Negative rates and bank profit and cost efficiency: evidence for Eurozone

Figures & data

Table 1. Descriptive information and summary statistics.

Variable name	Definition	Units	Mean	St. Dev
Frontier Variables
PROFIT	Pre-tax profits	Million EUR	11.872	35.189
Q1	Total loans	Million EUR	1,419	3,120
Q2	Other earning assets	Million EUR	421	1,290
Q3	Non-interest income	Million EUR	19.322	54.856
W1	Interest expense/Deposits	Ratio	0.014	0.015
W2	Personnel expenses/Total assets	Ratio	0.012	0.004
W3	Operating expenses/Fixed assets	Ratio	2.862	37.949
EQ	Total Equity	Million EUR	173.013	387.260
Inefficiency Variables
GDP	GDP per Capita	EURO per Capita	33,042	5,823
CONC	Banking Concentration	Ratio (%)	16.916	19.045
CAP	Total Capital Ratio	Ratio (%)	18.241	4.277
NIM	Net interest margin	Ratio (%)	2.179	0.682
SIZE	1 for 0bn < total assets ≤1bn, 2 for 1bn < total assets ≤10bn and 3 for 10bn < total assets	Ordinal	1.431	0.576
RISK	Provisions/Total Loans	Ratio (%)	0.241	0.663

Note: This table reports summary statistics of the variables used in the empirical analysis.

Figure 1. Average deposits, loans and other earning assets per year.

Figure 2. Average loan loss provisions per year.

Figure 3. Average NIM per year.

Figure 4. Average non-interest income and profits per year.

Table 2. Estimated parameters of the Profit efficiency model.

	Estimate	Std. Error
a_0	8.0143***	0.6107
a_1	0.9942***	0.0884
a_2	−0.204**	0.0905
a_3	−2.0014***	0.1369
a_4	0.2751***	0.0658
a_5	1.3674***	0.1043
b_1_1	0.1598***	0.0097
b_1_2	−0.1731***	0.0100
b_1_3	−0.1422***	0.0117
b_1_4	0.0385***	0.0053
b_1_5	0.0631***	0.0106
b_2_2	0.1911***	0.0124
b_2_3	0.2188***	0.0123
b_2_4	−0.0485***	0.0058
b_2_5	−0.1568***	0.0114
b_3_3	0.5378***	0.0216
b_3_4	−0.086***	0.0097
b_3_5	−0.3871***	0.0166
b_4_4	0.0449***	0.0043
b_4_5	0.0391***	0.0078
b_5_5	0.319***	0.0171
d_1	0.6661***	0.0194
Z0	14.697***	2.3616
Z1 (T)	0.2126**	0.1084
Z2 (CONC)	−0.0286***	0.0103
Z3 (GDP)	−0.0002***	0,0000
Z4 (NIRP)	−2.5565***	0.3601
Z5 (NIM)	−8.1105***	1.3551
Z6 (CAP)	−0.1907***	0.0361
Z7 (SIZE)	−2.1609***	0.3729
Z8 (RISK)	2.143***	0.2784
sigmaSq	8.2543***	1.4426
gamma	0.9791***	0.0038

Notes: This table reports the results of the estimation of the model presented in (4) and (5). The dependent variable is the logarithmic form of pre-tax profits normalized by operating cost and the parameters are estimated by the maximum likelihood method.

*, **, and *** denote significance at the 10%, 5%, and 1% levels, respectively.

Table 3. Mean profit and cost efficiency per year.

Year	Mean Profit efficiency score	Mean Cost efficiency score
2010	0.699	0.891
2011	0.697	0.891
2012	0.672	0.896
2013	0.668	0.905
2014	0.690	0.919
2015	0.683	0.916
2016	0.687	0.912
2017	0.691	0.907
2018	0.661	0.903

Note: This table reports the mean profit efficiency score per year.

Table 4. Mean elasticities per input price or output.

Cost of funds $\text{ln}\left(\frac{{\text{w}}_{\text{1it}}}{{\text{w}}_{\text{3it}}}\right)$	Labour Cost $\ln \left(\frac{{\text{w}}_{\text{2it}}}{{\text{w}}_{\text{3it}}}\right)$	Loans $\ln (Q\text{1it )}$	Other earning assets $\ln (Q\text{2it)}$	Non-Interest Income $\ln (Q\text{3it)}$
0.161	0.686	0.372	0.050	−0.084

Notes: This table reports the mean elasticities of all the input and output variables in the context of the Battese and Coelli (1995) model, using the multiproduct-translog specification.

Table 5. Estimated parameters of the Profit efficiency models.

Model	(1)	(2)	(3)	(4)
Intercept	11.739***	14.03535***	14.03241***	12.053***
	(1.7179)	(3.40572)	(1.82933)	(1.9181)
T	0.18211***	0.20403	0.21348***	0.1764**
	(0.05551)	(0.12949)	(0.06685)	(0.08155)
CONC	−0.01355**	−0.03641***	−0.02551***	−0.01263*
	(0.00616)	(0.0115)	(0.00746)	(0.00652)
GDP	−0.00015***	−0.00024***	−0.0002***	−0.00016***
	(0.00003)	(0.00007)	(0.00003)	(0.00002)
NIRP	−2.0502***	−1.40718**	-3.01339***	−1.7825
	(0.19362)	(0.60015)	(0.45407)	(1.2904)
NIM	−7.7362***	−7.92855***	−8.01825***	−7.6414***
	(1.0959)	(1.69802)	(1.26596)	(1.3887)
CAP	−0.15505***	−0.17459***	−0.19197***	−0.16344***
	(0.03228)	(0.06038)	(0.03387)	(0.02309)
SIZE	−1.7563***	−1.14836***	−2.18947***	−2.1147***
	(0.20676)	(0.34378)	(0.29338)	(0,31076)
RISK	2.0396***	2.11527***	2.16101***	2.0733***
	(0.21278)	(0.32979)	(0.25899)	(0.22522)
NIRP*FEES	−0.0122***
	(0.003256)
NIRP*SEC		−0.00251***
		(0.0009)
NIRP*LIC			0.36918***
			(0.09515)
NIRP*NIM				−0.2668
				(0.4577)

Notes: The table presents the estimated coefficients of the four extensions to the baseline inefficiency model presented in Equation (5), after incorporating interaction terms of NIRP with FEES, SEC, LIQ and NIM. Standard errors are reported in parentheses. The dependent variable is profit inefficiency. The parameters are estimated by the maximum likelihood method.

*, **, and *** denote significance at the 10%, 5%, and 1% levels, respectively.

Table 6. Estimated parameters of the cost inefficiency model.

	Estimate	Std. Error
Z0	−59.568*	35.124
Z1 (T)	0.6236*	0.3336
Z2 (CONC)	0.8596**	0.4346
Z3 (GDP)	−0.0002*	0.0001
Z4 (NIRP)	−18.854**	8.7794
Z5 (NIM)	−19.081**	8.048
Z6 (CAP)	−1.1405**	0.4743
Z7 (SIZE)	4.2977**	2.0713
Z8 (RISK)	−5.8951**	2.6298

Notes: The table reports the results of the estimation of the inefficiency model presented in Equation (5), using Total Cost instead of Profit as the dependent variable in Equation (4). The parameters are estimated by the maximum likelihood method.

*, **, and *** denote significance at the 10%, 5%, and 1% levels, respectively.

Table 7. Estimated parameters of the cost efficiency models.

Model	(1)	(2)	(3)
Intercept	−73.126*	−61.022**	−73.107***
	(42.396)	(26.849)	(22.639)
T	0.88715*	0.72428**	0.91888***
	(0.5048)	(0.34281)	(0.25684)
CONC	1.0359**	0.87905***	1.3587***
	(0.52324)	(0.3369)	(0.39069)
GDP	−0.00032*	−0.00029**	−0.00074***
	(0.00017)	(0.00014)	(0.00023)
NIRP	−22.895**	−21.586***	−93.831***
	(11.049)	(7.4767)	(26.746)
NIM	−22.313**	−19.853***	−48.359***
	(9.2624)	(6.021)	(13.478)
CAP	−1.3584**	−1.1823***	−2.575***
	(0.57676)	(0.38161)	(0.67937)
SIZE	5.5326*	5.2626***	7.395***
	(2.8303)	(1.9184)	(2.2144)
RISK	−7.5717**	−6.5356***	−11.278***
	(3.1202)	(2.1444)	(3.1949)
NIRP*RISK	0.07739
	(0.3402)
NIRP*SIZE		0.38574***
		(0.01449)
NIRP*CONC			0.88414***
			(0.2493)

Notes: The table presents the estimated coefficients of the four extensions to the baseline inefficiency model presented in Equation (5), after incorporating interaction terms of NIRP with RISK, SIZE, and CONC. Standard errors are reported in parentheses. The dependent variable is cost inefficiency.

*, **, and *** denote significance at the 10%, 5%, and 1% levels, respectively.

Battese, G. E., and T. J. Coelli. 1995. “A Model for Technical Inefficiency Effects in a Stochastic Frontier Production Function for Panel Data.” Empirical Economics 20 (2): 325–332. https://doi.org/10.1007/BF01205442

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