Dynamics of bank capital ratios and risk-taking: Evidence from US commercial banks

Figures & data

Table 1. Descriptive statistics

Panel-A: Summary Statistics
Variable	Measurements	Mean	Std.Dev.	p^5	p^25	p^75
RWATA	Risk-weighted assets/total assets	.733	.12	0.487	0.640	0.814
LLAGL	Loan loss allowances/gross loans	.024	.003	0.018	0.012	0.016
TCAPR	Total equity/total assets	.112	.019	0.071	0.083	0.114
TITA	Tier I/total assets	.094	.014	0.072	0.082	0.103
TRBCR	Tier I plus Tier II/risk-weighted assets	.142	.026	0.106	0.117	0.158
TIRBR	Tier I/risk-weighted assets	.126	.03	0.103	0.107	0.147
BTRBCR	TRBCR less 8%	.049	.022	0.032	0.038	0.078
BTIRBCR	TIRBCR less 6%	.065	.018	0.042	0.046	0.086
ROA	Net income/total assets	.02	.004	−0.002	0.005	0.012
LR	Net loans/total assets	.656	.112	0.453	0.576	0.757
BE	Cost/income ratio	3.037	1.761	0.915	1.728	3.922
INDIV	Non-interest income/total assets	.453	.097	0.262	0.406	0.530
SIZE	Log of total assets	13.544	.94	12.258	12.855	14.130
LIQ	Liquid assets/total assets	.25	.124	0.088	0.166	0.324
RGDPR	Real growth rate of gross domestic product	2.083	1.039	−0.292	1.671	2.861
INFRATE	Consumer price index (CPI)	1.91	.664	0.758	1.534	2.064
Panel-B: Dummy variables codes
Before-crisis interactive dummy 1 for 2003–2006 otherwise zero
Post-crisis interactive dummy 1 for 2010–2019 otherwise zero
Well capitalized banks interactive dummy 1 for well-capitalized otherwise zero
Undercapitalized interactive dummy 1 for undercapitalized otherwise zero
Nationally chartered member banks interactive dummy 1 for nationally chartered banks otherwise zero
State-chartered member banks interactive dummy 1 for state-chartered member bank otherwise zero
State-chartered non-member banks interactive dummy 1 for state charted non-member banks otherwise zero

Table 2. Correlation matrix

Variables	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
RWATA	1
TCAPR	0.035	1
ROA	0.043	0.078	1
LR	0.059	−0.065	0.026	1
BE	−0.033	−0.042	−0.418	−0.016	1
INDIV	−0.005	0.012	0.083	−0.014	−0.019	1
SIZE	0.019	0.021	−0.006	−0.024	−0.036	0.021	1
LIQ	−0.038	0.004	0.015	−0.020	−0.021	0.015	0.016	1
RGDPR	−0.021	0.022	0.064	−0.015	−0.083	0.023	−0.012	0.026	1
INFRATE	0.021	−0.106	0.067	0.036	−0.015	−0.031	−0.042	−0.052	0.061	1

Source (author’s calculation Stata output)

Table 3. Risk and Capital ratios model (Full sample results): The dependent variable is risk-weighted assets to total assets ratios. Our predictions are the two-step GMM approach. (Robust standard errors are reported in parenthesis)

	(1)	(2)	(3)	(4)	(5)	(6)
VARIABLES	RWATA	RWATA	RWATA	RWATA	RWATA	RWATA
L. RWATA	0.854**	−0.523***	0.566***	0.788***	0.675***	0.769***
	(0.072)	(0.087)	(0.034)	(0.032)	(0.034)	(0.035)
Non-risk based capital	0.338***
	(0.0374)
Profitability	−0.0084	0.072	0.432***	0.336***	0.527***	0.356***
	(0.172)	(0.342)	(0.162)	(0.156)	(0.142)	(0.142)
Loan ratio	0.364*	0.581***	0.204***	0.388***	0.405***	0.203***
	(0.136)	(0.046)	(0.024)	(0.021)	(0.022)	(0.025)
Bank efficiency	0.001	−0.013*	0.001	0.002	0.003	0.002
	(0.001)	(0.001)	(0.001)	(0.003)	(0.003)	(0.001)
Income diversification	0.031***	0.033	0.0353***	0.036***	0.038***	0.039***
	(0.011)	(0.020)	(0.009)	(0.009)	(0.008)	(0.008)
Bank size	−0.003	0.018***	0.004*	0.002	0.003*	0.001
	(0.005)	(0.003)	(0.001)	(0.001)	(0.001)	(0.001)
Liquidity	0.088	−0.325***	−0.008	−0.004	−0.008	−0.005
	(0.145)	(0.052)	(0.018)	(0.017)	(0.018)	(0.018)
Economic growth	0.005	−0.003***	0.005***	0.004***	0.003***	0.002***
	(0.002)	(0.001)	(0.004)	(0.004)	(0.004)	(0.001)
Inflation rate	0.005**	−0.002	0.001	0.001	0.001	0.001
	(0.002)	(0.001)	(0.001)	(0.001)	(0.001)	(0.001)
Tier-I/TA		0.757***
		(0.119)
Risk-based capital			−0.357***
			(0.038)
Tier-I/RWA				−0.483***
				(0.049)
Capital buffer					−0.446***
					(0.045)
Tier-I buffer						−0.461***
						(0.047)
Constant	−0.220	0.366***	0.058**	0.0673***	0.0243	0.0225
	(0.232)	(0.015)	(0.023)	(0.0236)	(0.0218)	(0.0218)
Observations	14,976	14,976	14,992	14,976	14,992	14,992
Number of id	936	936	937	936	937	937
AR (2)	0.428	0.177	0.261	0.314	0.459	0.345
Hansen value	0.781	0.719	0.872	0.276	0.325	0.467

Robust Standard errors in parentheses*** p < 0.01, ** p < 0.05, * p < 0.1

Table 4. Risk and Capital ratios model (overall sample): The dependent variable is loan loss allowances to gross loans ratio. Our predictions are the two-step GMM approach. (Robust standard errors are reported in parenthesis)

	(1)	(2)	(3)	(4)	(5)	(6)
VARIABLES	LLAGL	LLAGL	LLAGL	LLAGL	LLAGL	LLAGL
L.LLAGL	0.836***	0.833***	0.922***	0.838***	0.739***	0.846***
	(0.013)	(0.013)	(0.024)	(0.024)	(0.013)	(0.015)
Non-risk based capital	−0.003**
	(0.001)
Profitability	−0.026***	−0.027***	−0.027***	−0.027***	−0.027***	−0.027***
	(0.008)	(0.007)	(0.007)	(0.007)	(0.007)	(0.008)
Loan ratio	−0.002***	−0.002***	−0.002***	−0.002***	−0.002***	−0.002***
	(0.001)	(0.001)	(0.001)	(0.001)	(0.001)	(0.001)
Bank efficiency	−0.001***	−0.001***	−0.001***	−0.001***	−0.001***	−0.001***
	(0.002)	(0.002)	(0.002)	(0.002)	(0.002)	(0.002)
Income diversification	−0.004***	−0.004***	−0.004***	−0.004***	−0.004***	−0.004***
	(0.001)	(0.001)	(0.001)	(0.001)	(0.001)	(0.001)
Bank size	−0.003	−0.004*	−0.003	−0.005**	−0.003	−0.004**
	(0.002)	(0.002)	(0.002)	(0.002)	(0.002)	(0.002)
Liquidity	−0.002**	−0.001**	−0.002**	−0.001**	−0.002**	−0.001**
	(0.006)	(0.006)	(0.006)	(0.006)	(0.006)	(0.006)
Economic growth	−0.004***	−0.003***	−0.002***	−0.004***	−0.004***	−0.004***
	(0.002)	(0.002)	(0.002)	(0.002)	(0.002)	(0.002)
Inflation rate	−0.005***	−0.003***	−0.003***	−0.005***	−0.003***	−0.005***
	(0.004)	(0.004)	(0.004)	(0.004)	(0.004)	(0.004)
Tier-I/TA		−0.005
		(0.006)
Risk-based capital			0.002
			(0.001)
Tier-I/RWA				−0.003***
				(0.001)
Capital buffer					−0.004***
					(0.001)
Tier-I buffer						−0.004***
						(0.001)
Constant	0.008***	0.007***	0.008***	0.007***	0.008***	0.007***
	(0.008)	(0.008)	(0.008)	(0.008)	(0.008)	(0.008)
Observations	14,928	14,928	14,928	14,928	14,928	14,928
Number of id	933	933	933	933	933	933
AR (2)	0.234	0.231	0.212	0.322	0.235	0.225
Hansen value	0.432	0.321	0.234	0.411	0.433	0.237

Robust Standard errors in parentheses*** p < 0.01, ** p < 0.05, * p < 0.1

Table 5. Risk and Capital ratios model (post-crisis and before-crisis results): The dependent variable is risk-weighted assets to total assets. Our predictions are the two-step GMM approach. (Robust standard errors are reported in parenthesis): Note Post-crisis (AC) and Before-crisis (BC)

	(1)	(2)	(3)	(4)	(5)	(6)
VARIABLES	RWATA	RWATA	RWATA	RWATA	RWATA	RWATA
L. RWATA	0.511***	0.455***	0.624***	0.663***	0.612***	0.752***
	(0.033)	(0.046)	(0.035)	(0.033)	(0.038)	(0.037)
Non-risk based capital	0.355***
	(0.041)
Non-risk based capital*AC	−0.084***
	(0.013)
Non-risk based capital*BC	−0.038**
	(0.012)
Tier-I/TA		0.576***
		(0.056)
Tier-I/TA *AC		−0.122***
		(0.017)
Tier-I/TA *BC		−0.058***
		(0.011)
Risk-based capital			−0.341***
			(0.040)
Risk-based capital *AC			−0.006
			(0.015)
Risk-based capital *BC			−0.024*
			(0.016)
Tier-I/RWA				−0.553***
				(0.057)
Tier-I/RWA *AC				−0.005
				(0.012)
Tier-I/RWA *BC				−0.038**
				(0.018)
Capital buffer					−0.525***
					(0.068)
Capital buffer *AC					0.009
					(0.030)
Capital buffer *BC					−0.027
					(0.036)
Tier-I buffer						−0.456***
						(0.052)
Tier-I buffer *AC						0.001
						(0.025)
Tier-I buffer *BC						−0.031
						(0.026)
Constant	−0.029**	−0.032*	0.081**	0.023***	0.019	0.066
	(0.027)	(0.022)	(0.024)	(0.025)	(0.023)	(0.026)
Observations	14,976	14,976	14,992	14,976	14,992	14,992
Number of id	936	936	937	936	937	937
AR (2)	0.431	0.324	0.431	0.377	0.345	0.214
Hansen value	0.149	0.169	0.891	0.553	0.344	0.411

Robust Standard errors in parentheses*** p < 0.01, ** p < 0.05, * p < 0.1

Table 6. Risk and Capital ratios model (post-crisis and before-crisis period results): The dependent variable is loan loss allowances to gross loans ratio. Our predictions are the two-step GMM approach. (Robust standard errors are reported in parenthesis): Note Post-crisis (AC) and Before-crisis (BC)

	(1)	(2)	(3)	(4)	(5)	(6)
VARIABLES	LLAGL	LLAGL	LLAGL	LLAGL	LLAGL	LLAGL
L. LLAGL	0.511***	0.741***	0.952***	0.744***	0.822***	0.835***
	(0.022)	(0.014)	(0.010)	(0.015)	(0.015)	(0.014)
Non-risk based capital	0.001
	(0.002)
Non-risk based capital*AC	0.0036***
	(0.001)
Non-risk based capital*BC	0.005***
	(0.008)
Tier-I/TA		0.007***
		(0.002)
Tier-I/TA *AC		−0.009***
		(0.001)
Tier-I/TA *BC		0.006***
		(0.009)
Risk-based capital			0.058***
			(0.003)
Risk-based capital *AC			−0.005***
			(0.007)
Risk-based capital *BC			0.003***
			(0.006)
Tier-I /RWA				0.029*
				(0.016)
Tier-I /RWA *AC				−0.005***
				(0.007)
Tier-I /RWA *BC				0.026***
				(0.007)
Capital buffer					0.069***
					(0.019)
Capital buffer *AC					−0.041***
					(0.015)
Capital buffer *BC					0.062***
					(0.014)
Tier-I buffer						0.035*
						(0.019)
Tier-I buffer *AC						−0.006**
						(0.014)
Tier-I buffer *BC						0.005***
						(0.002)
Constant	0.014***	0.003***	0.066***	0.030***	0.007***	0.007***
	(0.014)	(0.009)	(0.008)	(0.009)	(0.008)	(0.008)
Observations	14,968	14,968	14,968	14,968	14,628	14,968
Number of id	935	935	935	935	935	935
AR (2)	0.291	0.334	0.419	0.426	0.452	0.422
Hansen value	0.911	0.412	0.295	0.191	0.522	0.911

Robust Standard errors in parentheses*** p < 0.01, ** p < 0.05, * p < 0.1

Table 7. Risk and Capital ratios model (Well (W) & Undercapitalized (U) banks results): The dependent variable is risk-weighted assets to total assets. Our predictions are the two-step GMM approach. (Robust standard errors are reported in parenthesis)

	(1)	(2)	(3)	(4)	(5)	(6)
VARIABLES	RWATA	RWATA	RWATA	RWATA	RWATA	RWATA
L. RWATA	0.424***	0.631***	0.632***	0.681***	0.752***	0.611***
	(0.040)	(0.033)	(0.034)	(0.036)	(0.035)	(0.037)
Non-risk based capital	0.483***
	(0.053)
Non-risk based capital*W	−0.236***
	(0.037)
Non-risk based capital*U	−0.084***
	(0.023)
Tier-I/TA		0.557***
		(0.059)
Tier-I/TA *W		−0.153***
		(0.032)
Tier-I/TA *U		−0.077***
		(0.084)
Risk-based capital			−0.413***
			(0.044)
Risk-based capital *W			0.054***
			(0.013)
Risk-based capital *U			0.002
			(0.012)
Tier-I/RWA				−0.522***
				(0.010)
Tier-I/RWA *W				0.067***
				(0.086)
Tier-I/RWA *U				0.012
				(0.012)
Capital buffer					−0.469***
					(0.072)
Capital buffer *W					0.101***
					(0.036)
Capital buffer *U					0.023
					(0.028)
Tier-I buffer						−0.588***
						(0.048)
Tier-I buffer *W						0.081**
						(0.039)
Tier-I buffer *U						0.019
						(0.024)
Constant	0.061**	−0.031	0.039**	0.051**	0.010	0.018
	(0.031)	(0.023)	(0.027)	(0.022)	(0.025)	(0.025)
Observations	14,976	14,976	14,992	14,976	14,992	14,992
Number of id	936	936	937	936	937	937
AR (2)	0.721	0.528	0.321	0.487	0.419	0.414
Hansen value	0.511	0.311	0.223	0.446	0.439	0.212

Robust Standard errors in parentheses*** p < 0.01, ** p < 0.05, * p < 0.1

Table 8. Risk and Capital ratios model (Well (W) & Undercapitalized (U) banks results): The dependent variable is loan loss allowances to gross loans ratio. Our predictions are the two-step GMM approach. (Robust standard errors are reported in parenthesis)

	(1)	(2)	(3)	(4)	(5)	(6)
VARIABLES	LLAGL	LLAGL	LLAGL	LLAGL	LLAGL	LLAGL
L. LLAGL	0.946***	0.912***	0.835***	0.837***	0.926***	0.925***
	(0.014)	(0.030)	(0.027)	(0.016)	(0.016)	(0.014)
Non-risk based capital	−0.035**
	(0.016)
Non-risk based capital*W	0.001
	(0.006)
Non-risk based capital*U	0.005
	(0.004)
Tier-I/TA		−0.025
		(0.003)
Tier-I/TA *W		−0.004
		(0.007)
Tier-I/TA *U		0.003
		(0.004)
Risk-based capital			0.022
			(0.014)
Risk-based capital *W			−0.009**
			(0.004)
Risk-based capital *U			−00001
			(0.003)
Tier-I/RWA				−0.024
				(0.016)
Tier-I/RWA *W				−0.003
				(0.005)
Tier-I/RWA *U				0.002
				(0.003)
Capital buffer					0.009*
					(0.016)
Capital buffer *W					−0.017*
					(0.008)
Capital buffer *U					−0.005
					(0.007)
Tier-I buffer						−0.008
						(0.017)
Tier-I buffer *W						−0.005
						(0.008)
Tier-I buffer *U						−0.002
						(0.005)
Constant	0.007***	0.004***	0.009***	0.006***	0.006***	0.002***
	(0.008)	(0.009)	(0.008)	(0.008)	(0.008)	(0.008)
Observations	14,938	14,938	14,938	14,938	14,938	14,938
Number of id	934	934	934	934	934	934
AR (2)	0.316	0.244	0.234	0.242	0.254	0.235
Hansen value	0.424	0.816	0.221	0.422	0.322	0.282

Robust Standard errors in parentheses*** p < 0.01, ** p < 0.05, * p < 0.1

Table 9. Risk and Capital ratios model (Nationally chartered member banks (NAT), State-chartered member banks (SMB), State-chartered non-member banks (SNM) results): The dependent variable is risk-weighted assets to total assets. Our predictions are the two-step GMM approach. (Robust standard errors are reported in parenthesis)

	(1)	(2)	(3)	(4)	(5)
VARIABLES	RWATA	RWATA	RWATA	RWATA	RWATA
L.RWATA	−0.362***	−0.428***	0.567***	0.798***	0.757***
	(0.080)	(0.090)	(0.030)	(0.034)	(0.033)
Non-risk based capital	0.395***
	(0.001)
NAT* Non-risk based capital	−0.115*
	(0.058)
SMB* Non-risk based capital	−0.032
	(0.052)
Tier-I/TA		0.701***
		(0.121)
NAT* Tier-I/TA		−0.132**
		(0.066)
SMB* Tier-I/TA		−0.041
		(0.060)
Risk-based capital			−0.344***
			(0.032)
NAT* Risk-based capital			−0.002
			(0.014)
SMB* Risk-based capital			−0.004
			(0.011)
Tier-I/RWA				−0.486***
				(0.096)
NAT* Tier-I/RWA				0.045
				(0.013)
SMB* Tier-I/RWA				0.007
				(0.012)
Capital buffer					−0.420***
					(0.047)
NAT* Capital buffer					−0.0111
					(0.033)
SMBB* Capital buffer					−0.009
					(0.027)
Constant	0.324***	0.352***	0.047**	0.066***	0.025
	(0.016)	(0.041)	(0.028)	(0.026)	(0.028)
Observations	14,966	14,966	14,962	14,976	14,972
Number of id	935	935	936	937	936
AR (2)	0.610	0.310	0.621	0.382	0.593
Hansen value	0.242	0.352	0.821	0.154	0.326

Robust Standard errors in parentheses*** p < 0.01, ** p < 0.05, * p < 0.1

Table 10. Risk and Capital ratios model (Nationally chartered member banks (NAT), State-chartered member banks (SMB), State-chartered non-member banks (SNM) results): The dependent variable is loan loss allowances to gross loans ratio. Our predictions are the two-step GMM approach. (Robust standard errors are reported in parenthesis)

	(1)	(2)	(3)	(4)	(5)
VARIABLES	LLAGL	LLAGL	LLAGL	LLAGL	LLAGL
L.LLAGL	0.837***	0.639***	0.634***	0.835***	0.634***
	(0.014)	(0.027)	(0.031)	(0.014)	(0.030)
Non-risk based capital	−0.003**
	(0.001)
NAT* Non-risk based capital	0.001*
	(0.004)
SMB* Non-risk based capital	0.007
	(0.004)
Tier-I/TA		0.013***
		(0.009)
NAT* Tier-I/TA		0.004
		(0.001)
SNM* Tier-I/TA		0.001
		(0.001)
Risk-based capital			0.015***
			(0.001)
NAT* Risk-based capital			0.003
			(0.009)
SMB* Risk-based capital			0.004
			(0.008)
Tier-I/RWA				−0.003**
				(0.003)
NAT* Tier-I/RWA				0.007**
				(0.003)
SMB* Tier-I/RWA				0.002
				(0.003)
Capital buffer					0.014***
					(0.003)
NAT* Capital buffer					0.004
					(0.002)
SMB* Capital buffer					0.008
					(0.009)
Constant	0.007***	0.013***	0.015***	0.006***	0.012***
	(0.008)	(0.001)	(0.002)	(0.008)	(0.012)
Observations	14,938	14,938	14,938	14,938	14,938
Number of id	934	934	934	934	934
AR (2)	0.312	0.432	0.145	0.231	0.322
Hansen value	0.242	0.171	0.172	0.238	0.161

Robust Standard errors in parentheses*** p < 0.01, ** p < 0.05, * p < 0.1