
ν ∼ i.i.d.N(0, σν²)	(0.1580)	(0.1700)	(0.1760)	(0.1830)	(0.1730)	(0.1960)
N. Obs	338	338	338	338	338	338
Log likelihood	492.16	462.06	479.98	509.24	554.93	598.02
συ	0.0327	0.0391	0.0367	0.0357	0.0283	0.0234
σν	0.0466	0.0488	0.0466	0.0415	0.0381	0.0345
Lambda	0.7004	0.8011	0.7878	0.86	0.7417	0.6793

Variables	2017	2016	2015	2014	2013	2012
(a) Time period: 2012–2017
Gross Loans	−0.0011**	−0.0012	−0.0013	−0.0012	−0.0015**	−0.0010**
Gross Loans	(0.0000)	(0.0010)	(0.0010)	(0.0010)	(0.0010)	(0.0010)
(GrossLoans)²	0.0000	0.0000	0.0000	0.0000	0.0000**	0.0000*
(GrossLoans)²	(0.0000)	(0.0000)	(0.0000)	(0.0000)	(0.0000)	(0.0000)
Bank overdrafts/Loans	−0.9635***	−0.8004***	−0.5468*	−0.5354*	−0.6598***	−0.2392
Bank overdrafts/Loans	(0.1340)	(0.2550)	(0.2810)	(0.3080)	(0.2360)	(0.1840)
(Bank overdrafts/Loans)²	0.8001***	0.0614	−0.472	−0.2918	0.1153	−0.3804
(Bank overdrafts/Loans)²	(0.2220)	(0.6440)	(0.6520)	(0.7370)	(0.4890)	(0.3550)
Mortgage/Loans	0.9979***	1.0789***	1.1276***	1.0260***	0.9156***	0.5819***
Mortgage/Loans	(0.1770)	(0.2060)	(0.200)	(0.1860)	(0.1630)	(0.1240)
(Mortgage/Loans)²	−1.1609***	−1.3025***	−1.3952***	−1.2697***	−1.1780***	−0.7857***
(Mortgage/Loans)²	(0.1560)	(0.1890)	(0.1790)	(0.1730)	(0.1550)	(0.1190)
Consumer Loans/Loans	−0.5023***	−0.5482***	−0.9283***	−0.9820***	−0.7598***	−0.5211***
Consumer Loans/Loans	(0.1100)	(0.1900)	(0.1980)	(0.1810)	(0.1550)	(0.1400)
(Consumer Loans/Loans)²	0.3799***	0.4759**	1.7244***	1.7511***	1.1080***	0.6017**
(Consumer Loans/Loans)²	(0.1080)	(0.200)	(0.5260)	(0.4600)	(0.4140)	(0.3030)
Average Rate of Loans	1.8792***	1.2215***	1.8821***	2.2005***	2.4343***	2.1457***
Average Rate of Loans	(0.3780)	(0.4640)	(0.5050)	(0.4890)	(0.4030)	(0.3720)
Constant	0.046	0.0693	0.0344	0.0179	0.0411	0.026
Constant	(0.0510)	(0.0530)	(0.0540)	(0.0520)	(0.0480)	(0.0400)
μ_i(≥ 0) ∼ i.i.d.θ exp(−θυ)	−6.8434***	−6.4832***	−6.6101***	−6.6651***	−7.1313***	−7.5086***
μ_i(≥ 0) ∼ i.i.d.θ exp(−θυ)	(0.4820)	(0.4680)	(0.3870)	(0.3020)	(0.3720)	(0.4850)
ν ∼ i.i.d.N(0, σν²)	−6.1312***	−6.0397***	−6.1331***	−6.3634***	−6.5338***	−6.7351***
ν ∼ i.i.d.N(0, σν²)	(0.1580)	(0.1700)	(0.1760)	(0.1830)	(0.1730)	(0.1960)
N. Obs	338	338	338	338	338	338
Log likelihood	492.16	462.06	479.98	509.24	554.93	598.02
συ	0.0327	0.0391	0.0367	0.0357	0.0283	0.0234
σν	0.0466	0.0488	0.0466	0.0415	0.0381	0.0345
Lambda	0.7004	0.8011	0.7878	0.86	0.7417	0.6793

Variables	2011	2010	2009	2008	2007	2006
(b) Time period: 2011–2006
Gross Loans	0.0003	0.0004*	0.0005**	0.0004	0.0005*	0.0005
Gross Loans	(0.0000)	(0.0000)	(0.0000)	(0.0010)	(0.0000)	(0.0000)
(GrossLoans)²	0.0000	0.0000	−0.0000*	0.0000	−0.0000*	0.0000
(GrossLoans)²	(0.0000)	(0.0000)	(0.0000)	(0.0000)	(0.0000)	(0.0000)
Bank overdrafts/Loans	−0.1076	0.0002	−0.0537	0.0322	0.0031	−0.1320**
Bank overdrafts/Loans	(0.1120)	(0.1040)	(0.1090)	(0.0780)	(0.1670)	(0.0620)
(Bank overdrafts/Loans)²	0.1443	0.0043	0.1235	0.0521	0.1223	0.3103***
(Bank overdrafts/Loans)²	(0.2030)	(0.1900)	(0.200)	(0.1310)	(0.2140)	(0.100)
Mortgage/Loans	0.1910***	0.1483*	0.1135**	0.0286	−0.0481	−0.0501
Mortgage/Loans	(0.0590)	(0.0850)	(0.0530)	(0.0440)	(0.0960)	(0.0490)
(Mortgage/Loans)²	−0.1900***	−0.1383*	−0.1084*	0.0036	0.0753	0.0491
(Mortgage/Loans)²	(0.0640)	(0.0790)	(0.0560)	(0.0510)	(0.1140)	(0.0540)
Consumer Loans/Loans	0.0162	0.0151	0.115	0.5122***	0.4964*	0.9086***
Consumer Loans/Loans	(0.1090)	(0.1610)	(0.0750)	(0.1490)	(0.2720)	(0.1800)
(Consumer Loans/Loans)²	−0.1798	−0.0316	−0.1489*	−1.1079***	−12,239	−4.4541***
(Consumer Loans/Loans)²	(192.00)	(0.5750)	(0.0770)	(0.4210)	(1875.00)	(1404.00)
Average Rate of Loans	1.6210***	1.1840***	1.2079***	0.8396***	1.3295***	1.4643***
Average Rate of Loans	(0.3920)	(0.2700)	(0.2990)	(0.2900)	(0.3590)	(0.1890)
Constant	−0.0334**	−0.0373	−0.0378**	−0.0584***	−0.0661**	−0.0410***
Constant	(0.0160)	(0.0260)	(0.0170)	(0.0150)	(0.0260)	(0.0100)
μ_i(≥ 0) ∼ i.i.d.θ exp(−θυ)	−6.3178***	−6.2533***	−6.4654***	−6.6824***	−6.7442***	−6.7398***
μ_i(≥ 0) ∼ i.i.d.θ exp(−θυ)	(0.1760)	(0.1850)	(0.2060)	(0.1640)	(0.2760)	(0.1780)
ν ∼ i.i.d.N(0, σν²)	−7.7599***	−8.3061***	−8.1575***	−8.7179***	−8.6263***	−8.4551***
ν ∼ i.i.d.N(0, σν²)	(0.2690)	(0.400)	(0.3200)	(0.2210)	(0.5620)	(0.2490)
N. Obs	338	338	338	338	338	338
Log likelihood	596.27	618.17	635.88	689.07	692.22	682.47
συ	0.0425	0.0439	0.0395	0.0354	0.0343	0.0344
σν	0.0207	0.0157	0.0169	0.0128	0.0134	0.0146
Lambda	20,566	2,791	23,304	2,767	25,626	23,576

Variables	2011	2010	2009	2008	2007	2006
(b) Time period: 2011–2006
Gross Loans	0.0003	0.0004*	0.0005**	0.0004	0.0005*	0.0005
Gross Loans	(0.0000)	(0.0000)	(0.0000)	(0.0010)	(0.0000)	(0.0000)
(GrossLoans)²	0.0000	0.0000	−0.0000*	0.0000	−0.0000*	0.0000
(GrossLoans)²	(0.0000)	(0.0000)	(0.0000)	(0.0000)	(0.0000)	(0.0000)
Bank overdrafts/Loans	−0.1076	0.0002	−0.0537	0.0322	0.0031	−0.1320**
Bank overdrafts/Loans	(0.1120)	(0.1040)	(0.1090)	(0.0780)	(0.1670)	(0.0620)
(Bank overdrafts/Loans)²	0.1443	0.0043	0.1235	0.0521	0.1223	0.3103***
(Bank overdrafts/Loans)²	(0.2030)	(0.1900)	(0.200)	(0.1310)	(0.2140)	(0.100)
Mortgage/Loans	0.1910***	0.1483*	0.1135**	0.0286	−0.0481	−0.0501
Mortgage/Loans	(0.0590)	(0.0850)	(0.0530)	(0.0440)	(0.0960)	(0.0490)
(Mortgage/Loans)²	−0.1900***	−0.1383*	−0.1084*	0.0036	0.0753	0.0491
(Mortgage/Loans)²	(0.0640)	(0.0790)	(0.0560)	(0.0510)	(0.1140)	(0.0540)
Consumer Loans/Loans	0.0162	0.0151	0.115	0.5122***	0.4964*	0.9086***
Consumer Loans/Loans	(0.1090)	(0.1610)	(0.0750)	(0.1490)	(0.2720)	(0.1800)
(Consumer Loans/Loans)²	−0.1798	−0.0316	−0.1489*	−1.1079***	−12,239	−4.4541***
(Consumer Loans/Loans)²	(192.00)	(0.5750)	(0.0770)	(0.4210)	(1875.00)	(1404.00)
Average Rate of Loans	1.6210***	1.1840***	1.2079***	0.8396***	1.3295***	1.4643***
Average Rate of Loans	(0.3920)	(0.2700)	(0.2990)	(0.2900)	(0.3590)	(0.1890)
Constant	−0.0334**	−0.0373	−0.0378**	−0.0584***	−0.0661**	−0.0410***
Constant	(0.0160)	(0.0260)	(0.0170)	(0.0150)	(0.0260)	(0.0100)
μ_i(≥ 0) ∼ i.i.d.θ exp(−θυ)	−6.3178***	−6.2533***	−6.4654***	−6.6824***	−6.7442***	−6.7398***
μ_i(≥ 0) ∼ i.i.d.θ exp(−θυ)	(0.1760)	(0.1850)	(0.2060)	(0.1640)	(0.2760)	(0.1780)
ν ∼ i.i.d.N(0, σν²)	−7.7599***	−8.3061***	−8.1575***	−8.7179***	−8.6263***	−8.4551***
ν ∼ i.i.d.N(0, σν²)	(0.2690)	(0.400)	(0.3200)	(0.2210)	(0.5620)	(0.2490)
N. Obs	338	338	338	338	338	338
Log likelihood	596.27	618.17	635.88	689.07	692.22	682.47
συ	0.0425	0.0439	0.0395	0.0354	0.0343	0.0344
σν	0.0207	0.0157	0.0169	0.0128	0.0134	0.0146
Lambda	20,566	2,791	23,304	2,767	25,626	23,576

Note(s): The tables report regressions using the stochastic frontier approach. The dependent variable is the gross 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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