Excerpt

## 1. Introduction

This paper uses *t* and *f* statistical tests to evaluate empirically the competitive conditions in the German banking system for the period 2003-2007. For this purpose we implement the non-structural estimation technique in logarithmic form (Hondroyiannis, Lolos, Papapetrou, 1999, p.377):

lnTrev = α1+α2 lnPL+α3 lnPK+α4 lnPF+α5 lnRISKASS+α6 lnASSET+α7 lnEMP

Dependent variable Trev represents the ratio of total revenue to total assets. Inedependent variables are PL (the ratio of personal expenses to employees, in other words unit price of labor), PK (ratio of capital expenses to fixed assets or unit price of capital), PF (ratio of annual interest expenses to own funds or unit price of funds, RISKASS (ratio of provisions to total assets), ASSET (bank total assets), EMP (total number of employees). αο is constant or intercept of the equation. Total number of employees is taken as an alternative measure or bank size because of data insufficiency on the total number of bank branches (Hondroyiannis, Lolos, Papapetrou, 1999, p.383). Prior to presenting regression results, it must be mentioned that the model introduced is somewhat limited in the sense that it is originally designed to test competitiveness in the Greek banking system. Furthermore, our sample consists of mixed nature of banking institutions, each one having specific structural and capital characteristics. Bank sample was drawn completely randomly from the bankscope database. We use ordinary least square method (OLS) to estimate weighting of relationships between the endogenous and exogenous variables. Please note that tables presented throughout this paper are in short form. Detailed data output is available in the appendix

Table 1

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Table 1 shows major regression estimates. Furthermore expected signs for coefficients are included as according to theory. Naturally, higher capital provisions should result in higher revenue. Increase in the total number of employees indicated growth and should therefore be related positively to total revenue. On the other hand increase in personal, capital or interest expenses all result in total revenue decrease. Increase in total assists leads to decrease in revenue, hence expecting negative relationship (expenses incurred in acquiring new assets would decrease total revenue).

Durbin-Watson, F and t statistical values and probabilities as well as squared sum of residuals are discussed at later stages in this paper.

Table 2

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Tables 2 and 3 illustrate mean and standard deviation values for our independent variables in logarithmic form (cumulative for 5 years). Because of the mixed nature of our sample interbank comparisons would be inappropriate. This is evident if we look at the price of labor elasticity (lnPL) where Sparkassen-Finanzgruppe Hessen-Thuringen (bank 15) has roughly 4 times higher personal expenses to employees ratio than AKA-ausfuhrkedit. At the same time cumulative standart deviation for Sparkassen-Finanzgruppe Hessen-Thuringen over 5 years is close to zero. This implies price of labor is higher possibly because of size of structural differences (higher number of employees and subsequently higher personal expenses).

Table 3

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**a) t and F statistical tests**

We use t statistics to test individual coefficients in a regression for statistical significance. If we want to analyze effect of multiple independent variables on the dependent, we use F statistics. We assume level of significance of 5% (95% confidence interval). Typically, we set a hypothesis (Ho) and an alternative (H1). Next we compare calculated values of F and t tests to critical F and t values (sign is irrelevant because tests are both sided) for given degrees of freedom (total number of observations less the number of exogenous variables). Using the level of significance approach, t statistics is calculated manually using the following formula:

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Table 4 illustrates our t-test results. The null hypotheses for each variable is that it is insignificant (αi=0), and the alternative hypothesis (H1) being that each variable is statistically significant. Based on comparison between t calculated and t critical values, we can conclude that two of our exogenous variables and the intercept have statistically significant influence on the endogenous variable (Ln Assets, Ln Pf and c).

The rest of the independent variables do not significantly explain variations in the dependent.

Table 4

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(according to table, t critical = 1.645)

Table 5 indicates findings based on conducting F test statistics. The null hypothesis implies that coefficients of variables are equal to zero and hence the set of variables do not explain changes in the dependent variable (they are insignificant). The alternative hypothesis (H1) states that the set of coefficients are not equal to zero and therefore set of exogenous variables are statistically significant, asserting that they do explain changes in the endogenous variable.

Table 5

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Using the same principle as with t testing, we compare F-calculated to F-critical value. Since F-calculated is greater than F-critical, we reject Ho at the 5% level of significance (95% confidence interval). Hence set of exogenous variables are statistically significant.

**b) F-test based on RSS**

Here we test the null hypothesis that there is no relationship between the set of independent variables and the dependent (Ho: α2=α3=α4=α5=α6=α7=0) using F-test based on restricted sum of squares (RSS). The alternative hypothesis implies that coefficients are significant. (H1: α2≠α3≠α4≠α5≠α6≠α7≠0). We use the following equation to manually calculate F test:

Table 6 shows f-test calculations based on RSS.

Table 6

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First we take the squared sum of residuals value from our unrestricted equation (lnTrev = α1+α2 lnPL+α3 lnPK+α4 lnPF+α5 lnRISKASS+α6 lnASSET+α7 lnEMP). Next step is estimating our restricted equation (lntrev=α1) and taking the squared sum of residuals value. In order to be able to calculate F statistics based on restricted RSS, we also need to find degrees of freedom (number of observations less the number of coefficients) and divide them by the number of restrictions. Once we computed essential individual components we use formula outlined above to calculate F test statistics. Following the procedure described in 1a), we reject Ho at the 5% level of significance and hence conclude that there is statistically significant relationship between our dependent and independent variables.

**c) Wald restrictions test**

Table 7 shows results from Eviews Wald test. As defined in the table, Ho assumes no statistically significant relationship between set of exogenous and the endogenous variable. Alternatively (H1), there is relationship between set of independent and dependent variable.

Table 7

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Because F-test probability is inside the significance level of 5% (0,00<0,05) we can conclude that Eviews output using Wald test correspond to manual F-test based on RSS.

**[...]**

- Quote paper
- Dimitar Vasilev (Author), 2010, Report on assessing competitiveness of the German banking system (2003-2008), Munich, GRIN Verlag, https://www.grin.com/document/180771

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