Abnormal loan growth and bank risk-taking in Vietnam: A quantile regression approach

Figures & data

Table 1. The descriptive statistics of variables

Variables	Obs.	Mean	S.D.	Min	Q (10)	Median	Q (90)	Max
Z	353	0.027	0.079	0.000	0.000	0.012	0.057	0.934
NPL	353	0.293	1.640	−1.000	−0.464	−0.043	0.952	16.852
ALG	353	0.120	0.407	−1.162	−0.202	0.035	0.819	1.374
SIZE	353	31.975	1.347	27.520	30.347	32.034	33.726	34.937
LIQ	353	0.323	0.128	0.062	0.177	0.312	0.513	0.816
CIR	353	0.154	0.076	0.040	0.080	0.140	0.22	0.640
HHI	353	0.003	0.007	0.000	0.000	0.000	0.013	0.059
GDP	353	0.062	0.007	0.052	0.054	0.062	0.071	0.071
INF	353	0.0761	0.062	0.006	0.026	6.593	0.186	0.231

Figure 1. Histogram for NPL and inverse of Z-score

Figure 2. Abnormal and annual loan growth in the Vietnamese banking system

Note: Abnormal loan growth is defined as the difference between an individual bank’s loan growth and the median loan growth of the Vietnamese entire banking system from the same year. Meanwhile, annual loan growth is the annual growth rate of loans to customers. Both abnormal and annual loan growth are yearly averaged based on the number of banks researched.

Table 2. The correlation matrix of variables

	Z	NPL	ALG	SIZ	LIQ	CIR	HHI	GDP	INF
Z	1.000
NPL	−0.028	1.000
ALG	−0.050	−0.030	1.000
SIZ	0.248	−0.141	0.100	1.000
LIQ	−0.174	0.102	0.004	−0.117	1.000
CIR	0.014	−0.048	−0.088	0.690	−0.195	1.000
HHI	−0.007	−0.033	0.011	0.121	−0.006	0.224	1.000
GDP	−0.054	−0.195	0.292	0.229	−0.251	−0.036	0.111	1.000
INF	0.008	0.309	−0.140	−0.189	0.196	0.031	−0.276	−0.418	1.000

Table 3. Baseline results for Z: Quantile regression

Quantiles	0.1	0.2	0.25	0.5	0.75	0.8	0.9
ALG	−0.000 (0.000)	0.000 (0.004)	0.002 (0.007)	0.005 (0.011)	−0.041** (0.018)	−0.026 (0.020)	−0.022 (0.019)
ALG^2	0.000 (0.000)	0.000 (0.004)	−0.003 (0.007)	−0.007 (0.011)	0.034* (0.017)	0.017 (0.020)	0.012 (0.018)
SIZE	−0.000 (0.000)	0.001 (0.001)	0.003** (0.001)	0.014*** (0.002)	0.017*** (0.003)	0.017*** (0.004)	0.018*** (0.004)
LIQ	−0.000** (0.000)	−0.003 (0.005)	−0.008 (0.009)	−0.048*** (0.014)	−0.064*** (0.022)	−0.079*** (0.025)	−0.060*** (0.023)
CIR	0.000 (0.000)	−0.002 (0.009)	−0.013 (0.016)	−0.004*** (0.024)	−2.800*** (0.691)	−3.063*** (0.790)	−3.346*** (0.732)
HHI	−0.000 (0.000)	−0.099 (0.164)	−0.022 (0.274)	−1.563 (0.422)	0.144*** (0.040)	0.136*** (0.045)	0.186*** (0.042)
GDP	−0.000 (0.000)	−0.039 (0.109)	−0.156 (0.181)	−0.672 (0.280)	−1.060** (0.458)	−1.057** (0.524)	−1.130** (0.485)
INF	0.000 (0.000)	0.002 (0.014)	0.008 (0.023)	0.055 (0.035)	0.067 (0.058)	0.140** (0.066)	0.188*** (0.061)
Constant	0.000 (0.000)	−0.026 (0.025)	−0.092 (0.042)	−0.367 (0.065)	−0.442 (0.107)	−0.453 (0.122)	−0.471 (0.113)
No. Obs.	262	262	262	262	262	262	262
Pseudo R^2	0.000	0.002	0.012	0.183	0.169	0.195	0.218

Note: This table presents pooled quantile regression for the 10^th, 20^th, 25^th, 5^th, 75^th, 80^th, and 90^th quantiles. The dependent variable is Z. Standard errors are in parentheses. *, **, and *** denote statistical significance at 10%, 5%, and 1%, respectively.

Table 4. Baseline results for NPL: Quantile regression

Quantiles	0.1	0.2	0.25	0.5	0.75	0.8	0.9
L.ALG	−0.004 (0.005)	−0.001 (0.005)	−0.002 (0.003)	−0.005 (0.003)	−0.012** (0.005)	−0.013** (0.006)	−0.002 (0.012)
L.ALG^2	0.005 (0.071)	0.088 (0.065)	0.113 (0.052)	0.148** (0.118)	0.254*** (0.085)	0.261*** (0.091)	0.069 (0.183)
L.SIZE	−0.012 (0.025)	−0.050 (0.023)	−0.033 (0.018)	−0.036 (0.017)	−0.057 (0.030)	−0.060 (0.033)	−0.109 (0.066)
L.LIQ	−0.160 (0.194)	0.010 (0.178)	0.027 (0.143)	−0.036 (0.130)	0.132 (0.233)	0.199 (0.250)	0.091 (0.500)
L.CIR	−0.366 (0.328)	0.068 (0.300)	0.045 (0.242)	−0.055 (0.220)	0.091 (0.394)	0.293 (0.423)	0.114 (0.846)
L.HHI	2.815 (4.467)	4.513 (4.082)	1.760 (3.302)	0.413 (2.998)	5.604 (5.304)	8.473 (5.761)	10.702 (11.511)
L.GDP	14.348*** (10.763)	9.324** (3.771)	8.025** (3.050)	6.329** (2.769)	5.718 (4.955)	5.430 (5.321)	7.409 (10.632)
L.INF	0.452 (0.455)	0.364 (0.416)	0.413 (0.336)	1.065*** (0.305)	2.174*** (0.547)	2.635*** (0.587)	3.652*** (1.174)
Constant	−0.649 (0.802)	0.850 (0.733)	0.429 (0.592)	0.714 (0.538)	1.427 (0.963)	1.504 (1.034)	3.094 (2.066)
No. Obs.	311	311	311	311	311	311	311
Pseudo R^2	0.096	0.057	0.068	0.079	0.141	0.156	0.216

Note: This table presents pooled quantile regression for the 10^th, 20^th, 25^th, 50^th, 75^th, 80^th, and 90^th quantiles. The dependent variable is NPL. Standard errors are in parentheses. *, **, and *** denote statistical significance at 10%, 5%, and 1%, respectively.

Table 5. The results of inter-quantile regression

	Z		NPL
Quantiles	(75–25)	Quantiles	(75–25)
ALG	−0.043** (0.021)	L.ALG	−0.009*** (0.101)
ALG^2	0.036* (0.021)	L.ALG^2	1.140* (0.120)
SIZE	0.013*** (0.004)	L.SIZE	−0.024 (0.028)
LIQ	−0.056** (0.024)	L.LIQ	0.104 (0.196)
CIR	−2.779*** (0.651)	L.CIR	0.045 (0.448)
HHI	0.157** (0.078)	L.HHI	3.844 (6.658)
GDP	−0.904* (0.464)	L.GDP	−2.306 (4.780)
INF	0.059 (0.064)	L.INF	1.760** (0.679)
Constant	−0.350 (0.111)	Constant	0.997 (0.913)
No. Obs.	262	No. Obs.	311

Notes: This table shows the difference in quantile regression estimates for an inter-quantile regression: ${\rho }_{\tau }$ The bootstrapped cluster standard errors (in parentheses) are obtained with 200 bootstrap replications. *, **, and *** denote statistical significance at 10%, 5%, and 1%, respectively.

Table 6. Baseline results for Z: quantile regression with subsample

Quantiles	0.10	0.20	0.25	0.50	0.75	0.80	0.90
ALG	0.000 (0.000)	0.001 (0.005)	0.001 (0.005)	−0.006 (0.012)	−0.049** (0.019)	−0.022 (0.018)	−0.027 (0.019)
ALG^2	0.000 (0.000)	0.000 (0.005)	−0.001 (0.005)	0.006 (0.012)	0.043** (0.019)	0.017 (0.017)	0.028 (0.019)
Constant	0.004 (0.003)	0.028 (0.043)	0.038 (0.045)	−0.071 (0.110)	−0.171 (0.175)	−0.173 (0.160)	−0.261 (0.171)
No. Obs.	231	231	231	231	231	231	231
Pseudo R^2	0.007	0.030	0.058	0.212	0.238	0.253	0.253

Note: This table presents pooled quantile regression for the 10^th, 20^th, 25^th, 50^th, 75^th, 80^th, and 90^th quantiles. The dependent variable is Z. Standard errors are in parentheses. *, **, and *** denote statistical significance at 10%, 5%, and 1%, respectively. The same set of variables in Equation (8)(8) ${\mathrm{Z}}_{\mathrm{i},\mathrm{t}}={\alpha }_{\mathrm{i}}+{\beta }_{1\tau }\mathrm{A}\mathrm{L}{\mathrm{G}}_{\mathrm{i},\mathrm{t}}+{\beta }_{2\tau }{\mathrm{A}\mathrm{L}\mathrm{G}}_{\mathrm{i},\mathrm{t}}^2+{\gamma }_{\tau }{\mathrm{B}}_{\mathrm{i},\mathrm{t}}+{\theta }_{\tau }{\mathrm{M}}_{\mathrm{t}}+{\epsilon }_{\tau \mathrm{i},\mathrm{t}}$(8) is used.

Table 7. Baseline results for NPL: quantile regression with subsample

Quantiles	0.10	0.20	0.25	0.50	0.75	0.80	0.90
L.ALG	−0.086 (0.079)	−0.001 (0.004)	−0.003 (0.004)	−0.005** (0.003)	−0.009* (0.005)	−0.008 (0.008)	−0.001 (0.188)
L.ALG^2	0.010 (0.005)	0.067 (0.059)	0.067 (0.057)	0.147*** (0.053)	0.200** (0.077)	0.185 (0.117)	0.001 (0.012)
Constant	1.236 (1.272)	2.115 (0.952)	1.521 (0.923)	1.493 (0.848)	1.827 (1.245)	2.231 (1.880)	6.974 (3.011)
No. Obs.	271	271	271	271	271	271	271
Pseudo R^2	0.132	0.101	0.098	0.098	0.162	0.183	0.255

Note: This table presents pooled quantile regression for the 10^th, 20^th, 25^th, 50^th, 75^th, 80^th, and 90^th quantiles. The dependent variable is NPL. Standard errors are in parentheses. *, **, and *** denote statistical significance at 10%, 5%, and 1%, respectively. The same set of variables in Equation (9)(9) $\mathrm{N}\mathrm{P}{\mathrm{L}}_{\mathrm{i},\mathrm{t}}={\alpha }_{\mathrm{i}}+{\beta }_{1\tau }\mathrm{A}\mathrm{L}{\mathrm{G}}_{\mathrm{i},\mathrm{t}-1}+{\beta }_{2\tau }{\mathrm{A}\mathrm{L}\mathrm{G}}_{\mathrm{i},\mathrm{t}-1}^2+{\gamma }_{\tau }{\mathrm{B}}_{\mathrm{i},\mathrm{t}-1}+{\theta }_{\tau }{\mathrm{M}}_{\mathrm{t}-1}+{\epsilon }_{\tau \mathrm{i},\mathrm{t}-1}$(9) is used.

Table 8. Baseline results for Z and NPL: inter-quantile regression with subsample

	Z		NPL
Quantiles	(75–25)	Quantiles	(75–25)
ALG	−0.050*** (0.017)	L.ALG	−0.909** (0.831)
ALG^2	0.043** (0.018)	L.ALG^2	0.132* (0.118)
Constant	−0.209 (0.109)	Constant	0.305 (1.611)
No. Obs.	231	No. Obs.	271

Notes: This table shows the difference in quantile regression estimates for an inter-quantile regression: ${\rho }_{\tau }$ The bootstrapped cluster standard errors (in parentheses) are obtained with 200 bootstrap replications. *, **, and *** denote statistical significance at 10%, 5%, and 1%, respectively. The same set of variables in Equations (8)(8) ${\mathrm{Z}}_{\mathrm{i},\mathrm{t}}={\alpha }_{\mathrm{i}}+{\beta }_{1\tau }\mathrm{A}\mathrm{L}{\mathrm{G}}_{\mathrm{i},\mathrm{t}}+{\beta }_{2\tau }{\mathrm{A}\mathrm{L}\mathrm{G}}_{\mathrm{i},\mathrm{t}}^2+{\gamma }_{\tau }{\mathrm{B}}_{\mathrm{i},\mathrm{t}}+{\theta }_{\tau }{\mathrm{M}}_{\mathrm{t}}+{\epsilon }_{\tau \mathrm{i},\mathrm{t}}$(8) and (9(9) $\mathrm{N}\mathrm{P}{\mathrm{L}}_{\mathrm{i},\mathrm{t}}={\alpha }_{\mathrm{i}}+{\beta }_{1\tau }\mathrm{A}\mathrm{L}{\mathrm{G}}_{\mathrm{i},\mathrm{t}-1}+{\beta }_{2\tau }{\mathrm{A}\mathrm{L}\mathrm{G}}_{\mathrm{i},\mathrm{t}-1}^2+{\gamma }_{\tau }{\mathrm{B}}_{\mathrm{i},\mathrm{t}-1}+{\theta }_{\tau }{\mathrm{M}}_{\mathrm{t}-1}+{\epsilon }_{\tau \mathrm{i},\mathrm{t}-1}$(9) ) is used.

Table 9. Abnormal loan growth and bank risk-taking, using system GMM

	Z	NPL
πt-1	0.566*** (0.149)	−0.033*** (0.009)
ALG	−0.041** (0.017)	−0.753** (0.293)
ALG^2	0.038** (0.016)	0.524* (0.288)
Constant	−0.042 (0.203)	−4.786 (2.271)
No. Obs.	233	265
No. of Groups	33	30
AR1 (p-value)	0.089	0.086
AR2 (p-value)	0.162	0.082
Hansen test (p-value)	0.187	0.378

Notes: This table presents a two-step GMM estimator to control for potential endogeneity between abnormal loam growth and bank risk-taking. The same set of variables in Equations (8)(8) ${\mathrm{Z}}_{\mathrm{i},\mathrm{t}}={\alpha }_{\mathrm{i}}+{\beta }_{1\tau }\mathrm{A}\mathrm{L}{\mathrm{G}}_{\mathrm{i},\mathrm{t}}+{\beta }_{2\tau }{\mathrm{A}\mathrm{L}\mathrm{G}}_{\mathrm{i},\mathrm{t}}^2+{\gamma }_{\tau }{\mathrm{B}}_{\mathrm{i},\mathrm{t}}+{\theta }_{\tau }{\mathrm{M}}_{\mathrm{t}}+{\epsilon }_{\tau \mathrm{i},\mathrm{t}}$(8) and (9(9) $\mathrm{N}\mathrm{P}{\mathrm{L}}_{\mathrm{i},\mathrm{t}}={\alpha }_{\mathrm{i}}+{\beta }_{1\tau }\mathrm{A}\mathrm{L}{\mathrm{G}}_{\mathrm{i},\mathrm{t}-1}+{\beta }_{2\tau }{\mathrm{A}\mathrm{L}\mathrm{G}}_{\mathrm{i},\mathrm{t}-1}^2+{\gamma }_{\tau }{\mathrm{B}}_{\mathrm{i},\mathrm{t}-1}+{\theta }_{\tau }{\mathrm{M}}_{\mathrm{t}-1}+{\epsilon }_{\tau \mathrm{i},\mathrm{t}-1}$(9) ) is used although they are not reported here due to the length constraints. Robust standard errors are reported in parentheses. *, **, and *** denote statistical significance at 10%, 5%, and 1%, respectively.