Introduction
Globally the levels of interest rates are of great concern in the banking industry. During the global financial crisis that occurred between 2007 and 2009 rates in most developed economies fell to almost zero which was a threat to banks’ customer bases (Lopez, Rose and Siegel, 2018). Some researchers for example (Jobst & Lin, 2016) argue low interest rates hinder bank profitability because of the low interest rate margins. Empirical evidence has demonstrated at low interest rates bank profitability declines sensitivity of profit is pronounced when there is a decline in interest rates (Borio, Claudio and Leonardo, 2017). Furthermore evidence has shown as interest rates approach zero the effectiveness of reducing policy rates in influencing bank lending diminishes meaning monetary transmission is weak at very low interest rates (Borio et al, 2017). Evidence from US has shown ultra-low interest rates negatively affected net interest margin (NIM) but changes in house prices and unemployment rate had a more pronounced effect on profitability as compared to interest rates (Genay and Podjasek, 2014). In Japan where banking sector has had a long period of ultra-low interest rates, low interest rates led to reduced NIM and earnings (Weistroffer, 2013)
Some researchers have argue in the short term banks benefit from low interest rates. For example (Campmas, 2015) argues although low interest rates erode NIM banks benefit from higher valuation of securities and reduced burden of non-performing loans. An exception to impact of low interest rates is in Sweden where it was found between 2009 and 2016 cost to income ratio fell from 51% to 47% while in other European countries it rose from 62% to 74% (Riskbank, 2016).
The reduced profitability from low interest rates is a major risk in banking sector. The European Central Bank (ECB) has noted reduced profitability due to low interest rates exposes banks in two ways. First accumulation of capital from retained earnings is hampered which harms ability to absorb shocks. Second long periods of low profitability leads to higher risk taking which can destabilize the financial sector (ECB, 2015).
The profitability of banking sector is also affected by other macroeconomic variables besides interest rate. In a study of Korean banking sector between 1994 and 2008 it was found inflation had a pro-cyclical effect while GDP had a counter-cyclical effect (Sufian, 2010). A study in Turkey found real interest rate positively affected bank profitability (Alpera and Anbar, 2011). A study on Nigerian banking sector found there was a positive but not significant relationship between bank performance and inflation (Chioma, Adanma and Clementina, 2014).
A study of Swiss banking sector between 1999 and 2008 revealed banks in stronger capital position were more profitable, cost-income ratio only affected return on assets before crisis andloan loss provisions relative to total loans had a negative effect on profitability during crisis (Dietrich and Wanzenried, 2010).
Even in an environment of low interest rates especially in Europe and Japan where interest rates are negative and financial stability of banks is under threat empirical evidence on this topic is limited (Campmas, 2015). The current analyses aims to bridge this gap in Polish banking sector by examining the impact of interest rates on bank profitability. Such an analysis is highly beneficial to banking sector policy makers and investors.
Data and methodology
This section explains the variables and econometric models applied.
Data description
This study focused on analysis of Polish banking data between 2010 and 2017.
Bank profitability
In this study it was found prudent to use established and reliable indicators of bank performance. These indicators are ROA, ROE and NIM. In line with work of other researchers such as (Borio et al, 2015) NIM was selected as the indicator of bank performance because this study focused on impact of low policy interest rates on performance of banks.
Policy interest rate
The National Bank of Poland (NBP) was used as the measure of policy interest rate. Monthly data from 2010 to 2017 was collected from NBP website.
Bank control variables
A set of bank specific variables that have been found to influence profitability were used as a control.
Aggregated equity ratio (ER)
Ratio of current liabilities to total liabilities (CDTD)
Government Bonds (GB) – findings from OECD analysis have shown an increase in government bond yields can negatively affect bank balance sheet but this effect varies depending on bank size, hedging and maturity.
Ratio of total reserves to total assets (RTA)
Macroeconomic variables
Inflation (INF) – inflation has been found to have a positive relationship with performance.
Unemployment rate (UR) – unemployment has been found to have a negative effect on profitability.
Because the period considered in this study was from 2010 to 2017 there was no need to include a crisis dummy because the crisis occurred between 2007 and 2008.
Econometric methodology
The econometric model used in this analysis is shown below
P= βo + βπ + ℮ where P is NIM, π is the set of interest rate, bank control and macroeconomic variables and ℮ is an error term. To estimate the model ordinary least squares (OLS) or generalized method of moments (GMM) can be used. Use of OLS estimation in this case may have shortcomings. There could be correlation between lagged dependent variable and error term and endogeneity could result from possible reverse causality and omitted variable bias (Campmas, 2015). The approach used in this analysis was to estimate an OLS model and test for endogeneity and omitted variable bias. If inconsistencies were found GMM estimation was used. Before variables were entered into the model they were tested for stationarity and any variables exhibiting non-stationarity were differenced and tested again for stationarity.
Results
Table 1
Descriptive statistics of variables
| Variable | Observations | Mean | Std Dev | Min | Max |
| GB | 94 | 4.13 | 1.21 | 2.19 | 6.27 |
| UR | 94 | 1.44 | 0.34 | 0.76 | 1.96 |
| INF | 93 | 0.10 | 0.29 | -0.4 | 1 |
| RTA | 94 | 0.02 | 0.002 | 0.02 | 0.03 |
| CDTD | 94 | 0.43 | 0.05 | 0.35 | 0.57 |
| ER | 94 | 0.10 | 0.004 | 0.09 | 0.11 |
| NIM | 94 | 1.98 | 1.03 | 0.27 | 3.90 |
| NBP | 94 | 2.75 | 1.20 | 1.5 | 4.75 |
Descriptive statistics of variables selected for model building are shown on Table 1.
Figure 1
Figure 1 shows a time series plot of GB, NIM and NBP. It can be observed NBP and GB exhibited a downward trend which suggests the series may be non-stationary. The two series NBP and GB did not exhibit any seasonality.
Figure 2
A time series plot of unemployment rate is shown on Figure 2 from where it can be observed the series had a downward trend which suggests non-stationarity.
Figure 3
Figure 3 shows time series plots of INF, RTA, CDTD and ER. The ER and RTA remained stable over the period under consideration suggesting they were stationary. The CDTD series had an upward trend after 2011 suggesting non-stationarity. The INF series had no trend but it had seasonality. To control for the seasonality effects a quarter dummy was introduced.
Table 3
| NBP | NIM | ER | CDTD | RTA | INF | UR | GB | |
| NBP | 1.00 | |||||||
| NIM | 0.10 | 1.00 | ||||||
| ER | -0.59** | -0.06 | 1.00 | |||||
| CDTD | -0.88** | 0.02 | 0.65** | 1.00 | ||||
| RTA | -0.76** | 0.04 | 0.70** | 0.82** | 1.00 | |||
| INF | 0.25* | -0.14 | -0.25* | -0.19 | -0.36** | 1.00 | ||
| UR | 0.77** | -0.12 | -0.45** | -0.91** | -0.65** | 0.13 | 1.00 | |
| GB | 0.82** | 0.06 | -0.78** | -0.71** | -0.70** | 0.42** | 0.59** | 1.00 |
Note ** p < 0.01, * p < 0.05
Correlation among variables is shown on Table 3. When examining correlation between variables to be used in regression two sets of correlation are important. The first set is correlation between dependent variable and predictors and the second set is correlation among predictor variables. The correlation between NIM and ER was negative, weak and not statistically significant. In the regression model the coefficient of ER would be expected to be negative. The correlation between NIM and CDTD was weak, positive and not statistically significant. The coefficient of CDTD in the regression model would be expected to be negative. The correlation between NIM and RTA was weak, positive and not statistically significant. The RTA coefficient in regression model would be expected to be positive. The correlation between INF and NIM was weak, negative and not statistically significant. The coefficient of NIM would be expected to be zero. The correlation between NIM and UR was weak, negative and statistically not significant. The regression coefficient of UR would be expected to be negative. The correlation between NIM and GB was weak positive and not statistically significant. The coefficient of GB would be expected to be positive. Generally the correlation between dependent and predictor variables was weak and not statistically significant. This was not a good property of predictors because a good set of predictors is strongly correlated with dependent variable.
The correlation between NBP and CDTD was negative, strong and statistically significant. This is an indication NBP and CDTD would be contributing the same information to the model. The correlation between CDTD and RTA was positive, strong and statistically significant. This means CDTD and RTA would be contributing same information in the model. The correlation between NBP and GB was positive, strong and statistically significant. This means NBP and GB were contributing same information in the model. The correlation between UR and CDTD was negative, strong and statistically significant. This means UR and CDTD would be contributing same information in the model. The strong correlations among the predictors were an indicator the problem of multi-collinearity may arise in the model. Instead of dropping some variables all variables would be included in the model then VIF and tolerances would be examined to identify multi-collinearity problems.
Table 4
| Variable | Dickey-Fuller | Phillips-Perron |
| NBP | 0.945 | 0.896 |
| NIM | 0.000 | 0.000 |
| ER | 0.583 | 0.683 |
| CDTD | 0.991 | 0.998 |
| RTA | 0.218 | 0.203 |
| INF | 0.000 | 0.000 |
| UR | 0.983 | 0.945 |
| GB | 0.692 | 0.643 |
The augmented Dickey-Fuller and Phillips-Perron test the null hypothesis a variable has a unit root against the alternative hypothesis the variable is stationary. A p value less than 0.05 showed the variable was stationary and a p value greater than 0.05 showed the variable had a unit root. The results of stationarity testing at level are shown on Table 4. Stationarity tests on the variable NBP had p values greater than 0.05 leading to failure to reject the null hypothesis. Therefore NBP had a unit root and differencing was required. Stationarity testing on NIM returned p values less than 0.05 leading to rejection of null hypothesis. Therefore NIM was stationary at level and no differencing was required. Stationarity testing on ER returned p values greater than 0.05 leading to failure to reject the null hypothesis. Therefore ER had a unit root and required differencing. Stationarity testing on CDTD returned p values greater than 0.05 and the null hypothesis of existence of a unit root could not be rejected. Therefore CDTD had a unit root and differencing was required. Unit root testing on INF resulted in p values less than 0.05 leading to rejection of null hypothesis of existence of a unit root. Therefore INF was stationary at level and required no differencing. Stationarity testing on UR resulted in p values greater than 0.05 and the null hypothesis of non stationarity could not be rejected. Therefore UR was non stationary and required differencing. Stationarity testing on GB resulted in p values greater than 0.05 and the null hypothesis of existence of a unit root could not be rejected. Therefore GB was non stationary and required differencing. It is important to note for all variables the Dickey-Fuller and Philips-Peron tests were consistent. The two tests did not give any conflicting results.
Table 5
| Variable | Dickey-Fuller | Phillips-Perron |
| GB | 0.000 | 0.000 |
| NBP | 0.000 | 0.000 |
| ER | 0.000 | 0.000 |
| CDTD | 0.000 | 0.000 |
| RTA | 0.000 | 0.000 |
| UR | 0.000 | 0.000 |
Six variables were non-stationary at level and required differencing. The results of stationarity testing on first difference of the variables is shown on Table 5. Stationarity testing on first difference of GB resulted in p values less than 0.05 leading to rejection of null hypothesis of existence of a unit root. Therefore the first difference of GB was stationary. Stationarity testing on first difference of NBP resulted in p values lower than 0.05 leading to rejection of null hypothesis of non stationarity. Therefore the first difference of NBP was stationary. Stationarity testing on ER resulted in p values lower than 0.05 leading to rejection of null hypothesis of existence of a unit root. Therefore the first difference was stationary. Stationarity testing on first difference of CDTD resulted in p values lower than 0.05 leading to rejection of null hypothesis of existence of a unit root. Therefore CDTD was stationary at first difference. Stationarity testing on first difference of RTA resulted in p values lower than 0.05 leading to rejection of null hypothesis of existence of unit root. Therefore the first difference of RTA was stationary. Stationarity testing on first difference of UR resulted in p values lower than 0.05 leading to rejection of null hypothesis of existence of unit root. Therefore the first difference of UR was stationary.
Table 6
| (1) | |
| VARIABLES | NIM |
| INF | 0.147 |
| (0.124) | |
| D.NBP | 0.0817 |
| (0.253) | |
| D.ER | -32.67 |
| (22.15) | |
| D.CDTD | 9.968*** |
| (3.569) | |
| D.RTA | -34.72 |
| (48.46) | |
| D.UR | 0.730 |
| (0.913) | |
| D.GB | -0.129 |
| (0.167) | |
| 2.QTR | 0.869*** |
| (0.117) | |
| 3.QTR | 1.829*** |
| (0.102) | |
| 4.QTR | 2.610*** |
| (0.0945) | |
| Constant | 0.605*** |
| (0.0742) | |
| Observations | 93 |
| R-squared | 0.929 |
Standard errors in parentheses
*** p<0.01, ** p<0.05, * p<0.1
Results of OLS estimation are shown on Table 6. The estimated model was able to explain 92.9% of variation in NIM. This was an excellent model and the high value of R-squared showed the model was able to capture a high percentage of variation in the data. A t test was used to test the significance of each predictor in the model. When the p value was less than a specific level of significance the predictor was considered statistically significant otherwise it was not. Inflation had a positive but insignificant effect on NIM. A unit increase in inflation led to a 0.147 increase in NIM. NBP had a positive but not statistically significant effect on NIM. A unit increase in NBP led to a 0.08 increase in NIM. ER had a negative but not statistically significant effect on NIM. A unit increase in ER led to -32.67 decrease in NIM. CDTD had a positive and statistically significant effect on NIM at 0.01 level of significance. A unit increase in CDTD led to 9.96 increase in NIM. RTA had a negative but not statistically significant effect on NIM. A unit increase in RTA led to -34.72 decrease in NIM. UR had a positive but not statistically significant effect on NIM. A unit increase in UR led to a 0.73 increase in NIM. GB had a negative but not statistically significant effect on NIM. A unit increase in GB led to 0.12 decrease in NIM. Due to seasonality observed earlier a dummy variable was introduced to control effects of seasonality. The first quarter was used as a reference. A change from the first quarter to second quarter was positive and statistically significant. A change from first quarter to second quarter led to an increase in NIM by 0.869. A change from first quarter to third quarter was positive and statistically significant. A change from first quarter to second quarter led to an increase in NIM by 1.82 units. A change from first quarter to fourth quarter was positive and statistically significant. A change from first to fourth quarter led to a 2.61 increase in NIM. The constant of the regression model was statistically significant. The value shows when all predictors were zero the value of NIM was 0.605. The constant in this model does not have a very meaningful interpretation.
Table 7
| Variable | VIF | 1/VIF |
| INF | 1.43 | 0.699973 |
| NBP | 1.1 | 0.910794 |
| D1.ER | 1.43 | 0.698541 |
| D1.CDTD | 1.34 | 0.744287 |
| D1.RTA | 1.54 | 0.64844 |
| D1.UR | 1.84 | 0.543498 |
| D1.GB | 1.15 | 0.871995 |
| Quarter2 | 2.87 | 0.348035 |
| Quarter 3 | 2.15 | 0.464606 |
| Quarter 4 | 1.86 | 0.536711 |
In a linear regression model multicollinearity occurs when predictors have a perfect relationship. Due to this problem reliable estimation of regression coefficients becomes problematic. Earlier examination of pairwise correlation among predictors suggesting multicolinearity. To identify multicollinearity in a linear regression model variance inflation factor (VIF) is used. VIF measures the extent to which the variance of the parameter estimates increases due to collinearity in predictors. When the VIF of a variable is 1 there is no correlation with the other predictors. VIF values higher than 4 need to be investigated and VIF values higher than 10 are an indicator of severe multicollinearity that needs correction. The VIFs of variables included in the model are shown on Table 7. The variables GB, INF, NBP, ER and CDTD had VIF values close to 1 therefore there was negligible inflation in variance of the parameter estimates of those variables. All the VIF values of variables included in the model were below 4. This shows multicollinearity was not a problem and no corrective actions were required.
The Ramsey test revealed the OLS model had no omitted variable bias F(3,79) = 1.57, p = 0.203. Therefore the OLS model did not have omitted variable bias.
Figure 4
A density plot of residuals is shown on Figure 4 from where it can be observed the residuals did not deviate from normality assumption.
Figure 5
A plot of residuals against fitted values is shown on Figure 5 from where it can be observed the residuals were constant across fitted values. Therefore the OLS model did not violate homoscedasticity assumption. The Breusch-Pagan test did not find deviation from constant variance assumption Chisq (1) = 0.52, p = 0.469
Figure 6
A plot of residuals against time is shown on Figure 6. The plot suggests there is no autocorrelation of residuals and Durbin-Watson d-statistic (11,93) = 2.18 is very close to 2 shows there was no autocorrelation.
Discussion
This analysis found the mean policy interest rate in Poland was 2.75 with a range of 1.5 to 4.75. It was further found the policy interest rate had a downward trend which was consistent with trends in advanced economies although in Poland the interest rate did not fall to negative during the period under study.
