Revisiting the interest margin literature: The impact of
non-interest income activities on the interest margin,
market power, and efficiency of banks
B.W. Troost
RijksUniversiteit Groningen
KOF Swiss Economic Institute, ETH Zürich
Abstract
This study has two main aims. The first is to contribute to the net interest margin theory of banks and secondly to review and extend the existing empirical net interest margin literature. The empirical analysis concerns a panel with 13,246 observations for 2,159 banks in
Germany and Switzerland for 1995-2005. The main empirical findings are fourfold: Controlling for interbank differences in specialization is important in measuring and comparing bank efficiency; Institutional features are important when studying financial markets; Evidence is found in favor of the cross-selling hypothesis for German banks. For their Swiss counterparts the evidence is mixed, and; the relevance of including opportunity costs of liquid reserves is confirmed empirically.
JEL classifications: G21; L11.
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1. Introduction
In macroeconomics one of the most important functions of a bank is channeling funds from lenders to borrowers. In this context the factors determining the net interest margin of banks are of great interest. Factors like for example market power, X-inefficiency and operating costs have a potential to increase the net interest margin, thereby increasing the costs of financial intermediation and the loss of social welfare1.
This study aims to investigate two main points. Firstly to contribute to the net interest margin theory by developing a formal role for opportunity costs of liquid reserves. Also the original static Ho and Saunders (1981) model of the interest margin is derived in a multi period setting. By doing this it enlarges the understanding of the determinants of the interest margin, highlights the intuition of the interest rate risk a bank faces and yields insight in the
underlying assumptions that are crucial to the model’s intuitive result. The second aim is to review and extend the existing empirical net interest margin literature. This results in improved measurement of the determinants market power, with a Lerner index for the
traditional financial intermediation market and managerial efficiency with a measure of cost x-efficiency. Also, insights from two strands of the existing literature are combined by
introducing non-interest income activities into the interest margin equation. The results presented here will provide policy makers with new information about which aspects of the banking business to regulate in order to minimize the interest spread and thereby the social costs of financial intermediation.
The strand of literature theoretically and empirically investigating the determinants of the interest spread starts with the previously indicated study by Ho and Saunders (1981). In this model a bank carries out a simple traditional intermediation function, financing loans with deposits and thereby facing an interest risk. In this framework the banks interest margin depends on the size of operations, managerial risk aversion, volatility of interest rates, and the market structure a bank faces. The theoretical model has grown to be the reference
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framework for most empirical studies on bank interest margins. During the last two decades it is further developed and extended by many other authors. McShane and Sharpe (1985) derive the model under uncertainty of money market interest rate instead of the deposit and credit rates. Allen (1988) extends the analysis to a multi-product setting. The formal role of credit risk is developed by Angbazo (1997). More recently Maudos and Guevara (2004) include operating costs with the previous extensions in the one-product model. Also, Carbó and Rodriguez (2007) use the multi-product framework of Allen (1988) to demonstrate the effect of non-interest income activities on the net interest margin. In this version of the model, also the size of the effects of market power on the interest margin depends on bank
specialization.
Another important focus in the recent literature is on the implications of banks diversifying into non-interest income activities, as in for example Allen and Santomero (2001). Relatively much attention is paid to the effects of this increased focus on non-interest income on bank risk. While few studies are able to show there is a positive effect of this diversification, several find an increase of income volatility in diversification [see for example De Young an Roland (2001), Stiroh (2004), Stiroh and Rumble (2006) and Lepetit, Nys, Rous and Tarazi (2008-1)]. De Young and Roland (2001) present detailed theoretical arguments for the apparent positive effect that the shift to fee income has on income volatility of a bank. Important observations are that increasing the focus on non-interest income activities might have a large influence on a banks income and cost structures. More precisely it increases operating as well as financial leverage.
Despite the recent attention for the apparent shift in bank specialization, its impact on the net interest margin and its determinants has not received much attention. This study is the first to introduce the insights of the ‘non interest income activities’-literature in a thorough
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margin, only including a few of its other determinants as control variables. This makes it impossible to give policy prescription or giving an impression of the relative importance of non interest income activities as determinant of the interest margin. The sample of bank types considered is restricted to commercial and cooperative banks.
The starting point is the paper of Maudos and Guevara (2003). This is appropriate as that paper comes close to a summary of the contemporary theoretical and empirical literature on the determinants of the net interest margin. The analysis presented here however differs in several aspects: i) the original Ho and Saunders (1981) model and its subsequent
developments is derived in a multi period setting; ii) a formal role is developed for the opportunity costs of liquid reserves iii) a direct measure of market power in the traditional banking activities is used instead of an overall market power measure; iv) cost x-efficiency is introduced to control for efficiency as opposed to a simple cost to income ratio; v) the bank’s focus on non-interest income activities is controlled for; vi) the sample considered contains Swiss and German banks instead of the large EU countries; vii) the analysis is extended up to the year 2005, starting in 1995.
Some of these items deserve additional attention. Firstly, in the original model all events take place in one period. In this period markups for loans and deposits are set, demand for loans and deposits is faced, loans and deposits are refinanced/reinvested in the short run money market and these money market positions mature. This paper derives the model in a four period setting, thereby highlighting the intuition of the interest rate risk a bank faces and the underlying assumptions that are crucial to the model’s intuitive result. By developing a formal role for opportunity costs of liquid reserves, which are an integral part of the traditional banking function, theory is brought closer to reality. The Lerner index as constructed by Maudos and Guevara (2003) has the downside that it is the complement of a cost to income ratio, a measure commonly known to reflect efficiency. In order to overcome this problem a financial Lerner index is constructed. This approach has important advantages. The
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Also, it is argued that this measure comes closest to a clean and usable measure for market power. As a fourth point about the differences between cost to income ratio’s and cost x-efficiency. Drawing on the arguments of De Young and Roland (2001) it is likely that banks with different specializations will have different cost and income structures. Cost to income ratio’s treat income and expenditures of interest and non-interest activities equally. In this light it is to be expected that cost to income ratios also partly reflect interbank differences in specialization. By using cost x-efficiency obtained by stochastic frontier estimation this problem is circumvented. In constructing this measure both interest income and non-interest income are treated as outputs, thereby controlling for these interbank differences in
specialization. Finally, the choice for two countries Germany and Switzerland allows for a detailed comparison between the different bank types and specializations and these banking sectors that are very different in size and structure.
The remainder of this paper is structured as follows. In section 2 the theoretical model is developed and an overview of the relevant theoretical literature is given. Section 3 discusses the determinants of the net interest margin, their proxies and the relevant empirical findings in the existing literature. Section 4 presents the data and methods used. Section 5 provides an overview of the Swiss and German banking systems. Results of the empirical analysis are presented in section 6 and the conclusions following from this analysis in section 7.
2. Model development
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formalizing their role brings the theory closer to reality without doing concessions to its intuitive solution. After giving an overview of the relevant theoretical literature, the
contribution of Maudos and Guevara (2003) is discussed in more detail. This is appropriate as this model will be the starting point for the further analysis of this paper.
One of the important classes of models that study bank behavior can be categorized as the industrial organization approach. A famous example is the Monti-Klein model as developed by Klein (1971) and Monti (1972). In this model banks maximize profits by setting a volume of loans and deposits. With a simple profit function the familiar equalities between the Lerner indices of market power and the inverse demand respectively supply elasticities of loans and deposits are shown. The Ho and Saunders (1981) model is the first to combine the main insight from this approach that banks maximize profits (or expected wealth) with the notion that banks try to match maturities of assets and liabilities in order to minimize their interest rate risk2. This insight follows from the strand of literature that analyzes bank portfolio behavior as described in Capital Markets and Institutions by H. Dougall and J.E. Gaumnitz. In these types of models unmatched maturities lead to reinvestment or refinancing risk for the bank.
The set up of the Ho and Saunders (1981) model is as follows. The bank is assumed to be a risk averse financial intermediary that provides immediacy of service3. In a static setting the bank sets deposits and lending rates to be unchanged during the whole period in order maximize expected utility of final wealth. Uncertainty comes from the asynchronous arrival of loan demand and deposit supply in combination with the bank providing immediacy of
service. This forces the bank to take a long or short position in the money market. In this setting a bank’s interest margin is shown to be a function of the market structure, the coefficient of risk aversion, the instantaneous variance of the interest rates on deposits and loans and the size of a banks operation.
2
More specifically the bank is assumed to maximize interest income. Obviously, banks also maximize other sources of income (for example fee-income and trading-income). As the focus in this paper will lie on the interest margin and its determinants and for the sake of simplicity, I choose not to investigate the banks decision making on these other sources of income.
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The first important critique on the model was given by Lerner (1981), who argues that the model fails to include the production costs of loans and deposits. McShane & Sharpe (1985) assume the interest rate risk sticks to the short run money market interest rate instead of the risk free rate and assume non-symmetrical probabilities for the arrival of loans and deposits. Allen (1988) allows for heterogeneous bank products and finds that cross elasticities
between banking products may decrease the pure spread. Angbazo (1997) introduces credit risk in the model. He finds credit risk to increase the interest margin charged by banks. Maudos and Guevara (2004) include Lerner’s (1981) critique along with the other
modifications into the single product model. This study can be seen as a summary of the literature up to date and will therefore be discussed in more detail below. A more recent theoretical modification is found in Carbó and Rodriguez (2007). They use the multi product framework of Allen (1988) to show that the non interest income activities potentially influence the net interest margin. This is of special interest as in the empirical section of this paper the important role non-interest income activities have in the interest margin will become clear. This theoretical model is discussed in more detail in Appendix B.
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there is uncertainty about the fraction of loans that is paid back. The interest spread is in this setting derived to be a function of market structure, operating costs, risk aversion, the
volatility of the market interest rates, the volatility of the expected returns on loans granted, the interaction between credit risk and interest rate risk and the average size of the portfolio. The model presented here differs from the Maudos and Guevara (2003) model in two
respects: a) in the original model all events take place in one and the same period. In this period it is assumed that markups are set, loan and deposit demand takes place, these funds are financed respectively invested in the money market and that these money market
positions mature. In this paper these events assumed to take place in four consecutive periods, thereby giving a dynamic interpretation to the model; b) Instead of assuming that a bank can invest all the funds in the short run money market in the case of a deposit, it is assumed that part of these funds have to be kept as liquid reserves at a lower interest rate. The opportunity costs of liquid reserves turn out to have a positive influence on the net interest margin.
First, the intuition of the model that is also graphically displayed in figure 1 will be discussed. The formal derivation of the equation for the net interest margin follows shortly below. For now the portfolio of loans and deposits the bank already owns is ignored.
At date 0 the bank offers a specific deposit and loan deal for date 1. In case of a deposit the creditor will receive a return somewhat lower than the money market rate at date 24. At date 3 the creditor again receives the money market rate of period one minus markup a. In the case of a loan the debtor pays the market interest rate at date 2, and the market interest rate plus markup b at date 3. At date 1 the bank receives requests for a loan ( )L1 or a
deposit(D1)
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. The probabilities of receiving a loan or deposit are mutually exclusive and a function of the markups a and b the bank sets at date 0. The bank finances respectively invests this loan or deposit with short run money market position one at interest rate 1
M
r . In
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More precisely, the customer receives period 1’s money market rate minus the foregone interest rate on the liquid reserves. In this period the bank lets the depositor pay for the interest rate differential between the short run market interest rate and the interest rate on liquid reserves. If compared to the markup the bank asks in period 3 this amount is small.
5 This can also be generalized to the case in which the bank receives loans and deposits, in this case L
1 and D1 can be seen as
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the case of a deposit only a fraction (1−δ)of the funds can be invested in the money market. The remainder of the funds is invested at the lower interest rate on liquid reserves 1
R
r . The
difference between the money market interest rate and the interest rate on liquid reserves
(
1 1)
M R
r =R −R is assumed to be fixed.
Figure 1. The time line of the dynamic Ho and Saunders (1981) model.
Money market position one matures at date 2. In the case of a deposit the bank receives interest from money market position one and its liquid reserves. This amount is exactly equal to the interest rate it pays the depositor. This leaves the bank with excess funds of(D1). An
amount of (1−δ)D1is again invested with short run money market position two at interest rate
2 M
r , the rest is kept as liquid reserves with return
2 R
r . In the case of a loan the bank receives
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position. The principal is funded by entering into money market position two at market interest rate 2
M
r . At date 3 the source of the interest rate risk becomes clear. In the case of a
deposit the bank pays a interest rate of (1 − )
M
r a to its depositors while it receives
2 M
r from its
money market position. The potential fluctuation of the date 2 money market rate relatively to the money market rate at date 1 is a factor of risk to the bank. In case of a loan this works the other way around. While the bank receives an interest rate of(1M + )
r b , it has to pay
2 M
r
for its money market position. Also, in this period the bank finds out which fraction of the lenders can pay back their loans and incurs operating costs.
The remainder of this section will describe the formal derivation of the model. Starting at date 0, the bank has an initial wealth W0 = I0 +E0. It consists of the credit inventory I0 =L0−D0
and assets (or liabilities) with short maturities E0 = M0 +R0 that finance respectively invests
the credit inventory and wealth carried over from earlier periods6. Assets with short maturities can be divided in the net money market position M0 =(1−δ)D0 −L0 +W−1 and liquid
reservesR0 =δD0, where δ is the fraction of deposits that has to be held as reserves.
Without a deposit or loan transaction date 3 wealth is given as7:
= + + + − 3 (1 ) 0 0 0 ( )0 N W M L W r W E Z Z L C I (1) Where = 0 − 0 0 L D I r L r D r I and δ + + = 0 0 0 0 I M R W r I r M r D r
W are the average return on the credit
inventory respectively initial wealth. ZM And ZL are random stochastic variables [jointly
normally distributed as N(0,σi), with i=M L, ] representing the interest rate risk respectively
the credit risk the bank faces. Expected date 3 wealth without deposit or loan transactions is equal to:
= [ 3 ]=(1+ ) 0 − ( )0
N W
W E W r W C I (2)
Expected utility of this wealth is approximated by the following second-order Taylor expansion:
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In order to be able to study the effects of one credit cycle, it is assumed here that returns from the credit inventory are not invested in the short run money market. As the bank is assumed to be risk averse, uncertainty with respect to the interest returns on these possible returns would again positively influence the markups of the loans and deposits contracted in period 1.
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11 2
[ ( )] ( ) '( ) [ ] 1 2 ''( ) [( ) ]
E U W =U W +U W E W −W + U W E W −W (3)
Using (1) and (2) in (3) yields the following expression for expected utility of date 3 wealth without a deposit or loan transaction:
2 2 2 2
0 0 0 0
[ ( N)] ( ) 1 2 ''( ) 2
T L M LM
E U W = U W + U W Lσ +E σ + L E σ (4)
Where σLM is the cross-variance of the stochastic variables ZM and ZL.
If we now consider the situation in which the bank receives a deposit transaction. The extra income and expenses in this case are the markup a, interest rate risk over the amount of the deposit, opportunity costs of the liquid reserves and operating costs. Date 3 wealth is
therefore in the case of a deposit given by:
3 (1 ) 0 ( )0 1 1 ( 1) 0 ( 0 1)
D W
L M
W = +r W −C I +aD +δD r −C D + L Z + E +D Z (5)
Now using (2) and (5) in (3), expected utility of date three wealth with a deposit transaction can be written as:
(
)
3 1 1 1 2 2 2 2 2 1 1 1 0 0 1 0 0 1 [ ( )] ( ) '( ) ( ) 1 2 ''( ) ( ) ( ) 2 ( ) D L M LM E U W U W U W aD D r C D U W aD D r C D L E D L E D δ δ σ σ σ = + − − + − − + + + + + (6)Now using (4) the increase in expected utility of date three wealth resulting from a deposit transaction is found to be:
(
)
3 1 1 1 2 2 1 1 1 1 0 1 0 1 ( ) '( ) ( ) 1 2 ''( ) ( ) ( 2 ) 2 D R M LM EU W U W aD r D C D U W aD r D C D D E D L D δ δ σ σ ∆ = − − + − − + + + (7)In the same way the increase in expected utility of date three wealth resulting from a loan transaction is found to be:
(
) (
)
(
)
2 2 2 3 1 1 1 1 1 0 1 1 0 1 0 0 1 1 ( )= '( ) ( ) 1 2 ''( ) ( ) 2 ( 2 ) 2 L L M LM EU W U W bL C L U W bL C L L L L L E L E L L L σ σ σ ∆ − + − + + + − + − − (8)Assuming as in the original Ho and Saunders (1981) model that bank knows the mutual exclusive probabilities of obtaining a loan or deposit as a function of the markups a and b it sets, its optimization problem is given by:
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Using (7) and (8) in (9) and solving for a and b yields the following first order conditions8:
2 3 1 1 0 0 1 ''( ) '( ) ( ) 1 ( ) 0 1 2 1 2 1 4 ( 2 ) 2 2 D D M LM D U W D U W EU W C D a r D E L a α δ σ σ β ∂ ∆ = ⇒ = + + − + + ∂ (10)
(
)
(
)
3 2 2 1 1 0 1 0 0 0 1 1 ''( ) '( ) ( ) 0 ( ) 1 2 1 2 1 4 2 ( 2 ) 2 L L L M LM L U W U W EU W b C L b L L L E E L L L α σ σ σ β ∂ ∆ = ∂ ⇒ = + − + + − + − − (11)The equation for the net interest spread s is given by:
( )
( )
(
)
α α δ σ β β σ σ = + = + + + + − + + + + − 2 1 1 1 0 1 1 2 1 1 0 1 '' ( ) ( ) 1 2 1 2 1 2 1 4 2 ' ( ) 2( ) D L R L D L M LM U W C D C L s a b r L L D L U W L D E L (12)Comparing equation (12) and equation (11) in Maudos and Guevara (2004) (pp 2264) the inclusion of a reserve requirement for banks, as is done in this paper, has one major effect on the equation for the interest spread9: it adds an extra term in the form of 1 2rRδ.
The theoretical model predicts the net interest margin to be determined by the following factors:
i) Market power
(
α βD D +α βL L)
. The α and β parameters display the market characteristicsin the loan and deposit markets. As the
β
' smeasure the price elasticity of demand, the ratio’s here are interpreted as the bank’s market power having a positive effect on the interest spread.ii) Opportunity costs of liquid reserves
(
1 2rRδ)
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. This new term is the fruit of the inclusion of a reserve requirement in the model as is done in this paper. Opportunity costs depend on two factors. First is the fraction δ of deposits that has to be kept as reserves. Second the difference between the market interest rate and the interest rate on liquid reserves. Both these factors have a positive influence on the interest spread.
iii) Average operating costs
(
C D( 1) D1+C L( )1 L1)
. The operating costs per unit of depositsand loans have a positive influence on the interest margin.
8
See Appendix A for the derivation of these first order conditions.
9
The difference between E0 and M0 is a pure result of definition.
10 The analysis presented here ignores the fact that the amount of liquid reserves might also decrease the institutional funding
costs of a bank by signalling financial health. As this factor would decrease rM in case of the refinancing of loans, it is expected
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iv) The absolute coefficient of absolute risk aversion
(
U''( ) ( )
W U' W)
. As banks are riskaverse, the termU''
( )
W U'( )
W is by definition negative. The higher the absolute coefficientof absolute risk aversion of the bank’s management, the higher the net interest margin will be.
v) Volatility of the expected return on loans
( )
σ2L . The greater the risk of default on the
granted loans is, the higher the interest margin a bank will use. vi) Volatility of the market interest rate
( )
σ2M . The more volatile the market interest rate is, the
greater the interest risk the bank assumes in taking a deposit or granting a loan. Such an increase in risk is translated into higher interest margins.
vii) The total volume of credits
(
L1+2L0)
and value at risk (L1+D1). As the bank is assumedto be risk averse, also the size of the potential loss the bank faces due to interest rate and credit risk increases its interest margin. In other words, the interest margin is increasing in the total volume of credits granted and the higher the excess of loans respectively deposits. viii) The interaction between interest rate risk and credit risk
(
σLM)
. The greater thisinteraction, the greater the interest margin the bank will use.
Next to the determinants highlighted in the theoretical model, some other institutional factors are commonly known to influence the interest margin. The following factors will also be controlled for in this study’s empirical part11.
viii) Non-interest income activities. Using the multi-product framework initiated by Allen (1988) it is shown by Carbó and Rodríguez (2007) that fee income activity is expected to have an influence on the interest margin. Possible explanations are the cross-selling hypothesis12 [see Lepetit et al. (2008)-2] or increased competition from non-bank financial institutions in the loans and deposits market [see Allen and Santomero (2001)]. In the
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Another variable included in a large part of the literature is implicit interest payments; the ‘free’ services consumers pay for through higher interest rates. As this variable is expected to partly reflect the effects of specialization it is not included in the analytical part of this paper. This concern is also confirmed by a high correlation between this variable and non-interest income activities.
12 This hypothesis states that banks decrease their interest margins in order to increase non interest income. One of the side
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theoretical framework of Carbó and Rodríguez (2007) the expected effect of non-interest income activities is ambiguous.
ix) Managerial efficiency. As is shown in Angbazo (1997) a good management team will be able to select assets with a high return to cost ratio. Therefore, banks with good
management will be able to earn higher margins.
3. Empirical set-up
The theoretical underpinning of the determinants presented in Section 2 determines the net interest margins as a function of the variables in equation (11). This section will first give a short overview of the relevant empirical literature. Subsequently, the measures used to proxy the variables discussed in Section 2 are presented. A summary of these measures and their precise definitions is presented in Figure 2.
There have been several studies that have investigated the determinants of the net interest margin. Noteworthy are Ho and Saunders (1981), McShane and Sharpe (1985), Angbazo (1997), Saunders and Schumacher (2000), Maudos and Guevara (2004) and Williams (2007). These studies all mostly confirm the significance and expected sign of the variables discussed in section 2 for different (groups of) countries. There are however some
exceptions. Williams (2007) finds that market power as measured by market share has a negative effect on the interest margin in Australia. This as opposed to the other findings up to this point. Also, opportunity costs of liquid reserves are found not significant in some studies. And where Maudos and Guevara (2004) find a positive effect of credit risk on the interest margin, Williams (2007) finds a negative effect.
Net Interest Margin (nim)
In line with the recent literature the net interest margin is proxied by net interest income divided by total earning assets.
Market power in the loan and deposit market (LI)
In the existing literature several different measures of market power are employed.
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characterized by a strong time trend in combination with only a few countries. Main explanation for this fact is that the large amount of bank specific data is not available on a large scale in most countries. The combination of a low number of countries and strong time trend makes it impossible to use this kind of measure that is only year and country specific. Another frequently used measure is market share, proxied by the share of assets in the total market. This however has the obvious downside that it is only a linear transformation of total assets, which reflects size. This makes it impossible to separate effects of market power and size. In order to overcome these problems Maudos and Guevara (2004) construct a Lerner index13 as a direct measure of market power. This is done by estimating a sector wide cost function and derive the bank specific marginal costs from the parameters of this function. Unfortunately this measure is by definition the complement of an overall cost to income ratio. This point is best made by looking at the function for marginal costs given in Maudos and Guevara (2007-2) (pp 281). In practice these ‘marginal costs’ of the banks are mainly driven by the average costs(TC TAi/ i). As the price is measured by the ratio of total revenues and total assets, the function for the Lerner index reduces to:
1 i i i i i i i i i i i i TR TA TC TA P MC TC LI P TR TA TR − − = = = − (13)
Where Pi is the price, MCi are the marginal costs, TRi are the total revenues, TAi is total assets and TCi are total costs of bank i.
In the sample used in this paper, constructing the Lerner index in the way described above yields a measure for ‘market power’ that is -.995 correlated with the cost to income ratio. Which is commonly used to measure efficiency.
In order to circumvent this problem this paper measures market power by constructing a Lerner index for the traditional financial intermediation market. Assuming the whole
infrastructure of physical capital and personnel already is in place, the bank’s marginal costs of writing an extra loan reduce to its refinancing costs. Therefore marginal costs (MCi) are
13
The Lerner index is calculated by i i i
i
P MC L
P −
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measured by interest expenses as a fraction of total assets. Price is approximated by the ratio of interest income and total assets. On of the downsides is that this measure can also be rewritten as the complement of a financial cost to income ratio. On the other hand the low correlation coefficient with X-efficiency makes it arguable that this measure is reflecting market power instead of efficiency. Although results have to be interpreted carefully, the approached here therefore has two advantages: (i) it is transparent, and (ii) it comes closest to a clear and usable measure of market power.
Opportunity costs of liquid reserves (oppcostliqres)
As argued in Section 2 the opportunity costs of liquid reserves contain two effects. Firstly the greater the fraction of deposits that has to be kept as liquid reserves, the larger the
opportunity costs will be. This fraction is measured by all funds cash and due from banks divided by total liabilities. Secondly, the interest rate difference between the market rate of return and the (lower) rate of return on liquid reserves. It is only possible to obtain economy wide data for this factor. Unfortunately the two country framework employed here, together with the significant time specific effects makes it impossible to include this variable in the analysis. Testing for the theoretical relevance of this factor is left to a multi-country study with a larger number of countries.
Average operating costs (aoc)
Operating costs are measured by total operating expenses divided by total assets. Risk aversion (capratio)
In order to proxy for the risk aversion of bank management the capital ratio (total equity/ total assets) is employed.14
Total volume of credit and value at risk
In the contemporary literature the total volume of credit is often proxied by the natural logarithm of loans granted or total assets. Here, these variables are not included in the analysis as it is correlated with market power and operating costs, introducing colinearity in
14 A better proxy for risk aversion would be the reserves in excess of regulatory reserves as a fraction of total liabilities.
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the regression analysis. Value at risk is not included as it is not available for a large part of the banks in the sample.
Credit risk (llprov)
Credit risk is measured by the ratio of profit and loss account’s loan loss provisions to total loans.
Interest rate risk
Earlier studies have highlighted the importance of interest rate risk as a determinant of a banks margins and it plays a central role in the theoretical framework developed in section 2. Unfortunately, data on bank specific interest rates are not available. Including country
specific data in a framework with a small number of countries with strong time effects will not lead to meaningful outcomes. Therefore, interest rate risk will be one of the factors reflected in the time and bank specific effects, leaving an investigation of the specific influences of interest risk to a study with a large number of countries.
Interaction of credit and interest rate risk
These variables are constructed as the product of the credit risk variable and the standard deviation of interest rates with two maturities. More precisely, the yearly standard deviation of the three month interbank and 10 year government bond yields, based on daily data. Interest rate data is obtained from the Bundes Bank and the Schweizerische National Bank.
The following institutional and regulatory factors that are not included in the theoretical model will be controlled for.
Non-interest income activities (nonintinc, nonintinc1)
As is theoretically shown in Carbó and Rodriguez (2007) and empirically tested for in Lepetit et al (2008-2) an increase in non-interest income activities might have a negative effect on the net interest margin. This is a determinant that has not been controlled for in the
contemporary literature, creating the possibility of an omitted variable bias. Here this
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Both ratios are expected to proxy for a banks relative focus on non-interest income activities. The expected sign of the effect of these variables on the interest margin is ambiguous as it depends on the different parameters in the model.15
Managerial Efficiency (XEF, costtoinc and opcosttoinc)
In the contemporary interest margin literature efficiency is proxied for with an (operating) cost to income ratio. Here it is argued that such a measure will also in part reflect bank
specialization. Important is the increasing importance of non-interest income as source of income for banks as is observed in Allen and Santomero (2001). As analyzed by De Young and Roland (2001) a bank’s specialization has an impact upon bank’s cost and income structure. More specifically one would expect a bank with high non-interest income activities to have a significant larger part of fixed costs and more volatile income. Measures like cost to income ratio’s treat income earned and costs made for both types of bank activities as equal. Combining these insights with the observation that there are significant differences in
specialization between banks16 leads to the expectation that a cost to income ratio is not a very precise measure for efficiency. In order to overcome this problem a cost x-efficiency measure is used here.
Following the methodology of Maudos and Guevara (2007), but adding non-interest income as an output, cost X-efficiency is measured with the stochastic frontier approach as
suggested by Aigner et al (1977) and Meeusen and van den Broeck (1977). Cost X-efficiency measures the distance of a specific bank to the sectors cost frontier. The error term is
assumed to be composed of two parts. The symmetrical normally distributed error term (v) and a one-sided variable (u) that measures (in)efficiency relative to the frontier.
Under assumption that the components of the composed error terms are distributed
independently, a frontier cost function can be estimated with maximum likelihood. Efficiency scores are extracted from the residuals of the regression. Efficiency scores for specific banks can be calculated by using the distribution of the inefficiency term conditional on the estimate
15 More precisely, it depends on the sign of the term:
2
1
2i L
U
b
Q
U
δ
σ
δ
′′
+
+
′
1619
of the composed error term. In the case of the half normal distribution Jundrow et al. (1982) show that the mean of this conditional distribution is given by:
(
)
(
)
* 1 i i i i i f E u Fε λ σ
ε λ
ε
σ
ε λ σ
σ
= − − (14)Where
ε
i =ui+vi,σ
*2=σ σ σ
u2 v2 2,σ
2 =σ
u2+σ
v2 andλ σ σ
= u v. Furthermore f and F are the standard normal density function respectively cumulative distribution function.In order to be able to separate effects of efficiency and market power efficiency will be defined as the ability to minimize operating costs in producing a certain combination of interest and non-interest income. By not including financial costs (price of deposits) into the cost function it is avoided that the efficiency measure partly reflects market power in the deposit market. Using a translog functional form the cost function employed is given by:
2 2 2 2 2 2 0 1 1 1 1 1 2 2 2 2 1 2 3 1 1 1 4 ln ln( ) ln( ) ln( ) ln( ) ln( ) ln( ) ln( ) ln( ) ln( ) ln( ) l l m j j k it l it lm it it j it jk it it l lm lm j j k l j l lj it it l it j l l j j it c y y y w w w
y w trend trend y trend w α β β α α β µ µ µ µ = = = = = = = = + + + + + + + + +
∑
∑ ∑
∑
∑ ∑
∑ ∑
∑
2 1 it j trend ε = +∑
(15)In equation (14) total operating expenses(cit)are a function of both outputs( l)
y and inputs
( j) it
w . Output in the traditional intermediation business is measured by total assets.
Non-interest income output is measured by net non-Non-interest income. The inputs included are average personnel costs [personnel expenses/total assets] and the cost of physical capital [(total operating expenses - personnel expenses)/total fixed assets]. Note that in order to control for technological progress a time trend is included. In order to allow for possible differences in effects of the inputs and outputs, the cost functions are separately estimated for the different sub-samples defined in this paper17. This however also implies that
comparing efficiency estimates between samples only yields information on the relative position of the banks to the best practice bank in the sub-sample it is in.
17 It is assumed that all banks in the same sample are exposed to the equal economic circumstances. Therefore there is no
20
4. Data
The bank specific financial statements for all German and Swiss banks are obtained from Bureau van Dijk’s Bankscope 2006. The database contains more observations than used here. The final dataset is obtained by applying two selection criteria. First, all observations for which one of the variables included in the interest margin equation is not available are not taken into account. Second, all observations that are more than 2.5 standard deviations away from the mean are not taken into account18. Balance dates other than 31/12 are rounded to the nearest year end. This leaves us with an unbalanced panel dataset with 13,246 observations for 2159 banks in Germany and Switzerland for the time period 1995-2005. One feature of the Swiss banking sector is that it has a large share of banks that mainly focus on non-interest income. This is highlighted by the ratio of net non-interest income to total net income (nonintinc). In order to make sure that results for Switzerland and Germany are comparable, also a smaller Swiss sub-sample is selected. And as in a later stadium bank types are compared, the sub-sample is selected by comparing bank type means for the ratio of net non-interest income to total net income. Descriptive data are
18 Because of their large size relative to the other Swiss banks, one exception is made for the Swiss major banks in the
21
shown in Table 1. Excluding banks by category makes sure that the bank types are still representative. The smaller Swiss sample is obtained by not taking into account Commercial, Foreign, Major and Merchant Banks. The German sample is unchanged.
In Table 2 descriptive statistics are presented. There are significant differences in almost all variables between the complete Swiss sample and the sub-sample. Remarkable are the differences for average operating costs (aoc), risk aversion (capratio), implicit interest payments (impintpay) and the non-interest income activities measures (nonintinc 1 & 2).
22
comparable Swiss sample, banks are on average closer to the efficient frontier than German banks. The composition of the sample used is given in Table 3.
5. A description of the Swiss and German Banking sectors
This section will provide some necessary background information on both the Swiss and German banking sector19. This will improve the understanding of the results and their implications presented below. First an overview of the Swiss banking sector will be given, followed by the German case.
In Switzerland banking is an important sector. In the year 2004 the banking sector produced 8.9 percent of the total Swiss GDP and provided 3.2 percent of the Swiss workforce. Around 50 percent if this output produced by the banks is the fruit of their wealth management activities. Looking at the composition of the sector, the two major banks, UBS AG and the Credit Suisse Group, are a good starting point. Although their main activities are abroad, Swiss retail banking is still an important part of their activities. Therefore both banks have a dense network of branches. Worldwide their core activities are asset management advisory and investment banking. In comparison to the other banks in the sector, these banks are relatively large. Together they accounted for around 66 percent of the total sectors combined balance sheets in 2004. The 24 cantonal banks are by law partly owned by the local
(cantonal) governments. These banks operate only in the canton they are situated in. The smaller banks mainly focus on mortgage lending and savings deposits, while the larger banks offer a wide range of services. The 83 regional banks are similar to the smaller cantonal banks in size and activities. The Raiffeisen Group is a cooperative bank with 451 small and independent member banks. Not only strategic management and marketing, but also it infrastructure and financial services are organized centrally. This leaves only the
19 These overviews are mainly based on The Swiss Banking Sector: Compendium edition 2006 and Banking in Germany.
23
activities of selling banking products and giving advice to the local banks. The 14 private banks are originally wealth managers, but in some cases also perform investment banking activities. Also, there are a large number of foreign banks that have subsidiaries or branches in Switzerland. These 124 banks mainly engage in private banking and fund management activities.
With a fraction of 3.2 percent of GDP the German banking sector is relatively smaller than the Swiss. In total 1.8 percent of the total workforce is employed in the banking sector. Also, the German banking system is very different. It is characterized by an extremely dense network of 2,400 relatively small banks that together had around 45,000 branches in the year 2005. Another important feature is that a relatively large part of the market is served by public sector banks. If we categorize the banks the main categories are the saving banks, commercial banks and cooperative banks. The Savings Banks are small, state owned banks that were originally funded to assure that savings products for all layers of the population. Nowadays they mostly focus on retail banking for individuals and small sized company’s. They operate only within their own small region or even city, but benefit the mainly
24
6. Results
The banking sectors of Germany and Switzerland have very different characteristics. In this light it is appropriate not to pool the samples and present the regression results for these two countries separately20. The unbalanced panel does not yield the opportunity to perform any robust unit root tests. However, taking into account the relatively small number of years that is available for most banks in the sample it is reasonable to assume that all series are stationary. The choice between bank fixed effects or random effects is made on the basis of the Hausman (1978) test. If the bank random effects model is found consistent the choice between bank random effects and pooled OLS is made on the basis of the Breusch and Pagan (1980) Lagrange Multiplier-test. Time fixed effects are included when jointly
significant. In order to investigate whether there exist bank type effects we also present panel random effects regression for the German sample21. All further inference will be performed using the fixed effects models. Standard deviations t-statistics are calculated using Huber-White sandwich estimators [Huber (1967), Huber-White (1980)]. The results for the German sample are presented first and are compared with the Swiss sub-sample at the end of this section. The estimation results for Germany are presented in Table 4. Columns (1) - (3) represent the fixed effects results with different measures for efficiency. The implied effects of efficiency from both cost to income ratios (costtoinc and opcosttoinc) are very different from those implied by the cost x-efficiency measure (XEF). Recalling the discussion in section 3, it is likely that differences in specialization between banks cause them to have different cost and income structures. If for example costs increase relatively to income because of a shift to non-interest income, a cost to income ratio would register this as a decrease in efficiency. The negative effect on the interest margin however in reality reflects the negative effect that non interest income activity has on a bank’s interest margin.
20
When included, interaction dummies between a Switzerland dummy and all explanatory variables are jointly significant in a pooled model. This indicates that the data of the banks in the two countries should not be pooled.
21
25
This shows how simple measures for efficiency like costtoinc and opcosttoinc can also reflect differences in specialization22. It is likely that differences in effects of efficiency between different types of measures is caused by this shortcoming of cost to income ratios. As XEF is corrected for differences in specialization and resulting differences in the input output mix and cost structure, it is a more precise measure of efficiency. This shows the importance of controlling for interbank differences in specialization when measuring and comparing bank efficiency. Further interpretation will be done on specification (3). Despite the fact that the
22
26
coefficient of determination of this specification is lower, this is appropriate as this specification for the reasons described above leads to the most robust results.
The effect of market power (LIa) is highly significant. The ability to set the prices of loans and deposits above their narrowly defined marginal costs has a positive effect on the interest margin. This confirms the importance of measuring market power in the markets for loans and deposits.
The result of average operating costs (aoc) is as expected and in line with the recent empirical findings of Maudos and Guevara (2004) and Williams (2007). Also, risk aversion (capital ratio) has the expected sign and is significant. The result for opportunity of liquid reserves (oppcostliqres) deserves special attention. The coefficient has the expected positive sign and is highly significant23. This result highlights the theoretical importance of the
formalization of the role of opportunity costs as a determinant of the interest spread as done in this paper. Also the control variable for non-interest income activities (nonintinc) is
significant at the .01 level and has a negative effect on the net interest margin. This confirms the findings of Lepetit et al (2008-2) that banks with a larger fraction of fee income set lower interest spreads. As argued in that paper, the causal direction between these two variables is unclear. Therefore, also a Hausman endogeneity test is performed. The null hypothesis of a possible endogeneity problem is rejected at the .05 level. In other words, the increasing focus on non-interest income activities seems to be causing decreasing interest margins and not the other way around.
The observed effects for efficiency (XEF) and credit risk (llprov) are significantly negative24. These results are contrary to expectations. Also taking into account the importance of market power as a determinant of the interest margin, a logical explanation of this result is that banks tend to price their loans competitively. Thereby increasing the number of loans and deposits, but also decreasing the quality of the loan book. These findings, together with the
23
Note that this positive effect could also be (partly) caused by the fact that higher liquid reserves signal financial wealth and thereby reduce institutional funding costs.
24 As both variables measuring interaction of interest and credit risk (interact1 and interact2) are highly correlated with credit risk
27
result for non interest income activities, provide evidence in favor of the cross-selling hypothesis.
In studies carried out by Maudos and Guevara (2004) and Williams (2007) time effects are highly significant and negative. Indicating that the interest spread has decreased over time. One of their explanations for this result is that it represents the negative influence of the increase in non interest income activities. Having controlled for this influence the time trend however still is highly significant. Possible explanations are a decrease in interest rate risk or a decrease in the scope for intertemporal risk-smoothing as argued in Allen and Santomero (2001). Data availability however does not allow a thorough exploration of this observation. The type dummy for Cooperative Banks is significant in specification (4). This indicates that in comparison to savings banks, cooperative banks have slightly lower interest margins. Table 5 presents the predicted percentage change in the interest spread from an increase of one standard deviation in its determinants. Comparing the specifications (1) and (2) with (3), the large differences between the effects of efficiency for the different measures is
highlighted. Both cost to income ratios leading to flawed estimates of the relative importance and sign of the relationship between efficiency and the interest margin. This again shows the relevance of correcting efficiency estimates for non interest income activities. Using
28
The developments of the determinants of the interest margin over the period 1995-2005 are presented in Table A.1 in Appendix C. Looking at its most important determinants, the interest margin of German banks has in the period analyzed mostly decreased due to the shift to non-interest income, a small decrease in average operating costs and sector specific effects like for example interest rate risk and overall economic circumstances. This decrease is however partly offset by an increase in market power.
In order to cross check our results the regressions for Switzerland are presented in Table 6. Results for the complete sample are presented in column (1)-(3), those of the smaller sample are in columns (4)-(6). Comparing the subsample with the complete sample shows that effects of many variables differ significantly. In this paper the smaller Swiss sample with banks that have a main focus on interest income will be of interest. Focusing attention on these bank types assures that the results can be compared with the results for Germany. This shows the importance of paying close attention to institutional features of the markets involved. Considering the significant differences in their banking sectors, it can well be the case that the limited poolability of the German and Swiss banking sectors extends to the other of the European countries.
In comparing the smaller Swiss sample with Germany, the analysis above mainly extends to the Swiss case. One main difference is that efficiency as measured by XEF is not significant. A probable explanation for this result is the relatively low variation in these variables in combination with the much lower amount of observations. Also, if at all, efficiency seems to have the expected positive effect in the Swiss case. As a last point the endogeneity test in the case of Switzerland indicates the possibility of an endogeneity problem25. All in all the results confirm the main findings of this paper. However, the results for Switzerland are somewhat less robust, mainly due to the substantial lower amount of observations.
25 This result does not necessarily imply an endogeneity problem. It could also indicate a specification problem. For example the
29
30
well have negative effects on competition and operating costs. This indicates that in order to decrease German bank nim’s, regulators should promote consolidation and improve
competitive circumstances. This finding supports the widely held view of the German banking sector being not very competitive, as evaluated by for example Saunders and Walter (1994) or Allen and Gale (2000).
In order to test the sensitivity of the presented results to changes in specification some robustness checks are performed. First the results are also estimated for the time span 1997-2004. This is appropriate as the number of observations is relatively low for the years 1995, 1996, and 2005. Although some minor differences arise, the model still supports the main findings of this paper26. Also the explanatory variables are scanned for possible leftover outliers that could drive the results. Excluding these does not in any way change the results. In order to prevent a selection bias it is appropriate to only display the results of the complete sample here. As a last check for the result for non-interest income activities results are cross checked with the ratio of fee income to total income (nonintinc1). These results are
presented in specification (5) and (7) of Table 4 respectively Table 6. Again non-interest income activity has a highly significant negative effect and also the effects of the other variables confirm the results as discussed above.
7. Conclusions
This section summarizes the most important results and advances of this paper and evaluate the two aims of the paper. The first aim is “to contribute to the net interest margin theory by developing a formal role for opportunity costs of liquid reserves and deriving the original static Ho and Saunders (1981) model in a multi period setting”. The dynamic interpretation of the Ho and Saunders (1981) model and its subsequent developments and the inclusion of opportunity costs of liquid reserves improve the model. The former adds an increased intuition of the interest risk a bank faces to the existing literature. The latter increases our
31
understanding of the determinants of the net interest margin. It brings the model closer to reality without doing concessions to its intuitive solution.
The second aim is “to review and extend the existing empirical net interest margin literature”. This has resulted in several improvements. In the first place this paper combines the insights of two strands of literature by introducing the intuition of an increasing focus on non-interest income into an analysis of the determinants of the net interest margin. Furthermore a better measure of market power is used and managerial efficiency is measured by cost x-efficiency, a more sophisticated measure that also controls for differences in bank specialization. As a last point a two country framework is chosen in order to be able to pay sufficient attention to the institutional features of the markets.
The main empirical findings can be summarized as follows: a) controlling for interbank differences in specialization is important in measuring and comparing bank efficiency; b) evidence is found in favor of the cross selling hypothesis for German banks, for their Swiss counterparts the evidence is mixed; c) the institutional features of the markets studied are important when studying financial institutions; d) results justify the inclusion of opportunity costs of liquid reserves in the theoretical model.
This first point follows from the different measures of efficiency employed in this paper. As elaborated in section 3 using a simple cost to income ratio to measure efficiency has some caveats. In order to circumvent these potential problems a cost x-efficiency measure is used. The empirical results confirm the hypothesis that cost to income ratios are not clear
measures of efficiency. Whereas cost x-efficiency has a negative effect on the interest margin, both cost to income ratios in the German sample imply a positive effect of efficiency on the interest margin. This effect probably reflects the relationship between non-interest income and a bank’s interest spread. Also, the relative importance of efficiency in
determining the interest margin is highly overstated when measured by different types of cost to income ratios.
32
runs from the former to the latter. This result indicates that the fall in interest margins in the German banking sector has different causes than increased competition in the loan and deposit markets, as argued in Allen and Santomero (2001). The observed shift to non-interest income activities, that partly causes the falling non-interest margins, takes place in a period with increasing market power. In this light this finding supports the hypothesis that the decrease in the interest margin is caused by a voluntary switch to a cross-selling strategy by banks. Some more indirect evidence comes from the negative effects from efficiency and credit risk on the interest margins. Banks pricing their loans and deposits competitively and make profits on cross-selling of other products and fees. More efficient banks are able to set lower margins and capture a larger piece of the pie. By doing this they also attract bad loans, decreasing the quality of their loan book. This explains the negative relationship between credit risk and the interest margin. The evidence for the Swiss sample is mixed. The Hausman endogeneity test indicates the possibility of an endogeneity problem. Also the effects of efficiency if at all have a positive effect on the interest margin. On the other hand there is again a negative relationship between the interest spread and credit risk.
Independent of the question of endogeneity, the observed increase in importance of non interest income activity is very likely to increase the bank risk. This is for example argued in De Young and Roland (2001) and Lepetit et al. (2008-1).
Drawing on the results for the Swiss sample the importance of institutional features of the markets becomes clear. The different types of institutions in this market tend to cluster in activities. The strategic focus of these bank types in turn seems to have its influence on the relative importance in, and in some cases even sign of, the relationship between the nim and its determinants. This result shows that in these kinds of studies, one should be careful in assuming poolability of different sub-samples.
33
importance of the determinants of the interest margin as found in this paper. By far market power seems to be the determinant with the largest influence, but also operating costs and efficiency play a significant role.
The two country framework also gives the possibility to compare the height of the interest margins in Germany and Switzerland. This leads to the conclusion that the observed higher margins in Germany are mainly caused by the ability to exercise market power and higher operating costs. These findings could well be explained by the features of the German banking system. The regionally segmented market with a large amount of very small banks decreases the level of competition and boosts operating costs. In this light promoting
consolidation and improving the competitive circumstances might be a first necessary step in decreasing German interest margins.
One question not addressed in this paper is what exactly the costs of financial intermediation are composed of. More specifically; Do the cost of financial intermediation decrease if banks decrease interest margins in order to increase profits on the cross selling of other bank products?; And what if banks thereby underprice its credit risk?; And if this causes them to go bust and forces the government to buy their bad loans? These are all questions that are left to future research.
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Lerner, E.M. (1981), Discussion. The determinants of banks interest margins: Theory and empirical evidence, Journal of Financial and Quantitative Analysis 41 601-602
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Data and A New Simple Test, Oxford Bulletin of Economics and Statistics 61, 631-652 Maudos, J., J. Fernandez de Guevara (2004), Factors explaining the interest margin in the banking sectors of the European Union, Journal of Banking and Finance 28, 2259-2281 Maudos, J., J. Fernandez de Guevara (2007)-1, The cost of market power in banking: Social welfare loss vs. cost inefficiency, Journal of Banking and Finance 31, 2103-2125
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36
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37
Appendix A: Some of the tedious calculations from the theoretical model
The intuition behind equation (1) is the following. In the case that the bank would receive no new loan or deposit it would receive the average interest rate on loans and pay out the average interest rate on deposits. It will also pay/ receive interest on its net money market position and liquid reserves, face credit risk over outstanding loans, face interest risk over its net money market position and liquid reserves and incur operating costs over the credit inventory. This will yield the following equation for date 3 wealth, which is equal to equation (1):
3 0 0 0 0 0 0 0 0 0 0 0 (1 ) (1 ) (1 ) ( ) ( ) (1 ) ( ) N I M R M L W M L W r I r M r D M R Z L Z C I r W E Z Z L C I δ = + + + + + + + + − = + + + − Where = 0 − 0 0 L D I r L r D r I , δ + + = 0 0 0 0 I M R W r I r M r D r W , R
r is the interest rate on liquid reserves and δ is the fraction of deposits that has to be kept
as liquid reserves.
In order to show how equations (10) and (11) are derived, some steps in between are showed here:
38
Appendix B: Using the multi-product framework of Allen (1988) to analyze the effects of non interest income activities on the net interest margin
This appendix discusses the theoretical contribution of Cárbo and Rodríguez (2007). That paper uses the multi-product framework of Allen (1988) to analyze the impact of non
traditional activities on the interest margin. The model assumes the same basic setting as the Ho and Saunders (1981) model. The bank is a risk averse financial intermediary that
39
expansion. Now maximizing the bank’s goal function and solving the first order conditions for the different fees yields the following function for the net interest margin:
2 2 1 1 2 1 2 4 L i i L U U a b Q b Q U U
δ
α
σ
σ
β
β
δ
′′ ′′ + = − + + + ′ ′ (A.1) Where U U ′′ −′is the coefficient of absolute risk aversion,
α
β
are the slope and intercept symmetrical arrival functions of the different bank products. It is shown by Allen (1988) that the only difference with the original Ho and Saunders (1981) model in this solution is the lastterm. It is clear that if
2
1
20
i L
U
b
Q
U
δ
σ
δ
′′
+
+
<
′
the possibility of a no-risk alternative to40
