Abstract
In this paper, we investigate the effect of bank size differences on cost efficiency heterogeneity using a heteroskedastic stochastic frontier model. This model is implemented by using an information theoretic maximum entropy approach. We explicitly model both bank size and variance heterogeneity simultaneously. We find that non-performing loans, federal insurance premium, legal expenses and director fees drive bank inefficiency as the bank becomes larger. Moral hazard, bank management and a “too big to fail” doctrine are likely explanations for the results from this study.
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Notes
The average price of labor is calculated by dividing total salary expenditure by the total number of bank employees. The average price of premises and fixed assets is calculated by dividing total expenditures on premises and fixed assets by total deposits. The average price of interest expense is obtained by dividing total interest expense by total deposits.
As explained in Caudill et al. (1995), this is done due to institutional age-related bias introduced if one divides physical capital spending by the book value of total physical capital, because physical capital is recorded at historical cost rather than market value.
For a detailed discussion on the different hypotheses, refer to Berger and DeYoung (1997).
This is consistent with Hughes and Mester (1993).
Refer to Boyd and De Nicolo (2005) for a thorough explanation on how a given market structure evolves.
Following Murray and White (1983), the cost elasticity is computed as follows:
$$ \eta = \sum\limits_i^n {\frac{{\partial \ln C}}{{\partial \ln {y_i}}} = \sum\nolimits_i^n {{\alpha_i} + \sum\nolimits_i^n {\sum\nolimits_k^n {{\sigma_{ik}}\ln {y_k}} + } } } \sum\nolimits_i^n {\sum\nolimits_j^m {{\delta_{ij}}\ln {p_j}} } $$If η > 1, the banks experience decreasing returns to scale as costs rise proportionately more than output.
An η = 1 indicates constant returns to scale and η < 1 indicates increasing returns to scale.
Panzar and Willig (1977) have shown that a multiproduct cost function exhibits economies of scope if \( \frac{{{\partial^2}C}}{{\partial {y_i}\partial {y_k}}} < 0 \). The approximate test for this condition is given by \( {\alpha_i}{\alpha_k} + {\sigma_{ik}} < 0 \).
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Balasubramanyan, L., Stefanou, S.E. & Stokes, J.R. An entropy approach to size and variance heterogeneity in U.S. commercial banks. J Econ Finan 36, 728–749 (2012). https://doi.org/10.1007/s12197-010-9148-5
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DOI: https://doi.org/10.1007/s12197-010-9148-5