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Accounting for heterogeneous technologies in the banking industry: a time-varying stochastic frontier model with threshold effects

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Abstract

This paper investigates the existence of heterogeneous technologies in the US commercial banking industry through the nondynamic panel threshold effects estimation technique proposed by Hansen (Econometrica 64:413–430, 1999, Econometrica 68:575–603, 2000a). We employ the total assets as a threshold variable, which is typically considered as a proxy for bank’s size in the banking literature. We modify the threshold effects model to allow for time-varying effects, wherein these are modeled by a time polynomial of degree two as in Cornwell et al. (J Econom 46:185–200, 1990) model. Threshold effects estimation allows us to sort banks into discrete groups based on their size in a structural and consistent manner. We determine seven such distinct technology-groups within which banks are allowed to share the same technology parameters. We provide estimates of individual and group efficiency scores, as well as of those of returns to scale and measures of technological change for each group. The presence of the threshold(s) is tested via bootstrap procedure outlined in Hansen (Econometrica 64:413–430, 1999) and the relationship between bank size and efficiency ratios is investigated.

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Notes

  1. Technology here refers to a mechanism by which a bank’s inputs are translated into outputs.

  2. Nonparametric alternative approaches are typically dealt with data envelopment analysis (DEA) model proposed by Charnes et al. (1978) and the free disposal hull (FDH) model of Deprins et al. (1984)

  3. Kumbhakar (1990) proposed u it  = w(t)u i specification for time-varying efficiency model, where w(t) = 1/[1 + exp(γ t + δt 2)] and u i ∼ iid N +(0, σ 2 u ) and estimated γ and δ, along with the rest model parameters, by the maximum likelihood techniques. Whereas, Battese and Coeli (1992), on the other hand, define \(w(t)=\exp (\eta (T-t))\) in their model. The latter model is more popular and widely employed in panel data SFMs due to the provision of the free software from the authors (Frontier 4.1 version).

  4. A similar example can be found in El-Gamal and Inanoglu (2005).

  5. The values of the threshold variable are sorted and the algorithm searches over all distinct values or certain quantiles of q. The value of q that minimizes the concentrated sum of squared errors is the solution of the optimization algorithm.

  6. \(EFF_{it}=\exp (\min_{j}\hat{u}_{jt}-\hat{u}_{it})\) for the cost frontier models.

  7. Translog function provides the second-order Taylor series approximation to any arbitrary function at a single point. In addition, the returns to scale measures and factor demand elasticities are not required to be constant as in the Cobb-Douglas case.

  8. Nonperfoming loans include the total loans and lease finance receivables that are nonacrual, past due 30–89 days and still accruing, and past due 90 days and still accruing.

  9. We abstain from including the cost share equations in the analysis due to the issues related to the allocative inefficiency ("Greene Problem"). Thus, the estimated overall efficiency represents the cost or economic inefficiency which can be due to technical or allocative inefficiency, or both.

  10. The reason for utilizing a balanced sample is to capture a stable technological behavior of the banks as they grow in size throughout the entire sample period and to film their switching the size-categories over time. This eliminates very small banks (those that failed or were acquired by other surviving banks) and the de novo banks (state member banks that have been in operation for 5 years or less), which could introduce a serious technological disruptions and bias the results. Another reason is that the threshold effects estimation method is computationally intensive and takes sufficient amount of time even for computers with superior computing power that utilize multiple nodes.

  11. 1984.Q1 (beginning of the sample), 1993.Q1 (prior to the introduction of the Reigle-Neal Act in 1994), 2000.Q1 (reference period), and 2009.Q3 (end of the sample).

  12. To determine the number of thresholds, a grid search was performed over 250 quantiles of the threshold variable in each sequential estimation step. For six thresholds, the total number of sequential steps was 29.

  13. ROA is defined as the ratio of the net income to the total assets and measures the profit earned relative to the bank’s assets. ROE is defined as the ratio of the net income to total equity capital and measures the overall profitability of the bank per dollar of equity. PM is defined as the ratio of the net income to the total operating income and measures the bank’s ability to pay expenses and generate net income from interest and non-interest income. AU is defined as the ratio of the total operating income to the total assets and measures the amount of the interest and non-interest income generated per dollar of the total assets.

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Acknowledgments

I would like to thank Robin Sickles, Mahmoud El-Gamal, Simon Grant, Subal Kumbhakar, and participants at the North American Productivity Workshop VI, Houston, Texas, June 2010, as well as two anonymous referees for comments and criticism that substantially strengthened this paper. I would also like to thank Robert Adams at the Board of Governors of the Federal Reserve System for his valuable help in the banking data construction. Financial support from the Social Sciences Research Institute at Rice University is gratefully acknowledged.

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    Pavlos Almanidis

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Almanidis, P. Accounting for heterogeneous technologies in the banking industry: a time-varying stochastic frontier model with threshold effects. J Prod Anal 39, 191–205 (2013). https://doi.org/10.1007/s11123-012-0306-y

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