c. Cost Complementarities

The linkage of various non-interest income activities with loan quality, composition and spreads may be due to informational and/or cost synergies. In this section, we investigate whether a pair-wise cost complementarity exists between lending and non-interest income activities that explains their joint production⁵⁵. As such, we examine whether the marginal cost of producing loans decreases when they are generated jointly with various non-interest income activities. For this purpose, using the intermediary approach (Berger and Mester, 1997 among others), we set-up the following multi-product cost function with a trans-logarithmic functional form (Berndt and Christensen, 1973):

55 Informational synergy analysis requires detailed data on clients’ relationship which is not available.

Wherein TCis the total costs including total interest and non-interest expenses; Y is the output vector consisting of:

Y1 = loans secured on real estate, Y2 = loans unsecured,

Y3 = securities plus federal funds sold and securities purchased under agreements to resell, Y4 = total nominal value of off-balance sheet items,

Y5 = non-interest income activities, Y6 = service Charges;

W is the input price vector comprising:

W1 = salary expenses divided by the number of full-time equivalent employees, W2 = expenses of premises and fixed assets divided by total fixed assets, W3 = total interest expense divided by interest-bearing liabilities.

Z is the total capital equity and is added to the model to control for unmeasured cost of equity capital. Banks with higher equity capital have lower total costs as they have less debt financing and hence interest expense, assuming all other factors equal (Hughes and Mester, 2013).Table A3 of the appendix presents the descriptive statistics of the total costs, output and input price vectors and total equity capital for Micro and Non-Micro Community Banks.

We consider the homogeneity and symmetry assumptions which require:

∑ ∑ ∑ ∑ ∑ ∑ (4-2)

(4-3) We also impose input price homogeneity restrictions (an. increase in all input prices increases the total costs by the same percentage) on the cost function parameters by dividing all input prices (W1 and W2) and total costs (TC) with one other factor price (W3).

The total cost function is estimated using a stochastic frontier approach introduced by Aigner et al. (1977) which fits the cost function to best practice banks. This approach assumes

that the error term (ɛ) has two components which are independently distributed: One idiosyncratic error (or random noise) term with a symmetric distribution (ʋ) and the inefficiency term with a strictly nonnegative distribution (u). We assume that the inefficiency component follows a time-varying decay model proposed by Battese and Coelli (1992), so ( ) . Ti is the last period in the i^th panel and ƞ is the parameter to be estimated.

In a multi-product firm the pair-wise cost complementarity (PCC) between two products exists when an increase in product A lowers the marginal cost of producing product B (Clark, 1988). The measure of cost complementarity is driven as follows:

( )

(

) [

(

) (

)] ( ) PCC < 0 implies the existence of cost complementarity between products A and B. The necessary condition for the existence of cost complementarity (PCC<0) is:

(6)

PCC = 0 implies the non-jointness or absence of cost complementarities. At any non-zero production level of YA and YB, . Hence, the non-jointness requires:

[ ( ) ( )] (7)

PCC > 0 implies existence of diseconomy of joint production.

Table VIII illustrates the empirical results on cost complementarity between non-interest income activities and lending (secured and unsecured loans (Y1 & Y2)) for Micro and Non-Micro Community Banks during the pre, acute and the post-crisis periods. The first two columns display the analysis for Non-Micro Community Banks and columns (3) and (4) exhibit the results for Micro Community Banks⁵⁶. In columns (1) and (3) the necessary condition for the existence of cost complementarity between non-interest income activities and Secured or

56 We do not report the measure of cost complementarity for Micro Community Banks during the acute and post-crisis, where we obtain a negative elasticity of total costs to either loans or non-interest income activities.

Unsecured Loans is presented. The results show that the necessary condition is achieved, except for Non-Micro Community Banks in the acute and post-crisis periods where the necessary condition for cost complementarity of non-interest income activities and Unsecured Loans is not satisfied. Columns (2) and (4) exhibit the measure of cost complementarity. The findings indicate that the sufficiency condition is not fulfilled suggesting non-jointness⁵⁷.

Table VIII. Cost Complementarities Analysis

This table reports Cost Complementarities analysis (Equation (5)), between non-interest income activities and loans (secured and unsecured loans (Y1 & Y2)) for Micro and Non-Micro Community Banks across pre, acute and post-crisis periods. Micro Community Banks are defined as banks with less than $100 million in total assets. Non-Micro Community Banks are community banks with total assets above $100 million.

The first two columns present the analysis for the Non-Micro Community Banks and columns (3) and (4) exhibit the results for Micro Community Banks. Columns (1) and (3) display the necessary condition for the existence of cost complementarities between non-interest income activities and secured or unsecured loans. In columns (2) and (4) the measure of cost complementarities are illustrated. See Table A2 for variable definitions.

Non-Micro Community Banks Micro Community Banks

NC_PCC(Yi, Y5) PCC(Yi, Y5) NC_PCC(Yi, Y5) PCC(Yi, Y5)

(1) (2) (3) (4)

Pre-Crisis Secured Loans (Y1) -0.0043 0.0000 -0.0028 0.0000

Unsecured Loans (Y2) -0.0014 0.0000 -0.0010 0.0000

Acute-Crisis Secured Loans (Y1) -0.0087 0.0000 -0.0031 ---*

Unsecured Loans (Y2) 0.0008 0.0000 -0.0010 ---*

Post-Crisis Secured Loans (Y1) -0.0229 0.0000 -0.0001 0.0000

Unsecured Loans (Y2) 0.0005 0.0000 -0.0018 ---*

* We do not report the measure of cost complementarity, since we obtain a negative elasticity of total costs to either loans or non-interest income activities.

57 Normally total costs is much less than the products of loans (whether Secured or Unsecured) with other financial services (in our case non-interest income businesses). Hence, the first component of the measure of cost complementarity, is too small such that its product with the second component makes the measure very close to zero, implying non-jointness.

As a robustness check, we also follow the production approach (Berger and DeYoung, 1997 among others) and include transaction deposits in our model as a further output. The results are similar to our previous findings. Overall, we find little evidence for the existence of cost complementarity between lending and non-interest income activities.

4.5. ROBUSTNESS CHECKS