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Productivity and efficiency at bank holding companies in the U.S.: a time-varying heterogeneity approach

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Abstract

This paper investigates the productivity and efficiency of large bank holding companies (BHCs) in the United States over the period 2004–2013, by estimating a translog stochastic distance frontier (SDF) model with time-varying heterogeneity. The main feature of this model is that a multi-factor structure is used to disentangle time-varying unobserved heterogeneity from inefficiency. Our empirical results strongly suggest that unobserved heterogeneity is not only present in the U.S. banking industry, but also varies over time. Our results from the translog SDF model with time-varying heterogeneity show that the majority of large BHCs in the U.S. exhibit increasing returns to scale, a small percentage exhibit constant returns to scale, and an even smaller percentage exhibit decreasing returns to scale. Our results also show that on average the BHCs have experienced small positive or even negative technical change and productivity growth.

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Notes

  1. There are two reasons why our analysis focuses on BHCs rather than individual commercial banks. First, total assets controlled by BHCs accounts for 99% of the industry assets in 2012 (Federal Reserve Board Annual Report 2012). Second, important business decisions are typically made at bank holding company level (Stiroh 2000).

  2. If (14) represents a panel data model with common factors where some factors are observable, (14) can be written as

    $$\begin{array}{*{20}{l}} {q_{it}} \hfill & \hskip-8pt = \hfill &\hskip-7pt {{\boldsymbol{z \prime}\!}_{it} {\boldsymbol{\beta }} + {\boldsymbol{f \prime}\!\!}_{1,t} \gamma _{1,i} + {\boldsymbol{f \prime }\!\!}_{2,t} {\mathrm{\gamma }\!}_{2,i} + u_{it} + v_{it}} \hfill \\ {} \hfill & \hskip-8pt = \hfill &\hskip-7pt {\widetilde {\boldsymbol{z \prime }\!}_{it} \widetilde {\boldsymbol{\beta }}_i + {\boldsymbol{f \prime }\!\!}_{2,t} {\mathrm{\gamma }}_{2,i} + u_{it} + v_{it}{\mathrm{,}}} \hfill \end{array}$$
    (15)

    where f 1,t is a h 1 × 1 vector of unobservables; f 2,t is a h 2 × 1 vector of unobservables; \(\widetilde {\boldsymbol{z}}_{it} = ({\boldsymbol{z}}_{it},{\boldsymbol{f \prime }\!\!}_{1,t})\); and \(\widetilde \beta _i = (\beta {\prime},\gamma\prime_{\!\!1,i} ){\prime}\). (15) is a random coefficient model with a new factor structure, represented by \({\boldsymbol{f \prime }\!\!}_{2,t} \gamma _{2,i}\). The identification restriction thus becomes \(h_2 \le (T - 1)/2\). Accordingly, the prior and posterior distribution for \(\widetilde {\boldsymbol{\beta }}_i\) needs to be changed. But, our specifications and discussions regarding the new factor structure remain the same. Further, if f 1,t is a constant scalar (say f 1), the above model reduces to

    \(q_{it} = {\boldsymbol{z \prime }\!}_{it} \beta + w_i + {\boldsymbol{f \prime }\!\!}_{2,t} \gamma _{2,i} + u_{it} + v_{it},\)

    where w i = f 1 γ 1,i . The identification restriction is still h 2 ≤ (T − 1)/2.

  3. $1 billion is widely accepted as a cutoff for separating large and small BHCs/banks (see, for example, Cole et al. 2004).

  4. The use of a balanced panel might result in survivorship bias. However, we also note that the use of an unbalanced panel may potentially distort inter-temporal comparisons of banking sector efficiency.

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Correspondence to Guohua Feng.

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Feng, G., Peng, B. & Zhang, X. Productivity and efficiency at bank holding companies in the U.S.: a time-varying heterogeneity approach. J Prod Anal 48, 179–192 (2017). https://doi.org/10.1007/s11123-017-0515-5

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